12
Research Article Establishment of the Credit Indicator System of Micro Enterprises Based on Support Vector Machine and R-Type Clustering Zhanjiang Li and Chengrong Yang College of Economics and Management, Inner Mongolia Agricultural University, No. 306 Zhaowuda Road, Saihan District, Hohhot, China Correspondence should be addressed to Zhanjiang Li; [email protected] Received 17 August 2017; Revised 6 February 2018; Accepted 20 February 2018; Published 8 April 2018 Academic Editor: Marco Mussetta Copyright © 2018 Zhanjiang Li and Chengrong Yang. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e micro enterprises’ credit indicators with credit identification ability are selected by the two classification models of Support Vector Machine for the first round of indicator selection and then for the second round of indicator selection, deleting credit indicators with redundant information by clustering variables through the principle of minimum sum of deviation squares. is paper provides a screening model for credit evaluation indicators of micro enterprises and uses credit data of 860 micro enterprises samples in Inner Mongolia in western China for application analysis. e test results show that, first, the constructed final micro enterprises’ credit indicator system is in line with the 5C model; second, the validity test based on the ROC (Receiver Operating Characteristic) curve reveals that each of the screened credit evaluation indicators is valid. 1. Introduction e large number of micro enterprises plays an irreplaceable role in promoting economic growth and the settlement of China’s social employment and people’s livelihood. But the financing difficulty of micro enterprises is becoming increasingly prominent, which seriously inhibit enterprises’ healthy development, so constructing a scientific credit evaluation indicator system for micro enterprises to help measure the credit risk of micro enterprises, help solve the problem of financing, and then promote enterprises’ healthy development becomes an urgent problem to be solved. For current status of foreign research, SBSS (Small Busi- ness Scoring Service) is a credit evaluation model of micro enterprises created by Fair Isaac Corporation (USA), which is constructed by the methods of mathematical statistics and historical data analysis. SOHO (Small Office Home Office) model, a credit evaluation method for micro enterprises established by the Yachiyo Bank of Japan, mainly focuses on the analysis of qualitative nonfinancial indicators. e evaluation model of the CRD (Credit Risk Database) Oper- ations Agreement uses a way to rate each of the negative aspects of micro enterprises and financing. By virtue of its corporate asset credit database and investigators, the Imperial Data Bank determines whether to lend to a micro enterprise through field interviews, visits, and indirect surveys. e micro enterprise credit indicators designed by India’s credit evaluation company, SMERA company, include 6 aspects, which conducts a different benchmark for enterprises of different industries and different registered capital size. For current status of domestic research, Zhanjiang [1] selected micro enterprise credit indicators through the Brown-Mood median test, Moses variance test, and the Kendall rank correlation test. Guotai et al. [2] selected the indicator system according to the ability of an evaluation indicator to discriminate an enterprise’s credit status based on probit regression. Zhang et al. [3] studied the comprehensive evaluation indicator system of low-carbon road transport by using analytic hierarchy process and the method of Delphi fuzzy evaluation. Honghai [4] selected the indicators that contain more information and lower degree of redun- dant information according to relative discrete coefficient, Pearson’s correlation coefficient, and cumulative information contribution rate criteria. Youxi [5] selected indicators by Hindawi Mathematical Problems in Engineering Volume 2018, Article ID 6390720, 11 pages https://doi.org/10.1155/2018/6390720

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Page 1: Establishment of the Credit Indicator System of Micro ...downloads.hindawi.com/journals/mpe/2018/6390720.pdf · ResearchArticle Establishment of the Credit Indicator System of Micro

Research ArticleEstablishment of the Credit IndicatorSystem of Micro Enterprises Based on Support VectorMachine and R-Type Clustering

Zhanjiang Li and Chengrong Yang

College of Economics and Management Inner Mongolia Agricultural University No 306 Zhaowuda Road Saihan DistrictHohhot China

Correspondence should be addressed to Zhanjiang Li lizhanjiang582163com

Received 17 August 2017 Revised 6 February 2018 Accepted 20 February 2018 Published 8 April 2018

Academic Editor Marco Mussetta

Copyright copy 2018 Zhanjiang Li and Chengrong Yang This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

The micro enterprisesrsquo credit indicators with credit identification ability are selected by the two classification models of SupportVector Machine for the first round of indicator selection and then for the second round of indicator selection deleting creditindicators with redundant information by clustering variables through the principle of minimum sum of deviation squares Thispaper provides a screening model for credit evaluation indicators of micro enterprises and uses credit data of 860 micro enterprisessamples in Inner Mongolia in western China for application analysis The test results show that first the constructed final microenterprisesrsquo credit indicator system is in line with the 5C model second the validity test based on the ROC (Receiver OperatingCharacteristic) curve reveals that each of the screened credit evaluation indicators is valid

1 Introduction

The large number of micro enterprises plays an irreplaceablerole in promoting economic growth and the settlementof Chinarsquos social employment and peoplersquos livelihood Butthe financing difficulty of micro enterprises is becomingincreasingly prominent which seriously inhibit enterprisesrsquohealthy development so constructing a scientific creditevaluation indicator system for micro enterprises to helpmeasure the credit risk of micro enterprises help solve theproblem of financing and then promote enterprisesrsquo healthydevelopment becomes an urgent problem to be solved

For current status of foreign research SBSS (Small Busi-ness Scoring Service) is a credit evaluation model of microenterprises created by Fair Isaac Corporation (USA) whichis constructed by the methods of mathematical statistics andhistorical data analysis SOHO (Small Office Home Office)model a credit evaluation method for micro enterprisesestablished by the Yachiyo Bank of Japan mainly focuseson the analysis of qualitative nonfinancial indicators Theevaluation model of the CRD (Credit Risk Database) Oper-ations Agreement uses a way to rate each of the negative

aspects of micro enterprises and financing By virtue of itscorporate asset credit database and investigators the ImperialData Bank determines whether to lend to a micro enterprisethrough field interviews visits and indirect surveys Themicro enterprise credit indicators designed by Indiarsquos creditevaluation company SMERA company include 6 aspectswhich conducts a different benchmark for enterprises ofdifferent industries and different registered capital size

For current status of domestic research Zhanjiang [1]selected micro enterprise credit indicators through theBrown-Mood median test Moses variance test and theKendall rank correlation test Guotai et al [2] selected theindicator system according to the ability of an evaluationindicator to discriminate an enterprisersquos credit status based onprobit regression Zhang et al [3] studied the comprehensiveevaluation indicator system of low-carbon road transportby using analytic hierarchy process and the method ofDelphi fuzzy evaluation Honghai [4] selected the indicatorsthat contain more information and lower degree of redun-dant information according to relative discrete coefficientPearsonrsquos correlation coefficient and cumulative informationcontribution rate criteria Youxi [5] selected indicators by

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 6390720 11 pageshttpsdoiorg10115520186390720

2 Mathematical Problems in Engineering

combining the chi-square test 119870-119878 test and 119880 test after theinitial construction of the indicator system

There are shortcomings in the previous studies Firstlythe enterprisersquos credit evaluation is mainly focused on thelarge enterprises for micro enterprise credit evaluationresearch is lacking Secondly the indicators that have beenscreened out cannot be guaranteed to significantly identifythe micro enterprisesrsquo credit status which leads to a higherfalse-positive rate in the final enterprise credit evaluationresults Thirdly there are information redundancy indicatorsin the final credit evaluation indicator system that is theselection of indicators does not consider eliminating repeatedinformation indicators

In this paper we first select indicators that can iden-tify the credit status of micro enterprises based on SVM(Support Vector Machine) and then construct an indicatorsystemby deleting the indicators with redundant informationand retaining the indicators with strong ability of creditidentification based on R-type clustering which makes theselected credit indicators be able to significantly identify thecredit status of micro enterprises and do not have duplicateinformation and finally apply the constructed model to thecredit data of micro enterprises in InnerMongolia in westernChina

The innovation of this paper lies in the following thenonlinearity of the credit indicator is mapped to the high-dimensional space by the Gaussian kernel SVM and then theevaluation indicators are filtered out with credit identificationability which solves the problem that the traditional linearweighting model cannot reflect the nonlinear relationshipbetween the credit indicator and the evaluation resultsThen we use Levenersquos variance homogeneity test statistic119882 value to recognize the credit identification ability ofindicator and then cluster clusters using the method of R-type hierarchical clustering within the criterion layer andkeep the indicators with largest119882 value in each cluster bothdeleting the redundant information indicators and retainingthe indicators with significant credit identification ability

2 Difficulties and Ideas of the Problem

21 Difficulties of the Problem

Difficulty 1 The first difficulty is how to ensure that eachmicro enterprise credit indicator that has been selected hasthe ability to identify the micro enterprisesrsquo credit statusThe commonly used indicators in credit evaluation do notnecessarily have significant credit capabilities in micro enter-prise credit ratings In order to prevent companies withhigh default risk from obtaining a higher credit score itis necessary to ensure that the selected indicators have theability to identify the credit status of micro enterprises

Difficulty 2 The second difficulty is how to avoid the sit-uation where micro enterprise credit indicators reflectrepeated information and how to ensure not mistakenlydeleting the indicators with strong ability to identify themicro enterprisesrsquo credit status when eliminating the redun-dant information indicators A good micro enterprise credit

indicator system must not contain redundant informationindicators each indicator in the final construction of themicro enterprise credit indicator model having significantcredit identification ability is essential for micro enterprisecredit evaluation Therefore in the process of constructingthe micro enterprise credit indicator model in addition toavoiding overlap information in credit indicators retainingthe indicators with significant credit identification ability onmicro enterprise credit status is more important

22 Ideas to Solve the Difficulties

(1) Ideas to Solve Difficulty 1 Credit identification ability of acredit indicator is the correct percentage to identify the creditstatus of micro enterprises In this paper we obtain the creditidentification ability of all the indicators 119860 and the creditidentification ability of the remaining indicator after deletingthe 119895th indicator 119860119895 by predicting the credit status of microenterprises and using the two classification models of SVMthe difference between 119860119895 and 119860 is defined as 119889119895 which hasbeen taken as the impact of the 119895th indicator on the evaluationresults

Remove or retain the 119895th indicator according to positive119889119895 or negative 119889119895 and then filter out the credit evaluationindicator Specifically if 119889119895 is greater than or equal to 0 thecredit identification ability of the remaining indicator afterdeleting the 119895th indicator is stronger than or equal to thecredit identification ability of all the indicators when the119895th indicator is not deleted which indicates that the 119895thindicator cannot identify the enterprisesrsquo credit status and sojust deletes it If 119889119895 is less than 0 the credit identificationability of the remaining indicators after the deletion of the 119895thindicator is weaker than the credit identification ability of allthe indicators when the 119895th indicator is not deleted whichindicates that the 119895th indicator can identify the credit statusof themicro enterprise and so just retains itThe ideas to solvedifficulty 1 are shown in Figure 1

(2) Ideas to Solve Difficulty 2 After R-type clusteringindicators in the same category are considered to reflectsimilar information and indicators in different categories areconsidered to reflect different information In this paperthe R-type hierarchical clustering method is used to clusterthe indicators of the same criterion layer which reflect thesame type of information according to the principle of theminimum sum of deviation squares in order to cluster theindicators that reflect the repetitive information into onecluster through retaining the indicator with strongest creditidentification ability in the indicators of same cluster anddeleting all other indicators of the cluster to achieve the goalof preserving the indicators with strong credit qualificationability and at the same time deleting the indicators thatreflect redundancy information The variance homogeneityLevenersquos test statistic 119882 value (hereinafter referred to as 119882value) is used to measure the credit qualification ability ofcredit indicator The 119882 value reflects the thought that thegreater the degree of deviation from the mean value of creditindicator in default enterprise samples to themean value of allenterprise samples the stronger the ability of the indicators to

Mathematical Problems in Engineering 3

Calculate the credit identification ability of all indicators A

Delete the jth indicator and calculate the credit

Calculate the influence of the jth

Are all the indicators calculated

Keep the jth indicator

Delete the jth indicator

No

No

YesYes

identification ability of the remaining indicatorsAj

indicator on the evaluation resultsdj

dj ge 0

Figure 1 Principle to solve difficulty 1

NoYes

Yes

No

Artificially set a total number of clustered clusters accordingto the final number of indicators L

Assign criteria layers to the remaining indicators and make eachindicator inside the same criteria layer into a cluster

e number of clusters of the ℎth criterion layer is calculatedaccording to the total number of clusters Lℎ

Use the method of hierarchical clustering to cluster the indicators within the ℎthcriterion layer according to the principle of minimum sum of deviationsquares until the number of clusters reaches Lℎ

Total number of clusters = L

Use K-W test for indicators within the cluster to determine therationality of the number of clusters L

Is L reasonable

Keep the indicators with largest W value ineach cluster and remove other indicators

Figure 2 Principle to solve difficulty 2

significantly identify the micro enterprisesrsquo credit status Theideas to solve difficulty 2 are shown in Figure 2

23 Principle of Building the Model The principle of buildingthe credit indicator model of micro enterprise based on themethods of SVM and R-type clustering is shown in Figure 3

3 Method of Building the Model

31 Initial Selection and Standardization of Credit IndicatorsThere are two principles in the mass selection of indicators

retaining classic and high-frequency indicators and reflectingthe characteristics of micro enterprises Directly delete unob-servable indicators or indicators with inability to obtain dataor loss of original data of more than 10 of the total sampleInterpolation is used to process data that has lost less than10 of the total number of samples

Set 119909119894119895 as the standardized value of the 119895th indicator of the119894th enterprise V119894119895 as the original value of the 119895th indicator ofthe 119894th enterprise 119899 as the total number of micro enterprisessamples 1199021 as the left border of the indicatorrsquos interval and1199022 as the right border of the indicatorrsquos interval

4 Mathematical Problems in Engineering

data of credit evaluatione selection of indicators from raw

indicators of micro enterpriseStage 1

Stage 2

Stage 3

Preprocessingof data Preliminary selection of credit evaluation indicators

Standardization of evaluation indicators

e classification forecasting of SVM is usedto filter out the indicators with ability to identifythe credit status of micro enterprises

Using the method of R-type clustering to deletethe indicators with redundant information andretain the indicators with strong ability toidentify the credit status of micro enterprises

Micro enterprise credit evaluation indicator system

Validity test of credit indicatorbased on ROC curve

e first roundof indicatorsselection

e second roundof indicatorsselection

e constructionof credit indicatormodel

e validity testof credit indicators

Figure 3 Principle of building the credit indicator model of micro enterprise

Then the standardized value of positive indicator 119909119894119895 is

119909119894119895 =V119894119895 minusmin1le119894le119899 (V119894119895)

max1le119894le119899 (V119894119895) minusmin1le119894le119899 (V119894119895) (1)

Then the standardized value of negative indicator 119909119894119895 is

119909119894119895 =max1le119894le119899 (V119894119895) minus V119894119895

max1le119894le119899 (V119894119895) minusmin1le119894le119899 (V119894119895) (2)

Then the standardized value of interval indicator 119909119894119895 is

119909119894119895= 1

minus1199021 minus V119894119895

max (1199021 minusmin1le119894le119899 (V119894119895) max1le119894le119899 (V119894119895) minus 1199022)

V119894119895 lt 1199021

(3a)

119909119894119895= 1

minusV119894119895 minus 1199022

max (1199021 minusmin1le119894le119899 (V119894119895) max1le119894le119899 (V119894119895) minus 1199022)

V119894119895 gt 1199022

(3b)

119909119894119895 = 1 1199021 le V119894119895 le 1199022 (3c)

The standardization rules for qualitative indicators areshown in Table 1

32 The Method of the First Round of Indicator SelectionBased on SVM

(1) The Determination of Kernel Function In this paper theGaussian radial basis function is selected as the kernel func-tion of the SVM in the first round of indicator selection usingthe method of classification prediction of SVM there arethree main reasons Firstly linear kernel function is suitablefor linearly separable situations whereas the Gaussian radialbasis function is suitable for linearly inseparable situationsfor the nonlinear relationship between credit indicators andevaluation results Gaussian radial basis function can getmore accurate results than linear kernel function Secondlythe number of parameters in the kernel function will affectthe accuracy of the model Kernel functions with fewerparameters help to improve the accuracy of the modelcompared to other kernel functions the Gaussian radial basisfunction has fewer parameters Thirdly the use of Gaussianradial basis function as SVMrsquos kernel function also reducesthe difficulty of the calculation

(2) The Criteria of Selection

Criterion 1 119889119895 gt 0 and 119860119895 gt A indicating that the creditidentification ability of the remaining indicators after deletingthe 119895th indicator is stronger than the credit identificationability of all the indicators when the 119895th indicator is notdeleted the 119895th indicator cannot identify default enterprisesand nondefault enterprises to be deleted

Criterion 2 119889119895 = 0 and is 119860119895 = A indicating that the creditidentification ability of the remaining indicators after deletingthe 119895th indicator is equal to the credit identification ability ofall the indicators when the 119895th indicator is not deleted the 119895thindicator cannot identify default enterprises and nondefaultenterprises to be deleted

Mathematical Problems in Engineering 5

Table 1 The standardization rules for qualitative indicators

Serialnumber

(1)Indicator name

(2)Content

(3)Standardized values

1 Living condition

(1) Full purchase or mortgage 100(2) Relatives buildings 075

(3) Renting 050(4) Collective dormitory or shared dwelling 025

(5) Other or missing data 000sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot

22

Legalrepresentativersquoseducationalbackground

(1) Bachelor degree or above 100(2) Specialist 090

(3)High school or secondary education 070(4) Junior or primary education 040

(5) Other or missing data 000

Criterion 3 119889119895 lt 0 and is 119860119895 lt A indicating that the creditidentification ability of the remaining indicators after deletingthe 119895th indicator is weaker than the credit identificationability of all the indicators when the 119895th indicator is notdeleted the 119895th indicator can identify default enterprises andnondefault enterprises to be kept

(3) Calculation of Credit Identification Ability of Credit Indi-cator Set A as the credit identification ability of all theindicators for all micro enterprise samples 1198990 as total numberof nondefault enterprises 119910119894 as the true value of the defaultstatus of the 119894th enterprise (119910119894 = 0 the true value of the defaultstatus of the 119894th enterprise is nondefault 119910119894 = 1 the true valueof the default status of the 119894th enterprise is default) 1199101015840119894 as thepredictive value of the default status of the 119894th enterprise and1198991 as total number of default enterprises Then 119860 is given asfollows119860

=(11198990) (1198990 minus sum1198990119894=1

10038161003816100381610038161003816119910119894 minus 1199101015840119894

10038161003816100381610038161003816) + (11198991) (1198991 minus sum1198991119894=1

10038161003816100381610038161003816119910119894 minus 1199101015840119894

10038161003816100381610038161003816)2

(4)

In this paper 119860119895 is a formula obtained by replacing 1199101015840119894 inthe molecule of formula (4) with 1199101198951015840119894 (the predictive value ofcredit status of the 119894th enterprise calculated by the indicatorsremained after deleting the 119895th indicator) then obtain119860119895 (thecredit identification ability of the indicators after deleting the119895th indicator for all micro enterprises samples)

Then 119889119895 is given as follows

119889119895 = 119860119895 minus 119860 (5)

33 The Method of the Second Round of Indicator SelectionBased on R-Type Clustering

(1) The Criteria of Selection After the first round of indicatorselection clustering the indicators inside the same criterialayer according to the principle ofminimumdeviation sumofsquares using the method of hierarchical clustering through

the R-type clustering the validity of the number of clusters Lis verified by the 119870-119882 test when the total number of clustersreaches the preset value L if the 119870-119882 test is not passedthen reset the number of clusters if the 119870-119882 test is passedthen retain the indicator with the strongest ability of creditidentification and delete redundant information indicators byretaining the indicator of the largest119882 value in each clusterand deleting all the other indicators

(2) The Calculation of Deviation Sum of Squares Set 119878ℎ asthe sum of the squares of the ℎth criterion layer 119871ℎ as thenumber of clusters in the ℎth criterion layer119898119905 as the numberof indicators of the 119905th cluster of the ℎth criterion layer119883119905119895 asthe vector of the 119895th indicator in the 119905th cluster of the ℎthcriterion layer and119883119905 as the mean vector of all the indicatorsin the 119905th class of the ℎth criterion layer Then 119878ℎ is given asfollows

119878ℎ =119871ℎ

sum119905=1

119898119905

sum119895=1

(119883119905119895 minus 119883119905) (119883119905119895 minus 119883

119905)1015840

(6)

(3) 119870-119882 Test In this paper the nonparametric 119870-119882 test isused to test the rationality of the number of clusters thatis to test whether there is a significant difference betweenthe credit indicators of the same cluster If the 119870-119882 test isnot passed which indicates that there is significant differencebetween these indicators of the same cluster they cannot beclustered into a cluster in this case the number of clustersneeds to be reset if the 119870-119882 test is passed which indicatesthat there is no significant difference between these indicatorsof the same cluster they can be clustered into a cluster in thiscase retain the indicator with the strongest ability of creditidentification and delete information redundancy indicatorsby retaining the indicator of the largest 119882 value in eachcluster and deleting all the other indicators to complete thesecond round of indicators selection

Specifically the119870-119882 test is as followsH0 there is no significant difference between theindicators within the cluster

6 Mathematical Problems in Engineering

Table 2 Indicators and standardized values

Serialnumber

(a)Criteria layer

(b)Indicator name

(c)Indicator type (1) sdot sdot sdot (860)

1Internal financial factors

The cash ratio of main business income Positive 0000 0142sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot35 The rate of capital accumulation Positive 0496 049836

Nonfinancial factors withinthe enterprise

Identification level of new product Qualitative 0000 0000sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot62 The range of product sales Qualitative 1000 050063

External macroenvironmental factors

Industry sentiment indicator Positive 0695 0656sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot68 The growth rate of GDP Positive 0356 035669 The true credit status of micro enterprise samples 1 sdot sdot sdot 0

H1 there is significant difference between the indica-tors within the clusterThe significance level is set to 001When sig gt 001 accept H0 so these indicators canbe clustered into a clusterWhen siglt 001 refuseH0 so these indicators cannotbe clustered into a cluster

(4) The Calculation of 119882 Value Set 119882119895 as the 119882 value ofthe 119895th indicator 119899 as total number of enterprise samples

1198990 as total number of nondefault enterprise samples 1198850119894119895 asthe absolute value of the difference between the 119895th indicatorof the 119894th nondefault enterprise and the mean value of the119895th indicator of all nondefault enterprises 1198851119894119895 as the absolutevalue of the difference between the 119895th indicator of the 119894thdefault enterprise and the mean value of the 119895th indicatorof all default enterprises and 1198991 as total number of defaultenterprises Then the 119895th indicatorrsquos119882 value119882119895 is given asfollows

119882119895

=(119899 minus 2) (1198990 ((sum1198990119894=1 1198850119894119895) 1198990 minus ((sum1198990119894=1 1198850119894119895) 1198990 + (sum1198991119894=1 1198851119894119895) 1198991) 2)

2) + (119899 minus 2) (1198991 ((sum1198991119894=1 1198851119894119895) 1198991 minus ((sum1198990119894=1 1198850119894119895) 1198990 + (sum1198991119894=1 1198851119894119895) 1198991) 2)2)

sum1198990119894=1 (1198850119894119895 minus (sum1198990119894=1 1198850119894119895) 1198990)2 + sum1198991119894=1 (1198851119894119895 minus (sum1198991119894=1 1198851119894119895) 1198991)

2

(7)

34 The Validity Test of Credit Indicators The ROC curveis a comprehensive indicator that reflects the sensitivity andspecificity of continuous variables the vertical coordinate ofROC curve sensitivity indicates the ratio at which the defaultsamples are judged to be correct the specificity indicates theratio at which nondefault samples are judged to be correctso the horizontal coordinate of ROC curve 1 minus specificityindicates the rate at which nondefault samples are judged tobe incorrect When the horizontal coordinate is constant thelarger the vertical coordinate is the higher the proportionof default samples judged to be correct is the larger theAUC (area under ROC curve) of the corresponding creditindicator is the stronger the ability of credit identificationof the indicator against the default samples is and the moreeffective the indicator is Based on the ROC curve this papertests the validity of the screened indicators the criteria forindicator to define whether it has the accuracy to identify thecredit status of enterprises samples are as follows when 0 leAUC lt 05 it does not have the accuracy of identificationwhen 05 le AUC lt 1 it has the accuracy of identification

4 The Application of the Model

41 Data and Standardization of Indicators We apply microenterprise credit data from 2010 to 2015 from a commercialbank in Inner Mongolia western China The 68 indicatorsremaining after the initial selection are shown in column (b)numbered from 1 to 68 in Table 2 the standardized valueof each indicator is obtained by instituting the raw dataand materials of indicators into Formulas (1)ndash(3a) (3b) and(3c) and Table 1 according to the type of indicators amongwhich the standardization values of qualitative indicators aredetermined by the professionals of universities and commu-nity The micro enterprisesrsquo true credit status (0 representingnondefault and 1 representing default) and other relatedinformation are shown in Table 2

42 The First Round of Indicator Selection Based on SVM

(1) Classification of Micro Enterprise Samples The 68 indica-tors of micro enterprises remaining after the initial selection

Mathematical Problems in Engineering 7

Table 3 The division of micro enterprise samples

Nondefault samples Default samples TotalTraining set 664 24 688Test set 166 6 172Total 830 30 860

Table 4 The results of first round of indicator selection based on SVM

Serialnumber

(a)Criteria layer

(b)Indicator name

(1)119860119895119860 ()

(2)119889119895 ()

(3)Selection results

0 mdash All indicators 8303 mdash mdash1

Internal financial factorsQuick ratio 9137 837 Delete

sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot35 The ratio of EBITDA and total debt 8303 000 Delete36

Nonfinancial factors withinthe enterprise

The years of employment in relevant industry 7470 minus833 Retainsdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot62 Gender 8303 000 Delete63

External macroenvironmental factors

The growth rate of GDP 8303 000 Deletesdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot68 Pledge score 7470 minus833 Retain

for the first round are filtered using classification and predic-tion of SVM so as to pick out the indicators that can identifythe credit status of micro enterprises The division of microenterprise samples is shown in Table 3

(2) Determination of Optimal Parameters It is necessary todetermine the penalty coefficient 119888 and the Gaussian radialbasis function parameter 119892 by using SVMrsquos classification andprediction to calculate 1199101015840119894 in formula (4) and 1199101198951015840119894 after deletingthe 119895th indicator MATLAB software and LIBSVM toolboxare used to determine the penalty coefficient c and theGaussian radial basis function parameter g c is selected insteps of 05 between 2minus4 and 26 and 119892 is selected in stepsof 05 between 2minus5 and 25 the cross validation number isset to 3-fold the accuracy rate discretization display step isset to 09 then the program is run in MATLAB based onthe parameters that have been set and the training set andtest set that have been selected according to Table 2 columns(1)ndash(860) then we have that the optimal Gaussian radialbasis function parameter 119892 is 56569 and the optimal penaltycoefficient 119888 is 0125

(3) Calculation of theDegree of the Influence of Credit Indicatoron Evaluation Results The training model is established onMATLAB using the selected training set and the optimalparameters 119888 and 119892 the value of 1199101015840119894 in column (4) is obtainedby predicting the credit status of the enterprise in the test setDelete the 119895th indicator in the training set and test set at thesame time establish the training model in MATLAB basedon the optimal parameters 119888 and 119892 using the training set thathas removed the 119895th indicator the value of1199101198951015840119894 can be obtainedby predicting the credit status of the enterprise in the test setwhere the 119895th indicator has been deleted The values shownat Table 4 column (1) are obtained by substituting the two

credit status predictive values obtained above and the creditstatus true values shown at Table 2 69th row into formula(4) the degree of the influence of each credit indicator onevaluation results or 119889119895 shown at Table 4 column (2) isobtained by substituting the values shown at Table 4 column(1) into formula (5)

(4) The First Round of Credit Indicator Selection 119889119895 shown atTable 4 column (2) represents the degree of the influence ofthe 119895th credit indicator on evaluation results the selectionresults obtained according to the first round of indicatorselection criteria are shown in column (3) of Table 4 whereldquoDeleterdquo indicates that the corresponding credit indicator isdeleted and ldquoRetainrdquo indicates that the corresponding creditindicator is retained in the first round of indicator selectionbased on the SVM

After the first round of indicator selection we delete 25indicators and keep 43 indicators that can identify the creditstatus of micro enterprises

43 The Second Round of Indicator Selection Based on R-Type Clustering The second round of indicator selection forthe 43 indicators remaining after the first round of indicatorselection based on R-type clustering is to filter out theindicators with strong ability of credit qualification and deletethe redundant information indicators

(1) Determine the Number of Clusters in Each CriterionLayer Calculate the number of clusters in each criteria layeraccording to the fact that there will be 20 credit indicatorsretained in the final indicator model specifically there are43 indicators remaining after the first round of indicatorselection where there are 18 indicators remaining from thefirst criterion layer the internal financial factors and theywould be divided into (1843) times 20 asymp 8 clusters There are

8 Mathematical Problems in Engineering

20 indicators remaining from the second criterion layer theinternal nonfinancial factors keeping the indicator-collateralscore directly in order to correspond to 5C factor analysismodel and treat it alone as a cluster the remaining 19indicators are divided into (1943)times20 asymp 9 clustersThere are5 indicators remaining from the third criterion layer externalmacro environmental factors and they would be divided into(543) times 20 asymp 2 clusters

(2) Clustering the Indicators within the Criteria Layer Theindicators in the first criterion layer financial internal factorsare used as an example for clustering the other two criterionlayers do similar processing

Firstly make all the indicators marked ldquoRetainrdquo inTable 4 column (3) numbers 1ndash35 from the first criterialayer the internal financial factors into a cluster respectivelywhich is formed into 18 clusters then cluster any two clustersof indicators into a new cluster which clusters the indicatorswithin the first criteria layer into 17 clusters adding up to 119862218= 153 clustering schemes Substitute the standardized valuesof the indicators of each clustering scheme into formula (6) tocalculate each clustering schemersquos deviation squared sum theclustering scheme with the smallest deviation squared sumis chosen and then the first round of clustering is completedContinue clustering in this way until the number of clustersin the first criteria layer reaches the preset quantity 8 Theclustering results of all the indicators are shown in Table 4column (1)

(3) The Test of the Rationality of the Number of ClustersCluster the 43 credit indicators marked ldquoRetainrdquo shown inTable 4 column (3) within the criteria layer based on R-type hierarchical clustering according to the principle ofminimum sum of deviation squares and the clustering resultsare shown in Table 5 column (1) in order to avoid some ofthe indicators misinterpreted in the second round of R-typeclustering because of the significant difference between theevaluation indicators within the cluster in this paper use themethod of 119870-119882 test in SAS software for the clustered creditindicators to complete the significant test at a significancelevel of 001 (except for the cluster with only one indicator)and the 119870-119882 test sig values for each cluster are shown inTable 5 column (2) according to the criterion of test 20clusters of indicators are clustered as reasonable so there isno need to reset the number of clusters

(4) The Calculation of 119882 Value Substitute the standardizedvalues of the 43 indicators marked rdquoRetainrdquo in column (3) ofTable 4 into formula (7) to calculate the 119882 values of the 43indicators and they are shown in Table 5 column (3)

(5)The Second Round of Credit Indicator SelectionThe secondround of indicator selection is achieved by keeping theindicator of the largest 119882 value in each cluster accordingto the clustering results shown in Table 5 column (1) theresults of selection are shown in Table 5 column (4) in whichthe indicators marked rdquoDeleterdquo are deleted and the indicatorsmarked rdquoRetainrdquo are retained in the second round of indicatorselection based on R-type clustering

After the second round of indicator selection we delete23 indicators and keep 20 indicators that can significantlyidentify the credit status of enterprises and do not containredundant information indicators

44 Contrast with the 5C Model Comparatively analyze theconstructedmicro enterprisesrsquo credit indicator model and 5Cfactor analysis model the results are shown in column (1) ofTable 6 in which legal representativersquos loan default recordsand four other evaluation indicators reflect the moral qualityof the 5C elements the cash recovery rate of all assets and 11other evaluation indicators reflect the repayment ability of the5C elements the fixed rate of capital and 2 other evaluationindicators reflect the capital strength of the 5C elementsthe collateral score reflects the secured collateral of the 5Celements the industry sentiment indicator and the Engelcoefficient reflect the operating environment conditions ofthe 5C elements

45 The Validity Test of Credit Indicators and the Final Indica-tor System After the pretreatment of micro enterprisersquo creditindicator and two rounds of indicator selection the paperconstructs a credit indicator system of micro enterprises with20 credit indicators shown in column (b) of Table 5

For the standardized values of the 20 credit indicatorsshown in column (b) of Table 6 remaining after the finalselection use the ROC curve in SPSS software to test thevalidity of the indicators in the constructed micro enterprisecredit indicator system the ROC curve of each indicator isshown in Figure 4 the AUC of each indicator is shown incolumn (2) of Table 6 As shown in column (2) of Table 6the AUC values of the 20 credit indicators remaining after thefinal selection are all greater than the critical value of 05 asshown in column (3) of Table 5 the results of the validity testof the credit indicators show that all the indicators remainedafter the final selection has passed the validity test

5 Conclusions

(1) In this paper the micro enterprise credit indicator modelis constructed through the double combination selectionmodel based on SVM and R-type clustering where internalfinancial factors nonfinancial factors and external macroenvironmental factors are criteria layers and the cash recov-ery rate of all assets and 20 other credit indicators areindicators layers

(2) Compared with the 5C element model the resultsshow that in this paper all the credit indicators of themicro enterprise credit indicator model can be related to theelements in the 5C element model so the information of theconstructed micro enterprise credit indicator model coversall the elements of the 5C element model

(3)Theresults of the validity test of the credit indicators ofmicro enterprise based on ROC curve show that all the creditindicators of the micro enterprise credit indicator modelconstructed in this paper pass the validity test so all theindicators in the micro enterprise credit indicator model arevalid

Mathematical Problems in Engineering 9

Table5Th

esecon

droun

dof

indicatorsele

ctionbasedon

R-type

cluste

ring

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Clusters

(2)Sigvalueo

f119870-119882

test

(3) 119882119895

(4)Selection

results

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

The1stclu

ster

02698

25820

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

4Netcash

flowfro

mop

eratingactiv

ities

10259

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot17

Ther

atio

ofshareholdersrsquoequ

ityTh

e8th

cluste

r00535

1653

3Re

tain

18Th

eratio

ofassetsandliabilities

16464

Dele

te

19

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

The9

thclu

ster

02161

8227

Retain

20Th

erange

ofprod

uctsales

4726

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot36

Thec

reditsitu

ationof

enterpris

einthelastthree

years

The18thclu

ster

00357

48551

Retain

37Th

elevelof

enterpris

ersquosin

placer

egistered

capital

11510

Delete

39Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

The19thclu

ster

mdash3324

Retain

40En

gelcoefficient

The2

0thclu

ster

08550

81689

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

43Perc

apita

disposableincomeo

furban

resid

ents

80611

Dele

te

10 Mathematical Problems in Engineering

Table6Micro

enterpris

esrsquocreditevaluationindicatorsystem

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Con

trastw

ith5C

elem

ents

(2)AU

Cvalue

(3)Va

lidity

test

Quality

Ability

Capital

Guarantee

Environm

ent

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

radic0630

Pass

2Netcash

flowratio

forn

onperfo

rmingliabilities

operatingactiv

ities

radic0571

3Th

egrowth

rateof

retained

earnings

radic0678

4Ca

shratio

ofmainbu

sinessincom

eradic

0689

5Th

eratio

ofshareholdersrsquoequ

ityradic

0689

6Netprofi

tradic

0752

7Fixedrateof

capital

radic0745

8Th

eratio

ofcurrentliabilitiestoEB

ITradic

0710

9

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

radic0704

Pass

10Th

elevelof

brandedprod

ucts

radic0564

11Th

eyearsof

employmentinrelated

indu

stry

radic0769

12Legalrepresentativersquos

loan

defaultrecord

radic0733

13Th

eyearsto

hold

thep

ost

radic0748

14Living

cond

ition

radic0724

15Th

ecreditsitu

ationof

enterpris

esin

recent

three

years

radic0757

16Th

esitu

ationof

enterpris

ersquoslaw-abiding

operation

radic0703

17Th

elegaldisputes

ituationof

enterpris

eradic

0764

18Pledge

score

radic0725

19Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

radic0578

Pass

20En

gelcoefficient

radic0855

Mathematical Problems in Engineering 11

Sens

itivi

ty

10

08

06

04

02

00

ROC curve

1 minus Mpecificity00 02 04 06 08 10

Curve sourceCashRatioOfMainBusinessIncomeeRatioOfCurrentLiabilitiesToEBITCashRecoveryRateOfAllAssetseEquitRatioOfShareholdersFixedRateOfCapitalNetCashFlowRatioForNonperformaingLiabilitiesOperatingActivitiesNetProfit

eGrowthRateOfRetainedEarningseYearsOfEmploymentInRelatedIndustryeLevelOfBrandedProductsRatioOfeMoneyWithdrawnByeEnterpriserougheBank

LoanDefaultRecordOfLegalRresentative

LivingConditioneYearsToHoldePost

eCreditSituationOfEnterprisesInRecentreeYearseLegalDisputeSituationOfEnterpriseeLawAbidingOperationSituationOfEnterpriseIndustrySentimentIndex

PledgeScoreEngelCoefficient

Reference Line

Figure 4 Validity test of credit evaluation indicator of micro enterprise

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Thiswork is supported by the Key Project of National NaturalScience Foundation of China (71731003) China PostdoctoralScience Foundation (2015M582746XB) and Natural ScienceFoundation of InnerMongolia Autonomous Region of China(2016MS0714)

References

[1] L Zhanjiang ldquoEstablishment of Evaluation indicator System ofCredit State of Micro Enterprisesrdquo Technology Economics vol36 no 02 pp 109ndash116 2017

[2] C Guotai Z Yajing and S Baofeng ldquoThe Debt Rating ForSmall Enterprises Based on Probit Regressionrdquo Journal of Man-agement Sciences in China vol 19 pp 136ndash156 2016

[3] W Zhang J Lu and Y Zhang ldquoComprehensive EvaluationIndex System of Low Carbon Road Transport Based on FuzzyEvaluation Methodrdquo in Proceedings of the Green IntelligentTransportation System and Safety GITSS 2015 pp 659ndash668China

[4] CHonghai ldquoStudy of Evaluation Indicators Screening Based onInformation Substitutabilityrdquo Statistics amp Information Forumvol 31 no 10 pp 17ndash22 2016

[5] L Youxi ldquoA Summary of Comprehensive Evaluation MethodsrdquoMarket Modernization vol 02 pp 254-255 2016

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Page 2: Establishment of the Credit Indicator System of Micro ...downloads.hindawi.com/journals/mpe/2018/6390720.pdf · ResearchArticle Establishment of the Credit Indicator System of Micro

2 Mathematical Problems in Engineering

combining the chi-square test 119870-119878 test and 119880 test after theinitial construction of the indicator system

There are shortcomings in the previous studies Firstlythe enterprisersquos credit evaluation is mainly focused on thelarge enterprises for micro enterprise credit evaluationresearch is lacking Secondly the indicators that have beenscreened out cannot be guaranteed to significantly identifythe micro enterprisesrsquo credit status which leads to a higherfalse-positive rate in the final enterprise credit evaluationresults Thirdly there are information redundancy indicatorsin the final credit evaluation indicator system that is theselection of indicators does not consider eliminating repeatedinformation indicators

In this paper we first select indicators that can iden-tify the credit status of micro enterprises based on SVM(Support Vector Machine) and then construct an indicatorsystemby deleting the indicators with redundant informationand retaining the indicators with strong ability of creditidentification based on R-type clustering which makes theselected credit indicators be able to significantly identify thecredit status of micro enterprises and do not have duplicateinformation and finally apply the constructed model to thecredit data of micro enterprises in InnerMongolia in westernChina

The innovation of this paper lies in the following thenonlinearity of the credit indicator is mapped to the high-dimensional space by the Gaussian kernel SVM and then theevaluation indicators are filtered out with credit identificationability which solves the problem that the traditional linearweighting model cannot reflect the nonlinear relationshipbetween the credit indicator and the evaluation resultsThen we use Levenersquos variance homogeneity test statistic119882 value to recognize the credit identification ability ofindicator and then cluster clusters using the method of R-type hierarchical clustering within the criterion layer andkeep the indicators with largest119882 value in each cluster bothdeleting the redundant information indicators and retainingthe indicators with significant credit identification ability

2 Difficulties and Ideas of the Problem

21 Difficulties of the Problem

Difficulty 1 The first difficulty is how to ensure that eachmicro enterprise credit indicator that has been selected hasthe ability to identify the micro enterprisesrsquo credit statusThe commonly used indicators in credit evaluation do notnecessarily have significant credit capabilities in micro enter-prise credit ratings In order to prevent companies withhigh default risk from obtaining a higher credit score itis necessary to ensure that the selected indicators have theability to identify the credit status of micro enterprises

Difficulty 2 The second difficulty is how to avoid the sit-uation where micro enterprise credit indicators reflectrepeated information and how to ensure not mistakenlydeleting the indicators with strong ability to identify themicro enterprisesrsquo credit status when eliminating the redun-dant information indicators A good micro enterprise credit

indicator system must not contain redundant informationindicators each indicator in the final construction of themicro enterprise credit indicator model having significantcredit identification ability is essential for micro enterprisecredit evaluation Therefore in the process of constructingthe micro enterprise credit indicator model in addition toavoiding overlap information in credit indicators retainingthe indicators with significant credit identification ability onmicro enterprise credit status is more important

22 Ideas to Solve the Difficulties

(1) Ideas to Solve Difficulty 1 Credit identification ability of acredit indicator is the correct percentage to identify the creditstatus of micro enterprises In this paper we obtain the creditidentification ability of all the indicators 119860 and the creditidentification ability of the remaining indicator after deletingthe 119895th indicator 119860119895 by predicting the credit status of microenterprises and using the two classification models of SVMthe difference between 119860119895 and 119860 is defined as 119889119895 which hasbeen taken as the impact of the 119895th indicator on the evaluationresults

Remove or retain the 119895th indicator according to positive119889119895 or negative 119889119895 and then filter out the credit evaluationindicator Specifically if 119889119895 is greater than or equal to 0 thecredit identification ability of the remaining indicator afterdeleting the 119895th indicator is stronger than or equal to thecredit identification ability of all the indicators when the119895th indicator is not deleted which indicates that the 119895thindicator cannot identify the enterprisesrsquo credit status and sojust deletes it If 119889119895 is less than 0 the credit identificationability of the remaining indicators after the deletion of the 119895thindicator is weaker than the credit identification ability of allthe indicators when the 119895th indicator is not deleted whichindicates that the 119895th indicator can identify the credit statusof themicro enterprise and so just retains itThe ideas to solvedifficulty 1 are shown in Figure 1

(2) Ideas to Solve Difficulty 2 After R-type clusteringindicators in the same category are considered to reflectsimilar information and indicators in different categories areconsidered to reflect different information In this paperthe R-type hierarchical clustering method is used to clusterthe indicators of the same criterion layer which reflect thesame type of information according to the principle of theminimum sum of deviation squares in order to cluster theindicators that reflect the repetitive information into onecluster through retaining the indicator with strongest creditidentification ability in the indicators of same cluster anddeleting all other indicators of the cluster to achieve the goalof preserving the indicators with strong credit qualificationability and at the same time deleting the indicators thatreflect redundancy information The variance homogeneityLevenersquos test statistic 119882 value (hereinafter referred to as 119882value) is used to measure the credit qualification ability ofcredit indicator The 119882 value reflects the thought that thegreater the degree of deviation from the mean value of creditindicator in default enterprise samples to themean value of allenterprise samples the stronger the ability of the indicators to

Mathematical Problems in Engineering 3

Calculate the credit identification ability of all indicators A

Delete the jth indicator and calculate the credit

Calculate the influence of the jth

Are all the indicators calculated

Keep the jth indicator

Delete the jth indicator

No

No

YesYes

identification ability of the remaining indicatorsAj

indicator on the evaluation resultsdj

dj ge 0

Figure 1 Principle to solve difficulty 1

NoYes

Yes

No

Artificially set a total number of clustered clusters accordingto the final number of indicators L

Assign criteria layers to the remaining indicators and make eachindicator inside the same criteria layer into a cluster

e number of clusters of the ℎth criterion layer is calculatedaccording to the total number of clusters Lℎ

Use the method of hierarchical clustering to cluster the indicators within the ℎthcriterion layer according to the principle of minimum sum of deviationsquares until the number of clusters reaches Lℎ

Total number of clusters = L

Use K-W test for indicators within the cluster to determine therationality of the number of clusters L

Is L reasonable

Keep the indicators with largest W value ineach cluster and remove other indicators

Figure 2 Principle to solve difficulty 2

significantly identify the micro enterprisesrsquo credit status Theideas to solve difficulty 2 are shown in Figure 2

23 Principle of Building the Model The principle of buildingthe credit indicator model of micro enterprise based on themethods of SVM and R-type clustering is shown in Figure 3

3 Method of Building the Model

31 Initial Selection and Standardization of Credit IndicatorsThere are two principles in the mass selection of indicators

retaining classic and high-frequency indicators and reflectingthe characteristics of micro enterprises Directly delete unob-servable indicators or indicators with inability to obtain dataor loss of original data of more than 10 of the total sampleInterpolation is used to process data that has lost less than10 of the total number of samples

Set 119909119894119895 as the standardized value of the 119895th indicator of the119894th enterprise V119894119895 as the original value of the 119895th indicator ofthe 119894th enterprise 119899 as the total number of micro enterprisessamples 1199021 as the left border of the indicatorrsquos interval and1199022 as the right border of the indicatorrsquos interval

4 Mathematical Problems in Engineering

data of credit evaluatione selection of indicators from raw

indicators of micro enterpriseStage 1

Stage 2

Stage 3

Preprocessingof data Preliminary selection of credit evaluation indicators

Standardization of evaluation indicators

e classification forecasting of SVM is usedto filter out the indicators with ability to identifythe credit status of micro enterprises

Using the method of R-type clustering to deletethe indicators with redundant information andretain the indicators with strong ability toidentify the credit status of micro enterprises

Micro enterprise credit evaluation indicator system

Validity test of credit indicatorbased on ROC curve

e first roundof indicatorsselection

e second roundof indicatorsselection

e constructionof credit indicatormodel

e validity testof credit indicators

Figure 3 Principle of building the credit indicator model of micro enterprise

Then the standardized value of positive indicator 119909119894119895 is

119909119894119895 =V119894119895 minusmin1le119894le119899 (V119894119895)

max1le119894le119899 (V119894119895) minusmin1le119894le119899 (V119894119895) (1)

Then the standardized value of negative indicator 119909119894119895 is

119909119894119895 =max1le119894le119899 (V119894119895) minus V119894119895

max1le119894le119899 (V119894119895) minusmin1le119894le119899 (V119894119895) (2)

Then the standardized value of interval indicator 119909119894119895 is

119909119894119895= 1

minus1199021 minus V119894119895

max (1199021 minusmin1le119894le119899 (V119894119895) max1le119894le119899 (V119894119895) minus 1199022)

V119894119895 lt 1199021

(3a)

119909119894119895= 1

minusV119894119895 minus 1199022

max (1199021 minusmin1le119894le119899 (V119894119895) max1le119894le119899 (V119894119895) minus 1199022)

V119894119895 gt 1199022

(3b)

119909119894119895 = 1 1199021 le V119894119895 le 1199022 (3c)

The standardization rules for qualitative indicators areshown in Table 1

32 The Method of the First Round of Indicator SelectionBased on SVM

(1) The Determination of Kernel Function In this paper theGaussian radial basis function is selected as the kernel func-tion of the SVM in the first round of indicator selection usingthe method of classification prediction of SVM there arethree main reasons Firstly linear kernel function is suitablefor linearly separable situations whereas the Gaussian radialbasis function is suitable for linearly inseparable situationsfor the nonlinear relationship between credit indicators andevaluation results Gaussian radial basis function can getmore accurate results than linear kernel function Secondlythe number of parameters in the kernel function will affectthe accuracy of the model Kernel functions with fewerparameters help to improve the accuracy of the modelcompared to other kernel functions the Gaussian radial basisfunction has fewer parameters Thirdly the use of Gaussianradial basis function as SVMrsquos kernel function also reducesthe difficulty of the calculation

(2) The Criteria of Selection

Criterion 1 119889119895 gt 0 and 119860119895 gt A indicating that the creditidentification ability of the remaining indicators after deletingthe 119895th indicator is stronger than the credit identificationability of all the indicators when the 119895th indicator is notdeleted the 119895th indicator cannot identify default enterprisesand nondefault enterprises to be deleted

Criterion 2 119889119895 = 0 and is 119860119895 = A indicating that the creditidentification ability of the remaining indicators after deletingthe 119895th indicator is equal to the credit identification ability ofall the indicators when the 119895th indicator is not deleted the 119895thindicator cannot identify default enterprises and nondefaultenterprises to be deleted

Mathematical Problems in Engineering 5

Table 1 The standardization rules for qualitative indicators

Serialnumber

(1)Indicator name

(2)Content

(3)Standardized values

1 Living condition

(1) Full purchase or mortgage 100(2) Relatives buildings 075

(3) Renting 050(4) Collective dormitory or shared dwelling 025

(5) Other or missing data 000sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot

22

Legalrepresentativersquoseducationalbackground

(1) Bachelor degree or above 100(2) Specialist 090

(3)High school or secondary education 070(4) Junior or primary education 040

(5) Other or missing data 000

Criterion 3 119889119895 lt 0 and is 119860119895 lt A indicating that the creditidentification ability of the remaining indicators after deletingthe 119895th indicator is weaker than the credit identificationability of all the indicators when the 119895th indicator is notdeleted the 119895th indicator can identify default enterprises andnondefault enterprises to be kept

(3) Calculation of Credit Identification Ability of Credit Indi-cator Set A as the credit identification ability of all theindicators for all micro enterprise samples 1198990 as total numberof nondefault enterprises 119910119894 as the true value of the defaultstatus of the 119894th enterprise (119910119894 = 0 the true value of the defaultstatus of the 119894th enterprise is nondefault 119910119894 = 1 the true valueof the default status of the 119894th enterprise is default) 1199101015840119894 as thepredictive value of the default status of the 119894th enterprise and1198991 as total number of default enterprises Then 119860 is given asfollows119860

=(11198990) (1198990 minus sum1198990119894=1

10038161003816100381610038161003816119910119894 minus 1199101015840119894

10038161003816100381610038161003816) + (11198991) (1198991 minus sum1198991119894=1

10038161003816100381610038161003816119910119894 minus 1199101015840119894

10038161003816100381610038161003816)2

(4)

In this paper 119860119895 is a formula obtained by replacing 1199101015840119894 inthe molecule of formula (4) with 1199101198951015840119894 (the predictive value ofcredit status of the 119894th enterprise calculated by the indicatorsremained after deleting the 119895th indicator) then obtain119860119895 (thecredit identification ability of the indicators after deleting the119895th indicator for all micro enterprises samples)

Then 119889119895 is given as follows

119889119895 = 119860119895 minus 119860 (5)

33 The Method of the Second Round of Indicator SelectionBased on R-Type Clustering

(1) The Criteria of Selection After the first round of indicatorselection clustering the indicators inside the same criterialayer according to the principle ofminimumdeviation sumofsquares using the method of hierarchical clustering through

the R-type clustering the validity of the number of clusters Lis verified by the 119870-119882 test when the total number of clustersreaches the preset value L if the 119870-119882 test is not passedthen reset the number of clusters if the 119870-119882 test is passedthen retain the indicator with the strongest ability of creditidentification and delete redundant information indicators byretaining the indicator of the largest119882 value in each clusterand deleting all the other indicators

(2) The Calculation of Deviation Sum of Squares Set 119878ℎ asthe sum of the squares of the ℎth criterion layer 119871ℎ as thenumber of clusters in the ℎth criterion layer119898119905 as the numberof indicators of the 119905th cluster of the ℎth criterion layer119883119905119895 asthe vector of the 119895th indicator in the 119905th cluster of the ℎthcriterion layer and119883119905 as the mean vector of all the indicatorsin the 119905th class of the ℎth criterion layer Then 119878ℎ is given asfollows

119878ℎ =119871ℎ

sum119905=1

119898119905

sum119895=1

(119883119905119895 minus 119883119905) (119883119905119895 minus 119883

119905)1015840

(6)

(3) 119870-119882 Test In this paper the nonparametric 119870-119882 test isused to test the rationality of the number of clusters thatis to test whether there is a significant difference betweenthe credit indicators of the same cluster If the 119870-119882 test isnot passed which indicates that there is significant differencebetween these indicators of the same cluster they cannot beclustered into a cluster in this case the number of clustersneeds to be reset if the 119870-119882 test is passed which indicatesthat there is no significant difference between these indicatorsof the same cluster they can be clustered into a cluster in thiscase retain the indicator with the strongest ability of creditidentification and delete information redundancy indicatorsby retaining the indicator of the largest 119882 value in eachcluster and deleting all the other indicators to complete thesecond round of indicators selection

Specifically the119870-119882 test is as followsH0 there is no significant difference between theindicators within the cluster

6 Mathematical Problems in Engineering

Table 2 Indicators and standardized values

Serialnumber

(a)Criteria layer

(b)Indicator name

(c)Indicator type (1) sdot sdot sdot (860)

1Internal financial factors

The cash ratio of main business income Positive 0000 0142sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot35 The rate of capital accumulation Positive 0496 049836

Nonfinancial factors withinthe enterprise

Identification level of new product Qualitative 0000 0000sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot62 The range of product sales Qualitative 1000 050063

External macroenvironmental factors

Industry sentiment indicator Positive 0695 0656sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot68 The growth rate of GDP Positive 0356 035669 The true credit status of micro enterprise samples 1 sdot sdot sdot 0

H1 there is significant difference between the indica-tors within the clusterThe significance level is set to 001When sig gt 001 accept H0 so these indicators canbe clustered into a clusterWhen siglt 001 refuseH0 so these indicators cannotbe clustered into a cluster

(4) The Calculation of 119882 Value Set 119882119895 as the 119882 value ofthe 119895th indicator 119899 as total number of enterprise samples

1198990 as total number of nondefault enterprise samples 1198850119894119895 asthe absolute value of the difference between the 119895th indicatorof the 119894th nondefault enterprise and the mean value of the119895th indicator of all nondefault enterprises 1198851119894119895 as the absolutevalue of the difference between the 119895th indicator of the 119894thdefault enterprise and the mean value of the 119895th indicatorof all default enterprises and 1198991 as total number of defaultenterprises Then the 119895th indicatorrsquos119882 value119882119895 is given asfollows

119882119895

=(119899 minus 2) (1198990 ((sum1198990119894=1 1198850119894119895) 1198990 minus ((sum1198990119894=1 1198850119894119895) 1198990 + (sum1198991119894=1 1198851119894119895) 1198991) 2)

2) + (119899 minus 2) (1198991 ((sum1198991119894=1 1198851119894119895) 1198991 minus ((sum1198990119894=1 1198850119894119895) 1198990 + (sum1198991119894=1 1198851119894119895) 1198991) 2)2)

sum1198990119894=1 (1198850119894119895 minus (sum1198990119894=1 1198850119894119895) 1198990)2 + sum1198991119894=1 (1198851119894119895 minus (sum1198991119894=1 1198851119894119895) 1198991)

2

(7)

34 The Validity Test of Credit Indicators The ROC curveis a comprehensive indicator that reflects the sensitivity andspecificity of continuous variables the vertical coordinate ofROC curve sensitivity indicates the ratio at which the defaultsamples are judged to be correct the specificity indicates theratio at which nondefault samples are judged to be correctso the horizontal coordinate of ROC curve 1 minus specificityindicates the rate at which nondefault samples are judged tobe incorrect When the horizontal coordinate is constant thelarger the vertical coordinate is the higher the proportionof default samples judged to be correct is the larger theAUC (area under ROC curve) of the corresponding creditindicator is the stronger the ability of credit identificationof the indicator against the default samples is and the moreeffective the indicator is Based on the ROC curve this papertests the validity of the screened indicators the criteria forindicator to define whether it has the accuracy to identify thecredit status of enterprises samples are as follows when 0 leAUC lt 05 it does not have the accuracy of identificationwhen 05 le AUC lt 1 it has the accuracy of identification

4 The Application of the Model

41 Data and Standardization of Indicators We apply microenterprise credit data from 2010 to 2015 from a commercialbank in Inner Mongolia western China The 68 indicatorsremaining after the initial selection are shown in column (b)numbered from 1 to 68 in Table 2 the standardized valueof each indicator is obtained by instituting the raw dataand materials of indicators into Formulas (1)ndash(3a) (3b) and(3c) and Table 1 according to the type of indicators amongwhich the standardization values of qualitative indicators aredetermined by the professionals of universities and commu-nity The micro enterprisesrsquo true credit status (0 representingnondefault and 1 representing default) and other relatedinformation are shown in Table 2

42 The First Round of Indicator Selection Based on SVM

(1) Classification of Micro Enterprise Samples The 68 indica-tors of micro enterprises remaining after the initial selection

Mathematical Problems in Engineering 7

Table 3 The division of micro enterprise samples

Nondefault samples Default samples TotalTraining set 664 24 688Test set 166 6 172Total 830 30 860

Table 4 The results of first round of indicator selection based on SVM

Serialnumber

(a)Criteria layer

(b)Indicator name

(1)119860119895119860 ()

(2)119889119895 ()

(3)Selection results

0 mdash All indicators 8303 mdash mdash1

Internal financial factorsQuick ratio 9137 837 Delete

sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot35 The ratio of EBITDA and total debt 8303 000 Delete36

Nonfinancial factors withinthe enterprise

The years of employment in relevant industry 7470 minus833 Retainsdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot62 Gender 8303 000 Delete63

External macroenvironmental factors

The growth rate of GDP 8303 000 Deletesdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot68 Pledge score 7470 minus833 Retain

for the first round are filtered using classification and predic-tion of SVM so as to pick out the indicators that can identifythe credit status of micro enterprises The division of microenterprise samples is shown in Table 3

(2) Determination of Optimal Parameters It is necessary todetermine the penalty coefficient 119888 and the Gaussian radialbasis function parameter 119892 by using SVMrsquos classification andprediction to calculate 1199101015840119894 in formula (4) and 1199101198951015840119894 after deletingthe 119895th indicator MATLAB software and LIBSVM toolboxare used to determine the penalty coefficient c and theGaussian radial basis function parameter g c is selected insteps of 05 between 2minus4 and 26 and 119892 is selected in stepsof 05 between 2minus5 and 25 the cross validation number isset to 3-fold the accuracy rate discretization display step isset to 09 then the program is run in MATLAB based onthe parameters that have been set and the training set andtest set that have been selected according to Table 2 columns(1)ndash(860) then we have that the optimal Gaussian radialbasis function parameter 119892 is 56569 and the optimal penaltycoefficient 119888 is 0125

(3) Calculation of theDegree of the Influence of Credit Indicatoron Evaluation Results The training model is established onMATLAB using the selected training set and the optimalparameters 119888 and 119892 the value of 1199101015840119894 in column (4) is obtainedby predicting the credit status of the enterprise in the test setDelete the 119895th indicator in the training set and test set at thesame time establish the training model in MATLAB basedon the optimal parameters 119888 and 119892 using the training set thathas removed the 119895th indicator the value of1199101198951015840119894 can be obtainedby predicting the credit status of the enterprise in the test setwhere the 119895th indicator has been deleted The values shownat Table 4 column (1) are obtained by substituting the two

credit status predictive values obtained above and the creditstatus true values shown at Table 2 69th row into formula(4) the degree of the influence of each credit indicator onevaluation results or 119889119895 shown at Table 4 column (2) isobtained by substituting the values shown at Table 4 column(1) into formula (5)

(4) The First Round of Credit Indicator Selection 119889119895 shown atTable 4 column (2) represents the degree of the influence ofthe 119895th credit indicator on evaluation results the selectionresults obtained according to the first round of indicatorselection criteria are shown in column (3) of Table 4 whereldquoDeleterdquo indicates that the corresponding credit indicator isdeleted and ldquoRetainrdquo indicates that the corresponding creditindicator is retained in the first round of indicator selectionbased on the SVM

After the first round of indicator selection we delete 25indicators and keep 43 indicators that can identify the creditstatus of micro enterprises

43 The Second Round of Indicator Selection Based on R-Type Clustering The second round of indicator selection forthe 43 indicators remaining after the first round of indicatorselection based on R-type clustering is to filter out theindicators with strong ability of credit qualification and deletethe redundant information indicators

(1) Determine the Number of Clusters in Each CriterionLayer Calculate the number of clusters in each criteria layeraccording to the fact that there will be 20 credit indicatorsretained in the final indicator model specifically there are43 indicators remaining after the first round of indicatorselection where there are 18 indicators remaining from thefirst criterion layer the internal financial factors and theywould be divided into (1843) times 20 asymp 8 clusters There are

8 Mathematical Problems in Engineering

20 indicators remaining from the second criterion layer theinternal nonfinancial factors keeping the indicator-collateralscore directly in order to correspond to 5C factor analysismodel and treat it alone as a cluster the remaining 19indicators are divided into (1943)times20 asymp 9 clustersThere are5 indicators remaining from the third criterion layer externalmacro environmental factors and they would be divided into(543) times 20 asymp 2 clusters

(2) Clustering the Indicators within the Criteria Layer Theindicators in the first criterion layer financial internal factorsare used as an example for clustering the other two criterionlayers do similar processing

Firstly make all the indicators marked ldquoRetainrdquo inTable 4 column (3) numbers 1ndash35 from the first criterialayer the internal financial factors into a cluster respectivelywhich is formed into 18 clusters then cluster any two clustersof indicators into a new cluster which clusters the indicatorswithin the first criteria layer into 17 clusters adding up to 119862218= 153 clustering schemes Substitute the standardized valuesof the indicators of each clustering scheme into formula (6) tocalculate each clustering schemersquos deviation squared sum theclustering scheme with the smallest deviation squared sumis chosen and then the first round of clustering is completedContinue clustering in this way until the number of clustersin the first criteria layer reaches the preset quantity 8 Theclustering results of all the indicators are shown in Table 4column (1)

(3) The Test of the Rationality of the Number of ClustersCluster the 43 credit indicators marked ldquoRetainrdquo shown inTable 4 column (3) within the criteria layer based on R-type hierarchical clustering according to the principle ofminimum sum of deviation squares and the clustering resultsare shown in Table 5 column (1) in order to avoid some ofthe indicators misinterpreted in the second round of R-typeclustering because of the significant difference between theevaluation indicators within the cluster in this paper use themethod of 119870-119882 test in SAS software for the clustered creditindicators to complete the significant test at a significancelevel of 001 (except for the cluster with only one indicator)and the 119870-119882 test sig values for each cluster are shown inTable 5 column (2) according to the criterion of test 20clusters of indicators are clustered as reasonable so there isno need to reset the number of clusters

(4) The Calculation of 119882 Value Substitute the standardizedvalues of the 43 indicators marked rdquoRetainrdquo in column (3) ofTable 4 into formula (7) to calculate the 119882 values of the 43indicators and they are shown in Table 5 column (3)

(5)The Second Round of Credit Indicator SelectionThe secondround of indicator selection is achieved by keeping theindicator of the largest 119882 value in each cluster accordingto the clustering results shown in Table 5 column (1) theresults of selection are shown in Table 5 column (4) in whichthe indicators marked rdquoDeleterdquo are deleted and the indicatorsmarked rdquoRetainrdquo are retained in the second round of indicatorselection based on R-type clustering

After the second round of indicator selection we delete23 indicators and keep 20 indicators that can significantlyidentify the credit status of enterprises and do not containredundant information indicators

44 Contrast with the 5C Model Comparatively analyze theconstructedmicro enterprisesrsquo credit indicator model and 5Cfactor analysis model the results are shown in column (1) ofTable 6 in which legal representativersquos loan default recordsand four other evaluation indicators reflect the moral qualityof the 5C elements the cash recovery rate of all assets and 11other evaluation indicators reflect the repayment ability of the5C elements the fixed rate of capital and 2 other evaluationindicators reflect the capital strength of the 5C elementsthe collateral score reflects the secured collateral of the 5Celements the industry sentiment indicator and the Engelcoefficient reflect the operating environment conditions ofthe 5C elements

45 The Validity Test of Credit Indicators and the Final Indica-tor System After the pretreatment of micro enterprisersquo creditindicator and two rounds of indicator selection the paperconstructs a credit indicator system of micro enterprises with20 credit indicators shown in column (b) of Table 5

For the standardized values of the 20 credit indicatorsshown in column (b) of Table 6 remaining after the finalselection use the ROC curve in SPSS software to test thevalidity of the indicators in the constructed micro enterprisecredit indicator system the ROC curve of each indicator isshown in Figure 4 the AUC of each indicator is shown incolumn (2) of Table 6 As shown in column (2) of Table 6the AUC values of the 20 credit indicators remaining after thefinal selection are all greater than the critical value of 05 asshown in column (3) of Table 5 the results of the validity testof the credit indicators show that all the indicators remainedafter the final selection has passed the validity test

5 Conclusions

(1) In this paper the micro enterprise credit indicator modelis constructed through the double combination selectionmodel based on SVM and R-type clustering where internalfinancial factors nonfinancial factors and external macroenvironmental factors are criteria layers and the cash recov-ery rate of all assets and 20 other credit indicators areindicators layers

(2) Compared with the 5C element model the resultsshow that in this paper all the credit indicators of themicro enterprise credit indicator model can be related to theelements in the 5C element model so the information of theconstructed micro enterprise credit indicator model coversall the elements of the 5C element model

(3)Theresults of the validity test of the credit indicators ofmicro enterprise based on ROC curve show that all the creditindicators of the micro enterprise credit indicator modelconstructed in this paper pass the validity test so all theindicators in the micro enterprise credit indicator model arevalid

Mathematical Problems in Engineering 9

Table5Th

esecon

droun

dof

indicatorsele

ctionbasedon

R-type

cluste

ring

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Clusters

(2)Sigvalueo

f119870-119882

test

(3) 119882119895

(4)Selection

results

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

The1stclu

ster

02698

25820

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

4Netcash

flowfro

mop

eratingactiv

ities

10259

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot17

Ther

atio

ofshareholdersrsquoequ

ityTh

e8th

cluste

r00535

1653

3Re

tain

18Th

eratio

ofassetsandliabilities

16464

Dele

te

19

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

The9

thclu

ster

02161

8227

Retain

20Th

erange

ofprod

uctsales

4726

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot36

Thec

reditsitu

ationof

enterpris

einthelastthree

years

The18thclu

ster

00357

48551

Retain

37Th

elevelof

enterpris

ersquosin

placer

egistered

capital

11510

Delete

39Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

The19thclu

ster

mdash3324

Retain

40En

gelcoefficient

The2

0thclu

ster

08550

81689

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

43Perc

apita

disposableincomeo

furban

resid

ents

80611

Dele

te

10 Mathematical Problems in Engineering

Table6Micro

enterpris

esrsquocreditevaluationindicatorsystem

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Con

trastw

ith5C

elem

ents

(2)AU

Cvalue

(3)Va

lidity

test

Quality

Ability

Capital

Guarantee

Environm

ent

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

radic0630

Pass

2Netcash

flowratio

forn

onperfo

rmingliabilities

operatingactiv

ities

radic0571

3Th

egrowth

rateof

retained

earnings

radic0678

4Ca

shratio

ofmainbu

sinessincom

eradic

0689

5Th

eratio

ofshareholdersrsquoequ

ityradic

0689

6Netprofi

tradic

0752

7Fixedrateof

capital

radic0745

8Th

eratio

ofcurrentliabilitiestoEB

ITradic

0710

9

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

radic0704

Pass

10Th

elevelof

brandedprod

ucts

radic0564

11Th

eyearsof

employmentinrelated

indu

stry

radic0769

12Legalrepresentativersquos

loan

defaultrecord

radic0733

13Th

eyearsto

hold

thep

ost

radic0748

14Living

cond

ition

radic0724

15Th

ecreditsitu

ationof

enterpris

esin

recent

three

years

radic0757

16Th

esitu

ationof

enterpris

ersquoslaw-abiding

operation

radic0703

17Th

elegaldisputes

ituationof

enterpris

eradic

0764

18Pledge

score

radic0725

19Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

radic0578

Pass

20En

gelcoefficient

radic0855

Mathematical Problems in Engineering 11

Sens

itivi

ty

10

08

06

04

02

00

ROC curve

1 minus Mpecificity00 02 04 06 08 10

Curve sourceCashRatioOfMainBusinessIncomeeRatioOfCurrentLiabilitiesToEBITCashRecoveryRateOfAllAssetseEquitRatioOfShareholdersFixedRateOfCapitalNetCashFlowRatioForNonperformaingLiabilitiesOperatingActivitiesNetProfit

eGrowthRateOfRetainedEarningseYearsOfEmploymentInRelatedIndustryeLevelOfBrandedProductsRatioOfeMoneyWithdrawnByeEnterpriserougheBank

LoanDefaultRecordOfLegalRresentative

LivingConditioneYearsToHoldePost

eCreditSituationOfEnterprisesInRecentreeYearseLegalDisputeSituationOfEnterpriseeLawAbidingOperationSituationOfEnterpriseIndustrySentimentIndex

PledgeScoreEngelCoefficient

Reference Line

Figure 4 Validity test of credit evaluation indicator of micro enterprise

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Thiswork is supported by the Key Project of National NaturalScience Foundation of China (71731003) China PostdoctoralScience Foundation (2015M582746XB) and Natural ScienceFoundation of InnerMongolia Autonomous Region of China(2016MS0714)

References

[1] L Zhanjiang ldquoEstablishment of Evaluation indicator System ofCredit State of Micro Enterprisesrdquo Technology Economics vol36 no 02 pp 109ndash116 2017

[2] C Guotai Z Yajing and S Baofeng ldquoThe Debt Rating ForSmall Enterprises Based on Probit Regressionrdquo Journal of Man-agement Sciences in China vol 19 pp 136ndash156 2016

[3] W Zhang J Lu and Y Zhang ldquoComprehensive EvaluationIndex System of Low Carbon Road Transport Based on FuzzyEvaluation Methodrdquo in Proceedings of the Green IntelligentTransportation System and Safety GITSS 2015 pp 659ndash668China

[4] CHonghai ldquoStudy of Evaluation Indicators Screening Based onInformation Substitutabilityrdquo Statistics amp Information Forumvol 31 no 10 pp 17ndash22 2016

[5] L Youxi ldquoA Summary of Comprehensive Evaluation MethodsrdquoMarket Modernization vol 02 pp 254-255 2016

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Page 3: Establishment of the Credit Indicator System of Micro ...downloads.hindawi.com/journals/mpe/2018/6390720.pdf · ResearchArticle Establishment of the Credit Indicator System of Micro

Mathematical Problems in Engineering 3

Calculate the credit identification ability of all indicators A

Delete the jth indicator and calculate the credit

Calculate the influence of the jth

Are all the indicators calculated

Keep the jth indicator

Delete the jth indicator

No

No

YesYes

identification ability of the remaining indicatorsAj

indicator on the evaluation resultsdj

dj ge 0

Figure 1 Principle to solve difficulty 1

NoYes

Yes

No

Artificially set a total number of clustered clusters accordingto the final number of indicators L

Assign criteria layers to the remaining indicators and make eachindicator inside the same criteria layer into a cluster

e number of clusters of the ℎth criterion layer is calculatedaccording to the total number of clusters Lℎ

Use the method of hierarchical clustering to cluster the indicators within the ℎthcriterion layer according to the principle of minimum sum of deviationsquares until the number of clusters reaches Lℎ

Total number of clusters = L

Use K-W test for indicators within the cluster to determine therationality of the number of clusters L

Is L reasonable

Keep the indicators with largest W value ineach cluster and remove other indicators

Figure 2 Principle to solve difficulty 2

significantly identify the micro enterprisesrsquo credit status Theideas to solve difficulty 2 are shown in Figure 2

23 Principle of Building the Model The principle of buildingthe credit indicator model of micro enterprise based on themethods of SVM and R-type clustering is shown in Figure 3

3 Method of Building the Model

31 Initial Selection and Standardization of Credit IndicatorsThere are two principles in the mass selection of indicators

retaining classic and high-frequency indicators and reflectingthe characteristics of micro enterprises Directly delete unob-servable indicators or indicators with inability to obtain dataor loss of original data of more than 10 of the total sampleInterpolation is used to process data that has lost less than10 of the total number of samples

Set 119909119894119895 as the standardized value of the 119895th indicator of the119894th enterprise V119894119895 as the original value of the 119895th indicator ofthe 119894th enterprise 119899 as the total number of micro enterprisessamples 1199021 as the left border of the indicatorrsquos interval and1199022 as the right border of the indicatorrsquos interval

4 Mathematical Problems in Engineering

data of credit evaluatione selection of indicators from raw

indicators of micro enterpriseStage 1

Stage 2

Stage 3

Preprocessingof data Preliminary selection of credit evaluation indicators

Standardization of evaluation indicators

e classification forecasting of SVM is usedto filter out the indicators with ability to identifythe credit status of micro enterprises

Using the method of R-type clustering to deletethe indicators with redundant information andretain the indicators with strong ability toidentify the credit status of micro enterprises

Micro enterprise credit evaluation indicator system

Validity test of credit indicatorbased on ROC curve

e first roundof indicatorsselection

e second roundof indicatorsselection

e constructionof credit indicatormodel

e validity testof credit indicators

Figure 3 Principle of building the credit indicator model of micro enterprise

Then the standardized value of positive indicator 119909119894119895 is

119909119894119895 =V119894119895 minusmin1le119894le119899 (V119894119895)

max1le119894le119899 (V119894119895) minusmin1le119894le119899 (V119894119895) (1)

Then the standardized value of negative indicator 119909119894119895 is

119909119894119895 =max1le119894le119899 (V119894119895) minus V119894119895

max1le119894le119899 (V119894119895) minusmin1le119894le119899 (V119894119895) (2)

Then the standardized value of interval indicator 119909119894119895 is

119909119894119895= 1

minus1199021 minus V119894119895

max (1199021 minusmin1le119894le119899 (V119894119895) max1le119894le119899 (V119894119895) minus 1199022)

V119894119895 lt 1199021

(3a)

119909119894119895= 1

minusV119894119895 minus 1199022

max (1199021 minusmin1le119894le119899 (V119894119895) max1le119894le119899 (V119894119895) minus 1199022)

V119894119895 gt 1199022

(3b)

119909119894119895 = 1 1199021 le V119894119895 le 1199022 (3c)

The standardization rules for qualitative indicators areshown in Table 1

32 The Method of the First Round of Indicator SelectionBased on SVM

(1) The Determination of Kernel Function In this paper theGaussian radial basis function is selected as the kernel func-tion of the SVM in the first round of indicator selection usingthe method of classification prediction of SVM there arethree main reasons Firstly linear kernel function is suitablefor linearly separable situations whereas the Gaussian radialbasis function is suitable for linearly inseparable situationsfor the nonlinear relationship between credit indicators andevaluation results Gaussian radial basis function can getmore accurate results than linear kernel function Secondlythe number of parameters in the kernel function will affectthe accuracy of the model Kernel functions with fewerparameters help to improve the accuracy of the modelcompared to other kernel functions the Gaussian radial basisfunction has fewer parameters Thirdly the use of Gaussianradial basis function as SVMrsquos kernel function also reducesthe difficulty of the calculation

(2) The Criteria of Selection

Criterion 1 119889119895 gt 0 and 119860119895 gt A indicating that the creditidentification ability of the remaining indicators after deletingthe 119895th indicator is stronger than the credit identificationability of all the indicators when the 119895th indicator is notdeleted the 119895th indicator cannot identify default enterprisesand nondefault enterprises to be deleted

Criterion 2 119889119895 = 0 and is 119860119895 = A indicating that the creditidentification ability of the remaining indicators after deletingthe 119895th indicator is equal to the credit identification ability ofall the indicators when the 119895th indicator is not deleted the 119895thindicator cannot identify default enterprises and nondefaultenterprises to be deleted

Mathematical Problems in Engineering 5

Table 1 The standardization rules for qualitative indicators

Serialnumber

(1)Indicator name

(2)Content

(3)Standardized values

1 Living condition

(1) Full purchase or mortgage 100(2) Relatives buildings 075

(3) Renting 050(4) Collective dormitory or shared dwelling 025

(5) Other or missing data 000sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot

22

Legalrepresentativersquoseducationalbackground

(1) Bachelor degree or above 100(2) Specialist 090

(3)High school or secondary education 070(4) Junior or primary education 040

(5) Other or missing data 000

Criterion 3 119889119895 lt 0 and is 119860119895 lt A indicating that the creditidentification ability of the remaining indicators after deletingthe 119895th indicator is weaker than the credit identificationability of all the indicators when the 119895th indicator is notdeleted the 119895th indicator can identify default enterprises andnondefault enterprises to be kept

(3) Calculation of Credit Identification Ability of Credit Indi-cator Set A as the credit identification ability of all theindicators for all micro enterprise samples 1198990 as total numberof nondefault enterprises 119910119894 as the true value of the defaultstatus of the 119894th enterprise (119910119894 = 0 the true value of the defaultstatus of the 119894th enterprise is nondefault 119910119894 = 1 the true valueof the default status of the 119894th enterprise is default) 1199101015840119894 as thepredictive value of the default status of the 119894th enterprise and1198991 as total number of default enterprises Then 119860 is given asfollows119860

=(11198990) (1198990 minus sum1198990119894=1

10038161003816100381610038161003816119910119894 minus 1199101015840119894

10038161003816100381610038161003816) + (11198991) (1198991 minus sum1198991119894=1

10038161003816100381610038161003816119910119894 minus 1199101015840119894

10038161003816100381610038161003816)2

(4)

In this paper 119860119895 is a formula obtained by replacing 1199101015840119894 inthe molecule of formula (4) with 1199101198951015840119894 (the predictive value ofcredit status of the 119894th enterprise calculated by the indicatorsremained after deleting the 119895th indicator) then obtain119860119895 (thecredit identification ability of the indicators after deleting the119895th indicator for all micro enterprises samples)

Then 119889119895 is given as follows

119889119895 = 119860119895 minus 119860 (5)

33 The Method of the Second Round of Indicator SelectionBased on R-Type Clustering

(1) The Criteria of Selection After the first round of indicatorselection clustering the indicators inside the same criterialayer according to the principle ofminimumdeviation sumofsquares using the method of hierarchical clustering through

the R-type clustering the validity of the number of clusters Lis verified by the 119870-119882 test when the total number of clustersreaches the preset value L if the 119870-119882 test is not passedthen reset the number of clusters if the 119870-119882 test is passedthen retain the indicator with the strongest ability of creditidentification and delete redundant information indicators byretaining the indicator of the largest119882 value in each clusterand deleting all the other indicators

(2) The Calculation of Deviation Sum of Squares Set 119878ℎ asthe sum of the squares of the ℎth criterion layer 119871ℎ as thenumber of clusters in the ℎth criterion layer119898119905 as the numberof indicators of the 119905th cluster of the ℎth criterion layer119883119905119895 asthe vector of the 119895th indicator in the 119905th cluster of the ℎthcriterion layer and119883119905 as the mean vector of all the indicatorsin the 119905th class of the ℎth criterion layer Then 119878ℎ is given asfollows

119878ℎ =119871ℎ

sum119905=1

119898119905

sum119895=1

(119883119905119895 minus 119883119905) (119883119905119895 minus 119883

119905)1015840

(6)

(3) 119870-119882 Test In this paper the nonparametric 119870-119882 test isused to test the rationality of the number of clusters thatis to test whether there is a significant difference betweenthe credit indicators of the same cluster If the 119870-119882 test isnot passed which indicates that there is significant differencebetween these indicators of the same cluster they cannot beclustered into a cluster in this case the number of clustersneeds to be reset if the 119870-119882 test is passed which indicatesthat there is no significant difference between these indicatorsof the same cluster they can be clustered into a cluster in thiscase retain the indicator with the strongest ability of creditidentification and delete information redundancy indicatorsby retaining the indicator of the largest 119882 value in eachcluster and deleting all the other indicators to complete thesecond round of indicators selection

Specifically the119870-119882 test is as followsH0 there is no significant difference between theindicators within the cluster

6 Mathematical Problems in Engineering

Table 2 Indicators and standardized values

Serialnumber

(a)Criteria layer

(b)Indicator name

(c)Indicator type (1) sdot sdot sdot (860)

1Internal financial factors

The cash ratio of main business income Positive 0000 0142sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot35 The rate of capital accumulation Positive 0496 049836

Nonfinancial factors withinthe enterprise

Identification level of new product Qualitative 0000 0000sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot62 The range of product sales Qualitative 1000 050063

External macroenvironmental factors

Industry sentiment indicator Positive 0695 0656sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot68 The growth rate of GDP Positive 0356 035669 The true credit status of micro enterprise samples 1 sdot sdot sdot 0

H1 there is significant difference between the indica-tors within the clusterThe significance level is set to 001When sig gt 001 accept H0 so these indicators canbe clustered into a clusterWhen siglt 001 refuseH0 so these indicators cannotbe clustered into a cluster

(4) The Calculation of 119882 Value Set 119882119895 as the 119882 value ofthe 119895th indicator 119899 as total number of enterprise samples

1198990 as total number of nondefault enterprise samples 1198850119894119895 asthe absolute value of the difference between the 119895th indicatorof the 119894th nondefault enterprise and the mean value of the119895th indicator of all nondefault enterprises 1198851119894119895 as the absolutevalue of the difference between the 119895th indicator of the 119894thdefault enterprise and the mean value of the 119895th indicatorof all default enterprises and 1198991 as total number of defaultenterprises Then the 119895th indicatorrsquos119882 value119882119895 is given asfollows

119882119895

=(119899 minus 2) (1198990 ((sum1198990119894=1 1198850119894119895) 1198990 minus ((sum1198990119894=1 1198850119894119895) 1198990 + (sum1198991119894=1 1198851119894119895) 1198991) 2)

2) + (119899 minus 2) (1198991 ((sum1198991119894=1 1198851119894119895) 1198991 minus ((sum1198990119894=1 1198850119894119895) 1198990 + (sum1198991119894=1 1198851119894119895) 1198991) 2)2)

sum1198990119894=1 (1198850119894119895 minus (sum1198990119894=1 1198850119894119895) 1198990)2 + sum1198991119894=1 (1198851119894119895 minus (sum1198991119894=1 1198851119894119895) 1198991)

2

(7)

34 The Validity Test of Credit Indicators The ROC curveis a comprehensive indicator that reflects the sensitivity andspecificity of continuous variables the vertical coordinate ofROC curve sensitivity indicates the ratio at which the defaultsamples are judged to be correct the specificity indicates theratio at which nondefault samples are judged to be correctso the horizontal coordinate of ROC curve 1 minus specificityindicates the rate at which nondefault samples are judged tobe incorrect When the horizontal coordinate is constant thelarger the vertical coordinate is the higher the proportionof default samples judged to be correct is the larger theAUC (area under ROC curve) of the corresponding creditindicator is the stronger the ability of credit identificationof the indicator against the default samples is and the moreeffective the indicator is Based on the ROC curve this papertests the validity of the screened indicators the criteria forindicator to define whether it has the accuracy to identify thecredit status of enterprises samples are as follows when 0 leAUC lt 05 it does not have the accuracy of identificationwhen 05 le AUC lt 1 it has the accuracy of identification

4 The Application of the Model

41 Data and Standardization of Indicators We apply microenterprise credit data from 2010 to 2015 from a commercialbank in Inner Mongolia western China The 68 indicatorsremaining after the initial selection are shown in column (b)numbered from 1 to 68 in Table 2 the standardized valueof each indicator is obtained by instituting the raw dataand materials of indicators into Formulas (1)ndash(3a) (3b) and(3c) and Table 1 according to the type of indicators amongwhich the standardization values of qualitative indicators aredetermined by the professionals of universities and commu-nity The micro enterprisesrsquo true credit status (0 representingnondefault and 1 representing default) and other relatedinformation are shown in Table 2

42 The First Round of Indicator Selection Based on SVM

(1) Classification of Micro Enterprise Samples The 68 indica-tors of micro enterprises remaining after the initial selection

Mathematical Problems in Engineering 7

Table 3 The division of micro enterprise samples

Nondefault samples Default samples TotalTraining set 664 24 688Test set 166 6 172Total 830 30 860

Table 4 The results of first round of indicator selection based on SVM

Serialnumber

(a)Criteria layer

(b)Indicator name

(1)119860119895119860 ()

(2)119889119895 ()

(3)Selection results

0 mdash All indicators 8303 mdash mdash1

Internal financial factorsQuick ratio 9137 837 Delete

sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot35 The ratio of EBITDA and total debt 8303 000 Delete36

Nonfinancial factors withinthe enterprise

The years of employment in relevant industry 7470 minus833 Retainsdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot62 Gender 8303 000 Delete63

External macroenvironmental factors

The growth rate of GDP 8303 000 Deletesdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot68 Pledge score 7470 minus833 Retain

for the first round are filtered using classification and predic-tion of SVM so as to pick out the indicators that can identifythe credit status of micro enterprises The division of microenterprise samples is shown in Table 3

(2) Determination of Optimal Parameters It is necessary todetermine the penalty coefficient 119888 and the Gaussian radialbasis function parameter 119892 by using SVMrsquos classification andprediction to calculate 1199101015840119894 in formula (4) and 1199101198951015840119894 after deletingthe 119895th indicator MATLAB software and LIBSVM toolboxare used to determine the penalty coefficient c and theGaussian radial basis function parameter g c is selected insteps of 05 between 2minus4 and 26 and 119892 is selected in stepsof 05 between 2minus5 and 25 the cross validation number isset to 3-fold the accuracy rate discretization display step isset to 09 then the program is run in MATLAB based onthe parameters that have been set and the training set andtest set that have been selected according to Table 2 columns(1)ndash(860) then we have that the optimal Gaussian radialbasis function parameter 119892 is 56569 and the optimal penaltycoefficient 119888 is 0125

(3) Calculation of theDegree of the Influence of Credit Indicatoron Evaluation Results The training model is established onMATLAB using the selected training set and the optimalparameters 119888 and 119892 the value of 1199101015840119894 in column (4) is obtainedby predicting the credit status of the enterprise in the test setDelete the 119895th indicator in the training set and test set at thesame time establish the training model in MATLAB basedon the optimal parameters 119888 and 119892 using the training set thathas removed the 119895th indicator the value of1199101198951015840119894 can be obtainedby predicting the credit status of the enterprise in the test setwhere the 119895th indicator has been deleted The values shownat Table 4 column (1) are obtained by substituting the two

credit status predictive values obtained above and the creditstatus true values shown at Table 2 69th row into formula(4) the degree of the influence of each credit indicator onevaluation results or 119889119895 shown at Table 4 column (2) isobtained by substituting the values shown at Table 4 column(1) into formula (5)

(4) The First Round of Credit Indicator Selection 119889119895 shown atTable 4 column (2) represents the degree of the influence ofthe 119895th credit indicator on evaluation results the selectionresults obtained according to the first round of indicatorselection criteria are shown in column (3) of Table 4 whereldquoDeleterdquo indicates that the corresponding credit indicator isdeleted and ldquoRetainrdquo indicates that the corresponding creditindicator is retained in the first round of indicator selectionbased on the SVM

After the first round of indicator selection we delete 25indicators and keep 43 indicators that can identify the creditstatus of micro enterprises

43 The Second Round of Indicator Selection Based on R-Type Clustering The second round of indicator selection forthe 43 indicators remaining after the first round of indicatorselection based on R-type clustering is to filter out theindicators with strong ability of credit qualification and deletethe redundant information indicators

(1) Determine the Number of Clusters in Each CriterionLayer Calculate the number of clusters in each criteria layeraccording to the fact that there will be 20 credit indicatorsretained in the final indicator model specifically there are43 indicators remaining after the first round of indicatorselection where there are 18 indicators remaining from thefirst criterion layer the internal financial factors and theywould be divided into (1843) times 20 asymp 8 clusters There are

8 Mathematical Problems in Engineering

20 indicators remaining from the second criterion layer theinternal nonfinancial factors keeping the indicator-collateralscore directly in order to correspond to 5C factor analysismodel and treat it alone as a cluster the remaining 19indicators are divided into (1943)times20 asymp 9 clustersThere are5 indicators remaining from the third criterion layer externalmacro environmental factors and they would be divided into(543) times 20 asymp 2 clusters

(2) Clustering the Indicators within the Criteria Layer Theindicators in the first criterion layer financial internal factorsare used as an example for clustering the other two criterionlayers do similar processing

Firstly make all the indicators marked ldquoRetainrdquo inTable 4 column (3) numbers 1ndash35 from the first criterialayer the internal financial factors into a cluster respectivelywhich is formed into 18 clusters then cluster any two clustersof indicators into a new cluster which clusters the indicatorswithin the first criteria layer into 17 clusters adding up to 119862218= 153 clustering schemes Substitute the standardized valuesof the indicators of each clustering scheme into formula (6) tocalculate each clustering schemersquos deviation squared sum theclustering scheme with the smallest deviation squared sumis chosen and then the first round of clustering is completedContinue clustering in this way until the number of clustersin the first criteria layer reaches the preset quantity 8 Theclustering results of all the indicators are shown in Table 4column (1)

(3) The Test of the Rationality of the Number of ClustersCluster the 43 credit indicators marked ldquoRetainrdquo shown inTable 4 column (3) within the criteria layer based on R-type hierarchical clustering according to the principle ofminimum sum of deviation squares and the clustering resultsare shown in Table 5 column (1) in order to avoid some ofthe indicators misinterpreted in the second round of R-typeclustering because of the significant difference between theevaluation indicators within the cluster in this paper use themethod of 119870-119882 test in SAS software for the clustered creditindicators to complete the significant test at a significancelevel of 001 (except for the cluster with only one indicator)and the 119870-119882 test sig values for each cluster are shown inTable 5 column (2) according to the criterion of test 20clusters of indicators are clustered as reasonable so there isno need to reset the number of clusters

(4) The Calculation of 119882 Value Substitute the standardizedvalues of the 43 indicators marked rdquoRetainrdquo in column (3) ofTable 4 into formula (7) to calculate the 119882 values of the 43indicators and they are shown in Table 5 column (3)

(5)The Second Round of Credit Indicator SelectionThe secondround of indicator selection is achieved by keeping theindicator of the largest 119882 value in each cluster accordingto the clustering results shown in Table 5 column (1) theresults of selection are shown in Table 5 column (4) in whichthe indicators marked rdquoDeleterdquo are deleted and the indicatorsmarked rdquoRetainrdquo are retained in the second round of indicatorselection based on R-type clustering

After the second round of indicator selection we delete23 indicators and keep 20 indicators that can significantlyidentify the credit status of enterprises and do not containredundant information indicators

44 Contrast with the 5C Model Comparatively analyze theconstructedmicro enterprisesrsquo credit indicator model and 5Cfactor analysis model the results are shown in column (1) ofTable 6 in which legal representativersquos loan default recordsand four other evaluation indicators reflect the moral qualityof the 5C elements the cash recovery rate of all assets and 11other evaluation indicators reflect the repayment ability of the5C elements the fixed rate of capital and 2 other evaluationindicators reflect the capital strength of the 5C elementsthe collateral score reflects the secured collateral of the 5Celements the industry sentiment indicator and the Engelcoefficient reflect the operating environment conditions ofthe 5C elements

45 The Validity Test of Credit Indicators and the Final Indica-tor System After the pretreatment of micro enterprisersquo creditindicator and two rounds of indicator selection the paperconstructs a credit indicator system of micro enterprises with20 credit indicators shown in column (b) of Table 5

For the standardized values of the 20 credit indicatorsshown in column (b) of Table 6 remaining after the finalselection use the ROC curve in SPSS software to test thevalidity of the indicators in the constructed micro enterprisecredit indicator system the ROC curve of each indicator isshown in Figure 4 the AUC of each indicator is shown incolumn (2) of Table 6 As shown in column (2) of Table 6the AUC values of the 20 credit indicators remaining after thefinal selection are all greater than the critical value of 05 asshown in column (3) of Table 5 the results of the validity testof the credit indicators show that all the indicators remainedafter the final selection has passed the validity test

5 Conclusions

(1) In this paper the micro enterprise credit indicator modelis constructed through the double combination selectionmodel based on SVM and R-type clustering where internalfinancial factors nonfinancial factors and external macroenvironmental factors are criteria layers and the cash recov-ery rate of all assets and 20 other credit indicators areindicators layers

(2) Compared with the 5C element model the resultsshow that in this paper all the credit indicators of themicro enterprise credit indicator model can be related to theelements in the 5C element model so the information of theconstructed micro enterprise credit indicator model coversall the elements of the 5C element model

(3)Theresults of the validity test of the credit indicators ofmicro enterprise based on ROC curve show that all the creditindicators of the micro enterprise credit indicator modelconstructed in this paper pass the validity test so all theindicators in the micro enterprise credit indicator model arevalid

Mathematical Problems in Engineering 9

Table5Th

esecon

droun

dof

indicatorsele

ctionbasedon

R-type

cluste

ring

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Clusters

(2)Sigvalueo

f119870-119882

test

(3) 119882119895

(4)Selection

results

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

The1stclu

ster

02698

25820

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

4Netcash

flowfro

mop

eratingactiv

ities

10259

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot17

Ther

atio

ofshareholdersrsquoequ

ityTh

e8th

cluste

r00535

1653

3Re

tain

18Th

eratio

ofassetsandliabilities

16464

Dele

te

19

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

The9

thclu

ster

02161

8227

Retain

20Th

erange

ofprod

uctsales

4726

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot36

Thec

reditsitu

ationof

enterpris

einthelastthree

years

The18thclu

ster

00357

48551

Retain

37Th

elevelof

enterpris

ersquosin

placer

egistered

capital

11510

Delete

39Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

The19thclu

ster

mdash3324

Retain

40En

gelcoefficient

The2

0thclu

ster

08550

81689

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

43Perc

apita

disposableincomeo

furban

resid

ents

80611

Dele

te

10 Mathematical Problems in Engineering

Table6Micro

enterpris

esrsquocreditevaluationindicatorsystem

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Con

trastw

ith5C

elem

ents

(2)AU

Cvalue

(3)Va

lidity

test

Quality

Ability

Capital

Guarantee

Environm

ent

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

radic0630

Pass

2Netcash

flowratio

forn

onperfo

rmingliabilities

operatingactiv

ities

radic0571

3Th

egrowth

rateof

retained

earnings

radic0678

4Ca

shratio

ofmainbu

sinessincom

eradic

0689

5Th

eratio

ofshareholdersrsquoequ

ityradic

0689

6Netprofi

tradic

0752

7Fixedrateof

capital

radic0745

8Th

eratio

ofcurrentliabilitiestoEB

ITradic

0710

9

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

radic0704

Pass

10Th

elevelof

brandedprod

ucts

radic0564

11Th

eyearsof

employmentinrelated

indu

stry

radic0769

12Legalrepresentativersquos

loan

defaultrecord

radic0733

13Th

eyearsto

hold

thep

ost

radic0748

14Living

cond

ition

radic0724

15Th

ecreditsitu

ationof

enterpris

esin

recent

three

years

radic0757

16Th

esitu

ationof

enterpris

ersquoslaw-abiding

operation

radic0703

17Th

elegaldisputes

ituationof

enterpris

eradic

0764

18Pledge

score

radic0725

19Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

radic0578

Pass

20En

gelcoefficient

radic0855

Mathematical Problems in Engineering 11

Sens

itivi

ty

10

08

06

04

02

00

ROC curve

1 minus Mpecificity00 02 04 06 08 10

Curve sourceCashRatioOfMainBusinessIncomeeRatioOfCurrentLiabilitiesToEBITCashRecoveryRateOfAllAssetseEquitRatioOfShareholdersFixedRateOfCapitalNetCashFlowRatioForNonperformaingLiabilitiesOperatingActivitiesNetProfit

eGrowthRateOfRetainedEarningseYearsOfEmploymentInRelatedIndustryeLevelOfBrandedProductsRatioOfeMoneyWithdrawnByeEnterpriserougheBank

LoanDefaultRecordOfLegalRresentative

LivingConditioneYearsToHoldePost

eCreditSituationOfEnterprisesInRecentreeYearseLegalDisputeSituationOfEnterpriseeLawAbidingOperationSituationOfEnterpriseIndustrySentimentIndex

PledgeScoreEngelCoefficient

Reference Line

Figure 4 Validity test of credit evaluation indicator of micro enterprise

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Thiswork is supported by the Key Project of National NaturalScience Foundation of China (71731003) China PostdoctoralScience Foundation (2015M582746XB) and Natural ScienceFoundation of InnerMongolia Autonomous Region of China(2016MS0714)

References

[1] L Zhanjiang ldquoEstablishment of Evaluation indicator System ofCredit State of Micro Enterprisesrdquo Technology Economics vol36 no 02 pp 109ndash116 2017

[2] C Guotai Z Yajing and S Baofeng ldquoThe Debt Rating ForSmall Enterprises Based on Probit Regressionrdquo Journal of Man-agement Sciences in China vol 19 pp 136ndash156 2016

[3] W Zhang J Lu and Y Zhang ldquoComprehensive EvaluationIndex System of Low Carbon Road Transport Based on FuzzyEvaluation Methodrdquo in Proceedings of the Green IntelligentTransportation System and Safety GITSS 2015 pp 659ndash668China

[4] CHonghai ldquoStudy of Evaluation Indicators Screening Based onInformation Substitutabilityrdquo Statistics amp Information Forumvol 31 no 10 pp 17ndash22 2016

[5] L Youxi ldquoA Summary of Comprehensive Evaluation MethodsrdquoMarket Modernization vol 02 pp 254-255 2016

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Page 4: Establishment of the Credit Indicator System of Micro ...downloads.hindawi.com/journals/mpe/2018/6390720.pdf · ResearchArticle Establishment of the Credit Indicator System of Micro

4 Mathematical Problems in Engineering

data of credit evaluatione selection of indicators from raw

indicators of micro enterpriseStage 1

Stage 2

Stage 3

Preprocessingof data Preliminary selection of credit evaluation indicators

Standardization of evaluation indicators

e classification forecasting of SVM is usedto filter out the indicators with ability to identifythe credit status of micro enterprises

Using the method of R-type clustering to deletethe indicators with redundant information andretain the indicators with strong ability toidentify the credit status of micro enterprises

Micro enterprise credit evaluation indicator system

Validity test of credit indicatorbased on ROC curve

e first roundof indicatorsselection

e second roundof indicatorsselection

e constructionof credit indicatormodel

e validity testof credit indicators

Figure 3 Principle of building the credit indicator model of micro enterprise

Then the standardized value of positive indicator 119909119894119895 is

119909119894119895 =V119894119895 minusmin1le119894le119899 (V119894119895)

max1le119894le119899 (V119894119895) minusmin1le119894le119899 (V119894119895) (1)

Then the standardized value of negative indicator 119909119894119895 is

119909119894119895 =max1le119894le119899 (V119894119895) minus V119894119895

max1le119894le119899 (V119894119895) minusmin1le119894le119899 (V119894119895) (2)

Then the standardized value of interval indicator 119909119894119895 is

119909119894119895= 1

minus1199021 minus V119894119895

max (1199021 minusmin1le119894le119899 (V119894119895) max1le119894le119899 (V119894119895) minus 1199022)

V119894119895 lt 1199021

(3a)

119909119894119895= 1

minusV119894119895 minus 1199022

max (1199021 minusmin1le119894le119899 (V119894119895) max1le119894le119899 (V119894119895) minus 1199022)

V119894119895 gt 1199022

(3b)

119909119894119895 = 1 1199021 le V119894119895 le 1199022 (3c)

The standardization rules for qualitative indicators areshown in Table 1

32 The Method of the First Round of Indicator SelectionBased on SVM

(1) The Determination of Kernel Function In this paper theGaussian radial basis function is selected as the kernel func-tion of the SVM in the first round of indicator selection usingthe method of classification prediction of SVM there arethree main reasons Firstly linear kernel function is suitablefor linearly separable situations whereas the Gaussian radialbasis function is suitable for linearly inseparable situationsfor the nonlinear relationship between credit indicators andevaluation results Gaussian radial basis function can getmore accurate results than linear kernel function Secondlythe number of parameters in the kernel function will affectthe accuracy of the model Kernel functions with fewerparameters help to improve the accuracy of the modelcompared to other kernel functions the Gaussian radial basisfunction has fewer parameters Thirdly the use of Gaussianradial basis function as SVMrsquos kernel function also reducesthe difficulty of the calculation

(2) The Criteria of Selection

Criterion 1 119889119895 gt 0 and 119860119895 gt A indicating that the creditidentification ability of the remaining indicators after deletingthe 119895th indicator is stronger than the credit identificationability of all the indicators when the 119895th indicator is notdeleted the 119895th indicator cannot identify default enterprisesand nondefault enterprises to be deleted

Criterion 2 119889119895 = 0 and is 119860119895 = A indicating that the creditidentification ability of the remaining indicators after deletingthe 119895th indicator is equal to the credit identification ability ofall the indicators when the 119895th indicator is not deleted the 119895thindicator cannot identify default enterprises and nondefaultenterprises to be deleted

Mathematical Problems in Engineering 5

Table 1 The standardization rules for qualitative indicators

Serialnumber

(1)Indicator name

(2)Content

(3)Standardized values

1 Living condition

(1) Full purchase or mortgage 100(2) Relatives buildings 075

(3) Renting 050(4) Collective dormitory or shared dwelling 025

(5) Other or missing data 000sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot

22

Legalrepresentativersquoseducationalbackground

(1) Bachelor degree or above 100(2) Specialist 090

(3)High school or secondary education 070(4) Junior or primary education 040

(5) Other or missing data 000

Criterion 3 119889119895 lt 0 and is 119860119895 lt A indicating that the creditidentification ability of the remaining indicators after deletingthe 119895th indicator is weaker than the credit identificationability of all the indicators when the 119895th indicator is notdeleted the 119895th indicator can identify default enterprises andnondefault enterprises to be kept

(3) Calculation of Credit Identification Ability of Credit Indi-cator Set A as the credit identification ability of all theindicators for all micro enterprise samples 1198990 as total numberof nondefault enterprises 119910119894 as the true value of the defaultstatus of the 119894th enterprise (119910119894 = 0 the true value of the defaultstatus of the 119894th enterprise is nondefault 119910119894 = 1 the true valueof the default status of the 119894th enterprise is default) 1199101015840119894 as thepredictive value of the default status of the 119894th enterprise and1198991 as total number of default enterprises Then 119860 is given asfollows119860

=(11198990) (1198990 minus sum1198990119894=1

10038161003816100381610038161003816119910119894 minus 1199101015840119894

10038161003816100381610038161003816) + (11198991) (1198991 minus sum1198991119894=1

10038161003816100381610038161003816119910119894 minus 1199101015840119894

10038161003816100381610038161003816)2

(4)

In this paper 119860119895 is a formula obtained by replacing 1199101015840119894 inthe molecule of formula (4) with 1199101198951015840119894 (the predictive value ofcredit status of the 119894th enterprise calculated by the indicatorsremained after deleting the 119895th indicator) then obtain119860119895 (thecredit identification ability of the indicators after deleting the119895th indicator for all micro enterprises samples)

Then 119889119895 is given as follows

119889119895 = 119860119895 minus 119860 (5)

33 The Method of the Second Round of Indicator SelectionBased on R-Type Clustering

(1) The Criteria of Selection After the first round of indicatorselection clustering the indicators inside the same criterialayer according to the principle ofminimumdeviation sumofsquares using the method of hierarchical clustering through

the R-type clustering the validity of the number of clusters Lis verified by the 119870-119882 test when the total number of clustersreaches the preset value L if the 119870-119882 test is not passedthen reset the number of clusters if the 119870-119882 test is passedthen retain the indicator with the strongest ability of creditidentification and delete redundant information indicators byretaining the indicator of the largest119882 value in each clusterand deleting all the other indicators

(2) The Calculation of Deviation Sum of Squares Set 119878ℎ asthe sum of the squares of the ℎth criterion layer 119871ℎ as thenumber of clusters in the ℎth criterion layer119898119905 as the numberof indicators of the 119905th cluster of the ℎth criterion layer119883119905119895 asthe vector of the 119895th indicator in the 119905th cluster of the ℎthcriterion layer and119883119905 as the mean vector of all the indicatorsin the 119905th class of the ℎth criterion layer Then 119878ℎ is given asfollows

119878ℎ =119871ℎ

sum119905=1

119898119905

sum119895=1

(119883119905119895 minus 119883119905) (119883119905119895 minus 119883

119905)1015840

(6)

(3) 119870-119882 Test In this paper the nonparametric 119870-119882 test isused to test the rationality of the number of clusters thatis to test whether there is a significant difference betweenthe credit indicators of the same cluster If the 119870-119882 test isnot passed which indicates that there is significant differencebetween these indicators of the same cluster they cannot beclustered into a cluster in this case the number of clustersneeds to be reset if the 119870-119882 test is passed which indicatesthat there is no significant difference between these indicatorsof the same cluster they can be clustered into a cluster in thiscase retain the indicator with the strongest ability of creditidentification and delete information redundancy indicatorsby retaining the indicator of the largest 119882 value in eachcluster and deleting all the other indicators to complete thesecond round of indicators selection

Specifically the119870-119882 test is as followsH0 there is no significant difference between theindicators within the cluster

6 Mathematical Problems in Engineering

Table 2 Indicators and standardized values

Serialnumber

(a)Criteria layer

(b)Indicator name

(c)Indicator type (1) sdot sdot sdot (860)

1Internal financial factors

The cash ratio of main business income Positive 0000 0142sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot35 The rate of capital accumulation Positive 0496 049836

Nonfinancial factors withinthe enterprise

Identification level of new product Qualitative 0000 0000sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot62 The range of product sales Qualitative 1000 050063

External macroenvironmental factors

Industry sentiment indicator Positive 0695 0656sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot68 The growth rate of GDP Positive 0356 035669 The true credit status of micro enterprise samples 1 sdot sdot sdot 0

H1 there is significant difference between the indica-tors within the clusterThe significance level is set to 001When sig gt 001 accept H0 so these indicators canbe clustered into a clusterWhen siglt 001 refuseH0 so these indicators cannotbe clustered into a cluster

(4) The Calculation of 119882 Value Set 119882119895 as the 119882 value ofthe 119895th indicator 119899 as total number of enterprise samples

1198990 as total number of nondefault enterprise samples 1198850119894119895 asthe absolute value of the difference between the 119895th indicatorof the 119894th nondefault enterprise and the mean value of the119895th indicator of all nondefault enterprises 1198851119894119895 as the absolutevalue of the difference between the 119895th indicator of the 119894thdefault enterprise and the mean value of the 119895th indicatorof all default enterprises and 1198991 as total number of defaultenterprises Then the 119895th indicatorrsquos119882 value119882119895 is given asfollows

119882119895

=(119899 minus 2) (1198990 ((sum1198990119894=1 1198850119894119895) 1198990 minus ((sum1198990119894=1 1198850119894119895) 1198990 + (sum1198991119894=1 1198851119894119895) 1198991) 2)

2) + (119899 minus 2) (1198991 ((sum1198991119894=1 1198851119894119895) 1198991 minus ((sum1198990119894=1 1198850119894119895) 1198990 + (sum1198991119894=1 1198851119894119895) 1198991) 2)2)

sum1198990119894=1 (1198850119894119895 minus (sum1198990119894=1 1198850119894119895) 1198990)2 + sum1198991119894=1 (1198851119894119895 minus (sum1198991119894=1 1198851119894119895) 1198991)

2

(7)

34 The Validity Test of Credit Indicators The ROC curveis a comprehensive indicator that reflects the sensitivity andspecificity of continuous variables the vertical coordinate ofROC curve sensitivity indicates the ratio at which the defaultsamples are judged to be correct the specificity indicates theratio at which nondefault samples are judged to be correctso the horizontal coordinate of ROC curve 1 minus specificityindicates the rate at which nondefault samples are judged tobe incorrect When the horizontal coordinate is constant thelarger the vertical coordinate is the higher the proportionof default samples judged to be correct is the larger theAUC (area under ROC curve) of the corresponding creditindicator is the stronger the ability of credit identificationof the indicator against the default samples is and the moreeffective the indicator is Based on the ROC curve this papertests the validity of the screened indicators the criteria forindicator to define whether it has the accuracy to identify thecredit status of enterprises samples are as follows when 0 leAUC lt 05 it does not have the accuracy of identificationwhen 05 le AUC lt 1 it has the accuracy of identification

4 The Application of the Model

41 Data and Standardization of Indicators We apply microenterprise credit data from 2010 to 2015 from a commercialbank in Inner Mongolia western China The 68 indicatorsremaining after the initial selection are shown in column (b)numbered from 1 to 68 in Table 2 the standardized valueof each indicator is obtained by instituting the raw dataand materials of indicators into Formulas (1)ndash(3a) (3b) and(3c) and Table 1 according to the type of indicators amongwhich the standardization values of qualitative indicators aredetermined by the professionals of universities and commu-nity The micro enterprisesrsquo true credit status (0 representingnondefault and 1 representing default) and other relatedinformation are shown in Table 2

42 The First Round of Indicator Selection Based on SVM

(1) Classification of Micro Enterprise Samples The 68 indica-tors of micro enterprises remaining after the initial selection

Mathematical Problems in Engineering 7

Table 3 The division of micro enterprise samples

Nondefault samples Default samples TotalTraining set 664 24 688Test set 166 6 172Total 830 30 860

Table 4 The results of first round of indicator selection based on SVM

Serialnumber

(a)Criteria layer

(b)Indicator name

(1)119860119895119860 ()

(2)119889119895 ()

(3)Selection results

0 mdash All indicators 8303 mdash mdash1

Internal financial factorsQuick ratio 9137 837 Delete

sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot35 The ratio of EBITDA and total debt 8303 000 Delete36

Nonfinancial factors withinthe enterprise

The years of employment in relevant industry 7470 minus833 Retainsdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot62 Gender 8303 000 Delete63

External macroenvironmental factors

The growth rate of GDP 8303 000 Deletesdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot68 Pledge score 7470 minus833 Retain

for the first round are filtered using classification and predic-tion of SVM so as to pick out the indicators that can identifythe credit status of micro enterprises The division of microenterprise samples is shown in Table 3

(2) Determination of Optimal Parameters It is necessary todetermine the penalty coefficient 119888 and the Gaussian radialbasis function parameter 119892 by using SVMrsquos classification andprediction to calculate 1199101015840119894 in formula (4) and 1199101198951015840119894 after deletingthe 119895th indicator MATLAB software and LIBSVM toolboxare used to determine the penalty coefficient c and theGaussian radial basis function parameter g c is selected insteps of 05 between 2minus4 and 26 and 119892 is selected in stepsof 05 between 2minus5 and 25 the cross validation number isset to 3-fold the accuracy rate discretization display step isset to 09 then the program is run in MATLAB based onthe parameters that have been set and the training set andtest set that have been selected according to Table 2 columns(1)ndash(860) then we have that the optimal Gaussian radialbasis function parameter 119892 is 56569 and the optimal penaltycoefficient 119888 is 0125

(3) Calculation of theDegree of the Influence of Credit Indicatoron Evaluation Results The training model is established onMATLAB using the selected training set and the optimalparameters 119888 and 119892 the value of 1199101015840119894 in column (4) is obtainedby predicting the credit status of the enterprise in the test setDelete the 119895th indicator in the training set and test set at thesame time establish the training model in MATLAB basedon the optimal parameters 119888 and 119892 using the training set thathas removed the 119895th indicator the value of1199101198951015840119894 can be obtainedby predicting the credit status of the enterprise in the test setwhere the 119895th indicator has been deleted The values shownat Table 4 column (1) are obtained by substituting the two

credit status predictive values obtained above and the creditstatus true values shown at Table 2 69th row into formula(4) the degree of the influence of each credit indicator onevaluation results or 119889119895 shown at Table 4 column (2) isobtained by substituting the values shown at Table 4 column(1) into formula (5)

(4) The First Round of Credit Indicator Selection 119889119895 shown atTable 4 column (2) represents the degree of the influence ofthe 119895th credit indicator on evaluation results the selectionresults obtained according to the first round of indicatorselection criteria are shown in column (3) of Table 4 whereldquoDeleterdquo indicates that the corresponding credit indicator isdeleted and ldquoRetainrdquo indicates that the corresponding creditindicator is retained in the first round of indicator selectionbased on the SVM

After the first round of indicator selection we delete 25indicators and keep 43 indicators that can identify the creditstatus of micro enterprises

43 The Second Round of Indicator Selection Based on R-Type Clustering The second round of indicator selection forthe 43 indicators remaining after the first round of indicatorselection based on R-type clustering is to filter out theindicators with strong ability of credit qualification and deletethe redundant information indicators

(1) Determine the Number of Clusters in Each CriterionLayer Calculate the number of clusters in each criteria layeraccording to the fact that there will be 20 credit indicatorsretained in the final indicator model specifically there are43 indicators remaining after the first round of indicatorselection where there are 18 indicators remaining from thefirst criterion layer the internal financial factors and theywould be divided into (1843) times 20 asymp 8 clusters There are

8 Mathematical Problems in Engineering

20 indicators remaining from the second criterion layer theinternal nonfinancial factors keeping the indicator-collateralscore directly in order to correspond to 5C factor analysismodel and treat it alone as a cluster the remaining 19indicators are divided into (1943)times20 asymp 9 clustersThere are5 indicators remaining from the third criterion layer externalmacro environmental factors and they would be divided into(543) times 20 asymp 2 clusters

(2) Clustering the Indicators within the Criteria Layer Theindicators in the first criterion layer financial internal factorsare used as an example for clustering the other two criterionlayers do similar processing

Firstly make all the indicators marked ldquoRetainrdquo inTable 4 column (3) numbers 1ndash35 from the first criterialayer the internal financial factors into a cluster respectivelywhich is formed into 18 clusters then cluster any two clustersof indicators into a new cluster which clusters the indicatorswithin the first criteria layer into 17 clusters adding up to 119862218= 153 clustering schemes Substitute the standardized valuesof the indicators of each clustering scheme into formula (6) tocalculate each clustering schemersquos deviation squared sum theclustering scheme with the smallest deviation squared sumis chosen and then the first round of clustering is completedContinue clustering in this way until the number of clustersin the first criteria layer reaches the preset quantity 8 Theclustering results of all the indicators are shown in Table 4column (1)

(3) The Test of the Rationality of the Number of ClustersCluster the 43 credit indicators marked ldquoRetainrdquo shown inTable 4 column (3) within the criteria layer based on R-type hierarchical clustering according to the principle ofminimum sum of deviation squares and the clustering resultsare shown in Table 5 column (1) in order to avoid some ofthe indicators misinterpreted in the second round of R-typeclustering because of the significant difference between theevaluation indicators within the cluster in this paper use themethod of 119870-119882 test in SAS software for the clustered creditindicators to complete the significant test at a significancelevel of 001 (except for the cluster with only one indicator)and the 119870-119882 test sig values for each cluster are shown inTable 5 column (2) according to the criterion of test 20clusters of indicators are clustered as reasonable so there isno need to reset the number of clusters

(4) The Calculation of 119882 Value Substitute the standardizedvalues of the 43 indicators marked rdquoRetainrdquo in column (3) ofTable 4 into formula (7) to calculate the 119882 values of the 43indicators and they are shown in Table 5 column (3)

(5)The Second Round of Credit Indicator SelectionThe secondround of indicator selection is achieved by keeping theindicator of the largest 119882 value in each cluster accordingto the clustering results shown in Table 5 column (1) theresults of selection are shown in Table 5 column (4) in whichthe indicators marked rdquoDeleterdquo are deleted and the indicatorsmarked rdquoRetainrdquo are retained in the second round of indicatorselection based on R-type clustering

After the second round of indicator selection we delete23 indicators and keep 20 indicators that can significantlyidentify the credit status of enterprises and do not containredundant information indicators

44 Contrast with the 5C Model Comparatively analyze theconstructedmicro enterprisesrsquo credit indicator model and 5Cfactor analysis model the results are shown in column (1) ofTable 6 in which legal representativersquos loan default recordsand four other evaluation indicators reflect the moral qualityof the 5C elements the cash recovery rate of all assets and 11other evaluation indicators reflect the repayment ability of the5C elements the fixed rate of capital and 2 other evaluationindicators reflect the capital strength of the 5C elementsthe collateral score reflects the secured collateral of the 5Celements the industry sentiment indicator and the Engelcoefficient reflect the operating environment conditions ofthe 5C elements

45 The Validity Test of Credit Indicators and the Final Indica-tor System After the pretreatment of micro enterprisersquo creditindicator and two rounds of indicator selection the paperconstructs a credit indicator system of micro enterprises with20 credit indicators shown in column (b) of Table 5

For the standardized values of the 20 credit indicatorsshown in column (b) of Table 6 remaining after the finalselection use the ROC curve in SPSS software to test thevalidity of the indicators in the constructed micro enterprisecredit indicator system the ROC curve of each indicator isshown in Figure 4 the AUC of each indicator is shown incolumn (2) of Table 6 As shown in column (2) of Table 6the AUC values of the 20 credit indicators remaining after thefinal selection are all greater than the critical value of 05 asshown in column (3) of Table 5 the results of the validity testof the credit indicators show that all the indicators remainedafter the final selection has passed the validity test

5 Conclusions

(1) In this paper the micro enterprise credit indicator modelis constructed through the double combination selectionmodel based on SVM and R-type clustering where internalfinancial factors nonfinancial factors and external macroenvironmental factors are criteria layers and the cash recov-ery rate of all assets and 20 other credit indicators areindicators layers

(2) Compared with the 5C element model the resultsshow that in this paper all the credit indicators of themicro enterprise credit indicator model can be related to theelements in the 5C element model so the information of theconstructed micro enterprise credit indicator model coversall the elements of the 5C element model

(3)Theresults of the validity test of the credit indicators ofmicro enterprise based on ROC curve show that all the creditindicators of the micro enterprise credit indicator modelconstructed in this paper pass the validity test so all theindicators in the micro enterprise credit indicator model arevalid

Mathematical Problems in Engineering 9

Table5Th

esecon

droun

dof

indicatorsele

ctionbasedon

R-type

cluste

ring

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Clusters

(2)Sigvalueo

f119870-119882

test

(3) 119882119895

(4)Selection

results

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

The1stclu

ster

02698

25820

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

4Netcash

flowfro

mop

eratingactiv

ities

10259

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot17

Ther

atio

ofshareholdersrsquoequ

ityTh

e8th

cluste

r00535

1653

3Re

tain

18Th

eratio

ofassetsandliabilities

16464

Dele

te

19

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

The9

thclu

ster

02161

8227

Retain

20Th

erange

ofprod

uctsales

4726

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot36

Thec

reditsitu

ationof

enterpris

einthelastthree

years

The18thclu

ster

00357

48551

Retain

37Th

elevelof

enterpris

ersquosin

placer

egistered

capital

11510

Delete

39Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

The19thclu

ster

mdash3324

Retain

40En

gelcoefficient

The2

0thclu

ster

08550

81689

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

43Perc

apita

disposableincomeo

furban

resid

ents

80611

Dele

te

10 Mathematical Problems in Engineering

Table6Micro

enterpris

esrsquocreditevaluationindicatorsystem

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Con

trastw

ith5C

elem

ents

(2)AU

Cvalue

(3)Va

lidity

test

Quality

Ability

Capital

Guarantee

Environm

ent

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

radic0630

Pass

2Netcash

flowratio

forn

onperfo

rmingliabilities

operatingactiv

ities

radic0571

3Th

egrowth

rateof

retained

earnings

radic0678

4Ca

shratio

ofmainbu

sinessincom

eradic

0689

5Th

eratio

ofshareholdersrsquoequ

ityradic

0689

6Netprofi

tradic

0752

7Fixedrateof

capital

radic0745

8Th

eratio

ofcurrentliabilitiestoEB

ITradic

0710

9

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

radic0704

Pass

10Th

elevelof

brandedprod

ucts

radic0564

11Th

eyearsof

employmentinrelated

indu

stry

radic0769

12Legalrepresentativersquos

loan

defaultrecord

radic0733

13Th

eyearsto

hold

thep

ost

radic0748

14Living

cond

ition

radic0724

15Th

ecreditsitu

ationof

enterpris

esin

recent

three

years

radic0757

16Th

esitu

ationof

enterpris

ersquoslaw-abiding

operation

radic0703

17Th

elegaldisputes

ituationof

enterpris

eradic

0764

18Pledge

score

radic0725

19Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

radic0578

Pass

20En

gelcoefficient

radic0855

Mathematical Problems in Engineering 11

Sens

itivi

ty

10

08

06

04

02

00

ROC curve

1 minus Mpecificity00 02 04 06 08 10

Curve sourceCashRatioOfMainBusinessIncomeeRatioOfCurrentLiabilitiesToEBITCashRecoveryRateOfAllAssetseEquitRatioOfShareholdersFixedRateOfCapitalNetCashFlowRatioForNonperformaingLiabilitiesOperatingActivitiesNetProfit

eGrowthRateOfRetainedEarningseYearsOfEmploymentInRelatedIndustryeLevelOfBrandedProductsRatioOfeMoneyWithdrawnByeEnterpriserougheBank

LoanDefaultRecordOfLegalRresentative

LivingConditioneYearsToHoldePost

eCreditSituationOfEnterprisesInRecentreeYearseLegalDisputeSituationOfEnterpriseeLawAbidingOperationSituationOfEnterpriseIndustrySentimentIndex

PledgeScoreEngelCoefficient

Reference Line

Figure 4 Validity test of credit evaluation indicator of micro enterprise

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Thiswork is supported by the Key Project of National NaturalScience Foundation of China (71731003) China PostdoctoralScience Foundation (2015M582746XB) and Natural ScienceFoundation of InnerMongolia Autonomous Region of China(2016MS0714)

References

[1] L Zhanjiang ldquoEstablishment of Evaluation indicator System ofCredit State of Micro Enterprisesrdquo Technology Economics vol36 no 02 pp 109ndash116 2017

[2] C Guotai Z Yajing and S Baofeng ldquoThe Debt Rating ForSmall Enterprises Based on Probit Regressionrdquo Journal of Man-agement Sciences in China vol 19 pp 136ndash156 2016

[3] W Zhang J Lu and Y Zhang ldquoComprehensive EvaluationIndex System of Low Carbon Road Transport Based on FuzzyEvaluation Methodrdquo in Proceedings of the Green IntelligentTransportation System and Safety GITSS 2015 pp 659ndash668China

[4] CHonghai ldquoStudy of Evaluation Indicators Screening Based onInformation Substitutabilityrdquo Statistics amp Information Forumvol 31 no 10 pp 17ndash22 2016

[5] L Youxi ldquoA Summary of Comprehensive Evaluation MethodsrdquoMarket Modernization vol 02 pp 254-255 2016

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Page 5: Establishment of the Credit Indicator System of Micro ...downloads.hindawi.com/journals/mpe/2018/6390720.pdf · ResearchArticle Establishment of the Credit Indicator System of Micro

Mathematical Problems in Engineering 5

Table 1 The standardization rules for qualitative indicators

Serialnumber

(1)Indicator name

(2)Content

(3)Standardized values

1 Living condition

(1) Full purchase or mortgage 100(2) Relatives buildings 075

(3) Renting 050(4) Collective dormitory or shared dwelling 025

(5) Other or missing data 000sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot

22

Legalrepresentativersquoseducationalbackground

(1) Bachelor degree or above 100(2) Specialist 090

(3)High school or secondary education 070(4) Junior or primary education 040

(5) Other or missing data 000

Criterion 3 119889119895 lt 0 and is 119860119895 lt A indicating that the creditidentification ability of the remaining indicators after deletingthe 119895th indicator is weaker than the credit identificationability of all the indicators when the 119895th indicator is notdeleted the 119895th indicator can identify default enterprises andnondefault enterprises to be kept

(3) Calculation of Credit Identification Ability of Credit Indi-cator Set A as the credit identification ability of all theindicators for all micro enterprise samples 1198990 as total numberof nondefault enterprises 119910119894 as the true value of the defaultstatus of the 119894th enterprise (119910119894 = 0 the true value of the defaultstatus of the 119894th enterprise is nondefault 119910119894 = 1 the true valueof the default status of the 119894th enterprise is default) 1199101015840119894 as thepredictive value of the default status of the 119894th enterprise and1198991 as total number of default enterprises Then 119860 is given asfollows119860

=(11198990) (1198990 minus sum1198990119894=1

10038161003816100381610038161003816119910119894 minus 1199101015840119894

10038161003816100381610038161003816) + (11198991) (1198991 minus sum1198991119894=1

10038161003816100381610038161003816119910119894 minus 1199101015840119894

10038161003816100381610038161003816)2

(4)

In this paper 119860119895 is a formula obtained by replacing 1199101015840119894 inthe molecule of formula (4) with 1199101198951015840119894 (the predictive value ofcredit status of the 119894th enterprise calculated by the indicatorsremained after deleting the 119895th indicator) then obtain119860119895 (thecredit identification ability of the indicators after deleting the119895th indicator for all micro enterprises samples)

Then 119889119895 is given as follows

119889119895 = 119860119895 minus 119860 (5)

33 The Method of the Second Round of Indicator SelectionBased on R-Type Clustering

(1) The Criteria of Selection After the first round of indicatorselection clustering the indicators inside the same criterialayer according to the principle ofminimumdeviation sumofsquares using the method of hierarchical clustering through

the R-type clustering the validity of the number of clusters Lis verified by the 119870-119882 test when the total number of clustersreaches the preset value L if the 119870-119882 test is not passedthen reset the number of clusters if the 119870-119882 test is passedthen retain the indicator with the strongest ability of creditidentification and delete redundant information indicators byretaining the indicator of the largest119882 value in each clusterand deleting all the other indicators

(2) The Calculation of Deviation Sum of Squares Set 119878ℎ asthe sum of the squares of the ℎth criterion layer 119871ℎ as thenumber of clusters in the ℎth criterion layer119898119905 as the numberof indicators of the 119905th cluster of the ℎth criterion layer119883119905119895 asthe vector of the 119895th indicator in the 119905th cluster of the ℎthcriterion layer and119883119905 as the mean vector of all the indicatorsin the 119905th class of the ℎth criterion layer Then 119878ℎ is given asfollows

119878ℎ =119871ℎ

sum119905=1

119898119905

sum119895=1

(119883119905119895 minus 119883119905) (119883119905119895 minus 119883

119905)1015840

(6)

(3) 119870-119882 Test In this paper the nonparametric 119870-119882 test isused to test the rationality of the number of clusters thatis to test whether there is a significant difference betweenthe credit indicators of the same cluster If the 119870-119882 test isnot passed which indicates that there is significant differencebetween these indicators of the same cluster they cannot beclustered into a cluster in this case the number of clustersneeds to be reset if the 119870-119882 test is passed which indicatesthat there is no significant difference between these indicatorsof the same cluster they can be clustered into a cluster in thiscase retain the indicator with the strongest ability of creditidentification and delete information redundancy indicatorsby retaining the indicator of the largest 119882 value in eachcluster and deleting all the other indicators to complete thesecond round of indicators selection

Specifically the119870-119882 test is as followsH0 there is no significant difference between theindicators within the cluster

6 Mathematical Problems in Engineering

Table 2 Indicators and standardized values

Serialnumber

(a)Criteria layer

(b)Indicator name

(c)Indicator type (1) sdot sdot sdot (860)

1Internal financial factors

The cash ratio of main business income Positive 0000 0142sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot35 The rate of capital accumulation Positive 0496 049836

Nonfinancial factors withinthe enterprise

Identification level of new product Qualitative 0000 0000sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot62 The range of product sales Qualitative 1000 050063

External macroenvironmental factors

Industry sentiment indicator Positive 0695 0656sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot68 The growth rate of GDP Positive 0356 035669 The true credit status of micro enterprise samples 1 sdot sdot sdot 0

H1 there is significant difference between the indica-tors within the clusterThe significance level is set to 001When sig gt 001 accept H0 so these indicators canbe clustered into a clusterWhen siglt 001 refuseH0 so these indicators cannotbe clustered into a cluster

(4) The Calculation of 119882 Value Set 119882119895 as the 119882 value ofthe 119895th indicator 119899 as total number of enterprise samples

1198990 as total number of nondefault enterprise samples 1198850119894119895 asthe absolute value of the difference between the 119895th indicatorof the 119894th nondefault enterprise and the mean value of the119895th indicator of all nondefault enterprises 1198851119894119895 as the absolutevalue of the difference between the 119895th indicator of the 119894thdefault enterprise and the mean value of the 119895th indicatorof all default enterprises and 1198991 as total number of defaultenterprises Then the 119895th indicatorrsquos119882 value119882119895 is given asfollows

119882119895

=(119899 minus 2) (1198990 ((sum1198990119894=1 1198850119894119895) 1198990 minus ((sum1198990119894=1 1198850119894119895) 1198990 + (sum1198991119894=1 1198851119894119895) 1198991) 2)

2) + (119899 minus 2) (1198991 ((sum1198991119894=1 1198851119894119895) 1198991 minus ((sum1198990119894=1 1198850119894119895) 1198990 + (sum1198991119894=1 1198851119894119895) 1198991) 2)2)

sum1198990119894=1 (1198850119894119895 minus (sum1198990119894=1 1198850119894119895) 1198990)2 + sum1198991119894=1 (1198851119894119895 minus (sum1198991119894=1 1198851119894119895) 1198991)

2

(7)

34 The Validity Test of Credit Indicators The ROC curveis a comprehensive indicator that reflects the sensitivity andspecificity of continuous variables the vertical coordinate ofROC curve sensitivity indicates the ratio at which the defaultsamples are judged to be correct the specificity indicates theratio at which nondefault samples are judged to be correctso the horizontal coordinate of ROC curve 1 minus specificityindicates the rate at which nondefault samples are judged tobe incorrect When the horizontal coordinate is constant thelarger the vertical coordinate is the higher the proportionof default samples judged to be correct is the larger theAUC (area under ROC curve) of the corresponding creditindicator is the stronger the ability of credit identificationof the indicator against the default samples is and the moreeffective the indicator is Based on the ROC curve this papertests the validity of the screened indicators the criteria forindicator to define whether it has the accuracy to identify thecredit status of enterprises samples are as follows when 0 leAUC lt 05 it does not have the accuracy of identificationwhen 05 le AUC lt 1 it has the accuracy of identification

4 The Application of the Model

41 Data and Standardization of Indicators We apply microenterprise credit data from 2010 to 2015 from a commercialbank in Inner Mongolia western China The 68 indicatorsremaining after the initial selection are shown in column (b)numbered from 1 to 68 in Table 2 the standardized valueof each indicator is obtained by instituting the raw dataand materials of indicators into Formulas (1)ndash(3a) (3b) and(3c) and Table 1 according to the type of indicators amongwhich the standardization values of qualitative indicators aredetermined by the professionals of universities and commu-nity The micro enterprisesrsquo true credit status (0 representingnondefault and 1 representing default) and other relatedinformation are shown in Table 2

42 The First Round of Indicator Selection Based on SVM

(1) Classification of Micro Enterprise Samples The 68 indica-tors of micro enterprises remaining after the initial selection

Mathematical Problems in Engineering 7

Table 3 The division of micro enterprise samples

Nondefault samples Default samples TotalTraining set 664 24 688Test set 166 6 172Total 830 30 860

Table 4 The results of first round of indicator selection based on SVM

Serialnumber

(a)Criteria layer

(b)Indicator name

(1)119860119895119860 ()

(2)119889119895 ()

(3)Selection results

0 mdash All indicators 8303 mdash mdash1

Internal financial factorsQuick ratio 9137 837 Delete

sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot35 The ratio of EBITDA and total debt 8303 000 Delete36

Nonfinancial factors withinthe enterprise

The years of employment in relevant industry 7470 minus833 Retainsdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot62 Gender 8303 000 Delete63

External macroenvironmental factors

The growth rate of GDP 8303 000 Deletesdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot68 Pledge score 7470 minus833 Retain

for the first round are filtered using classification and predic-tion of SVM so as to pick out the indicators that can identifythe credit status of micro enterprises The division of microenterprise samples is shown in Table 3

(2) Determination of Optimal Parameters It is necessary todetermine the penalty coefficient 119888 and the Gaussian radialbasis function parameter 119892 by using SVMrsquos classification andprediction to calculate 1199101015840119894 in formula (4) and 1199101198951015840119894 after deletingthe 119895th indicator MATLAB software and LIBSVM toolboxare used to determine the penalty coefficient c and theGaussian radial basis function parameter g c is selected insteps of 05 between 2minus4 and 26 and 119892 is selected in stepsof 05 between 2minus5 and 25 the cross validation number isset to 3-fold the accuracy rate discretization display step isset to 09 then the program is run in MATLAB based onthe parameters that have been set and the training set andtest set that have been selected according to Table 2 columns(1)ndash(860) then we have that the optimal Gaussian radialbasis function parameter 119892 is 56569 and the optimal penaltycoefficient 119888 is 0125

(3) Calculation of theDegree of the Influence of Credit Indicatoron Evaluation Results The training model is established onMATLAB using the selected training set and the optimalparameters 119888 and 119892 the value of 1199101015840119894 in column (4) is obtainedby predicting the credit status of the enterprise in the test setDelete the 119895th indicator in the training set and test set at thesame time establish the training model in MATLAB basedon the optimal parameters 119888 and 119892 using the training set thathas removed the 119895th indicator the value of1199101198951015840119894 can be obtainedby predicting the credit status of the enterprise in the test setwhere the 119895th indicator has been deleted The values shownat Table 4 column (1) are obtained by substituting the two

credit status predictive values obtained above and the creditstatus true values shown at Table 2 69th row into formula(4) the degree of the influence of each credit indicator onevaluation results or 119889119895 shown at Table 4 column (2) isobtained by substituting the values shown at Table 4 column(1) into formula (5)

(4) The First Round of Credit Indicator Selection 119889119895 shown atTable 4 column (2) represents the degree of the influence ofthe 119895th credit indicator on evaluation results the selectionresults obtained according to the first round of indicatorselection criteria are shown in column (3) of Table 4 whereldquoDeleterdquo indicates that the corresponding credit indicator isdeleted and ldquoRetainrdquo indicates that the corresponding creditindicator is retained in the first round of indicator selectionbased on the SVM

After the first round of indicator selection we delete 25indicators and keep 43 indicators that can identify the creditstatus of micro enterprises

43 The Second Round of Indicator Selection Based on R-Type Clustering The second round of indicator selection forthe 43 indicators remaining after the first round of indicatorselection based on R-type clustering is to filter out theindicators with strong ability of credit qualification and deletethe redundant information indicators

(1) Determine the Number of Clusters in Each CriterionLayer Calculate the number of clusters in each criteria layeraccording to the fact that there will be 20 credit indicatorsretained in the final indicator model specifically there are43 indicators remaining after the first round of indicatorselection where there are 18 indicators remaining from thefirst criterion layer the internal financial factors and theywould be divided into (1843) times 20 asymp 8 clusters There are

8 Mathematical Problems in Engineering

20 indicators remaining from the second criterion layer theinternal nonfinancial factors keeping the indicator-collateralscore directly in order to correspond to 5C factor analysismodel and treat it alone as a cluster the remaining 19indicators are divided into (1943)times20 asymp 9 clustersThere are5 indicators remaining from the third criterion layer externalmacro environmental factors and they would be divided into(543) times 20 asymp 2 clusters

(2) Clustering the Indicators within the Criteria Layer Theindicators in the first criterion layer financial internal factorsare used as an example for clustering the other two criterionlayers do similar processing

Firstly make all the indicators marked ldquoRetainrdquo inTable 4 column (3) numbers 1ndash35 from the first criterialayer the internal financial factors into a cluster respectivelywhich is formed into 18 clusters then cluster any two clustersof indicators into a new cluster which clusters the indicatorswithin the first criteria layer into 17 clusters adding up to 119862218= 153 clustering schemes Substitute the standardized valuesof the indicators of each clustering scheme into formula (6) tocalculate each clustering schemersquos deviation squared sum theclustering scheme with the smallest deviation squared sumis chosen and then the first round of clustering is completedContinue clustering in this way until the number of clustersin the first criteria layer reaches the preset quantity 8 Theclustering results of all the indicators are shown in Table 4column (1)

(3) The Test of the Rationality of the Number of ClustersCluster the 43 credit indicators marked ldquoRetainrdquo shown inTable 4 column (3) within the criteria layer based on R-type hierarchical clustering according to the principle ofminimum sum of deviation squares and the clustering resultsare shown in Table 5 column (1) in order to avoid some ofthe indicators misinterpreted in the second round of R-typeclustering because of the significant difference between theevaluation indicators within the cluster in this paper use themethod of 119870-119882 test in SAS software for the clustered creditindicators to complete the significant test at a significancelevel of 001 (except for the cluster with only one indicator)and the 119870-119882 test sig values for each cluster are shown inTable 5 column (2) according to the criterion of test 20clusters of indicators are clustered as reasonable so there isno need to reset the number of clusters

(4) The Calculation of 119882 Value Substitute the standardizedvalues of the 43 indicators marked rdquoRetainrdquo in column (3) ofTable 4 into formula (7) to calculate the 119882 values of the 43indicators and they are shown in Table 5 column (3)

(5)The Second Round of Credit Indicator SelectionThe secondround of indicator selection is achieved by keeping theindicator of the largest 119882 value in each cluster accordingto the clustering results shown in Table 5 column (1) theresults of selection are shown in Table 5 column (4) in whichthe indicators marked rdquoDeleterdquo are deleted and the indicatorsmarked rdquoRetainrdquo are retained in the second round of indicatorselection based on R-type clustering

After the second round of indicator selection we delete23 indicators and keep 20 indicators that can significantlyidentify the credit status of enterprises and do not containredundant information indicators

44 Contrast with the 5C Model Comparatively analyze theconstructedmicro enterprisesrsquo credit indicator model and 5Cfactor analysis model the results are shown in column (1) ofTable 6 in which legal representativersquos loan default recordsand four other evaluation indicators reflect the moral qualityof the 5C elements the cash recovery rate of all assets and 11other evaluation indicators reflect the repayment ability of the5C elements the fixed rate of capital and 2 other evaluationindicators reflect the capital strength of the 5C elementsthe collateral score reflects the secured collateral of the 5Celements the industry sentiment indicator and the Engelcoefficient reflect the operating environment conditions ofthe 5C elements

45 The Validity Test of Credit Indicators and the Final Indica-tor System After the pretreatment of micro enterprisersquo creditindicator and two rounds of indicator selection the paperconstructs a credit indicator system of micro enterprises with20 credit indicators shown in column (b) of Table 5

For the standardized values of the 20 credit indicatorsshown in column (b) of Table 6 remaining after the finalselection use the ROC curve in SPSS software to test thevalidity of the indicators in the constructed micro enterprisecredit indicator system the ROC curve of each indicator isshown in Figure 4 the AUC of each indicator is shown incolumn (2) of Table 6 As shown in column (2) of Table 6the AUC values of the 20 credit indicators remaining after thefinal selection are all greater than the critical value of 05 asshown in column (3) of Table 5 the results of the validity testof the credit indicators show that all the indicators remainedafter the final selection has passed the validity test

5 Conclusions

(1) In this paper the micro enterprise credit indicator modelis constructed through the double combination selectionmodel based on SVM and R-type clustering where internalfinancial factors nonfinancial factors and external macroenvironmental factors are criteria layers and the cash recov-ery rate of all assets and 20 other credit indicators areindicators layers

(2) Compared with the 5C element model the resultsshow that in this paper all the credit indicators of themicro enterprise credit indicator model can be related to theelements in the 5C element model so the information of theconstructed micro enterprise credit indicator model coversall the elements of the 5C element model

(3)Theresults of the validity test of the credit indicators ofmicro enterprise based on ROC curve show that all the creditindicators of the micro enterprise credit indicator modelconstructed in this paper pass the validity test so all theindicators in the micro enterprise credit indicator model arevalid

Mathematical Problems in Engineering 9

Table5Th

esecon

droun

dof

indicatorsele

ctionbasedon

R-type

cluste

ring

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Clusters

(2)Sigvalueo

f119870-119882

test

(3) 119882119895

(4)Selection

results

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

The1stclu

ster

02698

25820

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

4Netcash

flowfro

mop

eratingactiv

ities

10259

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot17

Ther

atio

ofshareholdersrsquoequ

ityTh

e8th

cluste

r00535

1653

3Re

tain

18Th

eratio

ofassetsandliabilities

16464

Dele

te

19

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

The9

thclu

ster

02161

8227

Retain

20Th

erange

ofprod

uctsales

4726

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot36

Thec

reditsitu

ationof

enterpris

einthelastthree

years

The18thclu

ster

00357

48551

Retain

37Th

elevelof

enterpris

ersquosin

placer

egistered

capital

11510

Delete

39Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

The19thclu

ster

mdash3324

Retain

40En

gelcoefficient

The2

0thclu

ster

08550

81689

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

43Perc

apita

disposableincomeo

furban

resid

ents

80611

Dele

te

10 Mathematical Problems in Engineering

Table6Micro

enterpris

esrsquocreditevaluationindicatorsystem

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Con

trastw

ith5C

elem

ents

(2)AU

Cvalue

(3)Va

lidity

test

Quality

Ability

Capital

Guarantee

Environm

ent

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

radic0630

Pass

2Netcash

flowratio

forn

onperfo

rmingliabilities

operatingactiv

ities

radic0571

3Th

egrowth

rateof

retained

earnings

radic0678

4Ca

shratio

ofmainbu

sinessincom

eradic

0689

5Th

eratio

ofshareholdersrsquoequ

ityradic

0689

6Netprofi

tradic

0752

7Fixedrateof

capital

radic0745

8Th

eratio

ofcurrentliabilitiestoEB

ITradic

0710

9

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

radic0704

Pass

10Th

elevelof

brandedprod

ucts

radic0564

11Th

eyearsof

employmentinrelated

indu

stry

radic0769

12Legalrepresentativersquos

loan

defaultrecord

radic0733

13Th

eyearsto

hold

thep

ost

radic0748

14Living

cond

ition

radic0724

15Th

ecreditsitu

ationof

enterpris

esin

recent

three

years

radic0757

16Th

esitu

ationof

enterpris

ersquoslaw-abiding

operation

radic0703

17Th

elegaldisputes

ituationof

enterpris

eradic

0764

18Pledge

score

radic0725

19Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

radic0578

Pass

20En

gelcoefficient

radic0855

Mathematical Problems in Engineering 11

Sens

itivi

ty

10

08

06

04

02

00

ROC curve

1 minus Mpecificity00 02 04 06 08 10

Curve sourceCashRatioOfMainBusinessIncomeeRatioOfCurrentLiabilitiesToEBITCashRecoveryRateOfAllAssetseEquitRatioOfShareholdersFixedRateOfCapitalNetCashFlowRatioForNonperformaingLiabilitiesOperatingActivitiesNetProfit

eGrowthRateOfRetainedEarningseYearsOfEmploymentInRelatedIndustryeLevelOfBrandedProductsRatioOfeMoneyWithdrawnByeEnterpriserougheBank

LoanDefaultRecordOfLegalRresentative

LivingConditioneYearsToHoldePost

eCreditSituationOfEnterprisesInRecentreeYearseLegalDisputeSituationOfEnterpriseeLawAbidingOperationSituationOfEnterpriseIndustrySentimentIndex

PledgeScoreEngelCoefficient

Reference Line

Figure 4 Validity test of credit evaluation indicator of micro enterprise

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Thiswork is supported by the Key Project of National NaturalScience Foundation of China (71731003) China PostdoctoralScience Foundation (2015M582746XB) and Natural ScienceFoundation of InnerMongolia Autonomous Region of China(2016MS0714)

References

[1] L Zhanjiang ldquoEstablishment of Evaluation indicator System ofCredit State of Micro Enterprisesrdquo Technology Economics vol36 no 02 pp 109ndash116 2017

[2] C Guotai Z Yajing and S Baofeng ldquoThe Debt Rating ForSmall Enterprises Based on Probit Regressionrdquo Journal of Man-agement Sciences in China vol 19 pp 136ndash156 2016

[3] W Zhang J Lu and Y Zhang ldquoComprehensive EvaluationIndex System of Low Carbon Road Transport Based on FuzzyEvaluation Methodrdquo in Proceedings of the Green IntelligentTransportation System and Safety GITSS 2015 pp 659ndash668China

[4] CHonghai ldquoStudy of Evaluation Indicators Screening Based onInformation Substitutabilityrdquo Statistics amp Information Forumvol 31 no 10 pp 17ndash22 2016

[5] L Youxi ldquoA Summary of Comprehensive Evaluation MethodsrdquoMarket Modernization vol 02 pp 254-255 2016

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Complex AnalysisJournal of

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OptimizationJournal of

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Page 6: Establishment of the Credit Indicator System of Micro ...downloads.hindawi.com/journals/mpe/2018/6390720.pdf · ResearchArticle Establishment of the Credit Indicator System of Micro

6 Mathematical Problems in Engineering

Table 2 Indicators and standardized values

Serialnumber

(a)Criteria layer

(b)Indicator name

(c)Indicator type (1) sdot sdot sdot (860)

1Internal financial factors

The cash ratio of main business income Positive 0000 0142sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot35 The rate of capital accumulation Positive 0496 049836

Nonfinancial factors withinthe enterprise

Identification level of new product Qualitative 0000 0000sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot62 The range of product sales Qualitative 1000 050063

External macroenvironmental factors

Industry sentiment indicator Positive 0695 0656sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot68 The growth rate of GDP Positive 0356 035669 The true credit status of micro enterprise samples 1 sdot sdot sdot 0

H1 there is significant difference between the indica-tors within the clusterThe significance level is set to 001When sig gt 001 accept H0 so these indicators canbe clustered into a clusterWhen siglt 001 refuseH0 so these indicators cannotbe clustered into a cluster

(4) The Calculation of 119882 Value Set 119882119895 as the 119882 value ofthe 119895th indicator 119899 as total number of enterprise samples

1198990 as total number of nondefault enterprise samples 1198850119894119895 asthe absolute value of the difference between the 119895th indicatorof the 119894th nondefault enterprise and the mean value of the119895th indicator of all nondefault enterprises 1198851119894119895 as the absolutevalue of the difference between the 119895th indicator of the 119894thdefault enterprise and the mean value of the 119895th indicatorof all default enterprises and 1198991 as total number of defaultenterprises Then the 119895th indicatorrsquos119882 value119882119895 is given asfollows

119882119895

=(119899 minus 2) (1198990 ((sum1198990119894=1 1198850119894119895) 1198990 minus ((sum1198990119894=1 1198850119894119895) 1198990 + (sum1198991119894=1 1198851119894119895) 1198991) 2)

2) + (119899 minus 2) (1198991 ((sum1198991119894=1 1198851119894119895) 1198991 minus ((sum1198990119894=1 1198850119894119895) 1198990 + (sum1198991119894=1 1198851119894119895) 1198991) 2)2)

sum1198990119894=1 (1198850119894119895 minus (sum1198990119894=1 1198850119894119895) 1198990)2 + sum1198991119894=1 (1198851119894119895 minus (sum1198991119894=1 1198851119894119895) 1198991)

2

(7)

34 The Validity Test of Credit Indicators The ROC curveis a comprehensive indicator that reflects the sensitivity andspecificity of continuous variables the vertical coordinate ofROC curve sensitivity indicates the ratio at which the defaultsamples are judged to be correct the specificity indicates theratio at which nondefault samples are judged to be correctso the horizontal coordinate of ROC curve 1 minus specificityindicates the rate at which nondefault samples are judged tobe incorrect When the horizontal coordinate is constant thelarger the vertical coordinate is the higher the proportionof default samples judged to be correct is the larger theAUC (area under ROC curve) of the corresponding creditindicator is the stronger the ability of credit identificationof the indicator against the default samples is and the moreeffective the indicator is Based on the ROC curve this papertests the validity of the screened indicators the criteria forindicator to define whether it has the accuracy to identify thecredit status of enterprises samples are as follows when 0 leAUC lt 05 it does not have the accuracy of identificationwhen 05 le AUC lt 1 it has the accuracy of identification

4 The Application of the Model

41 Data and Standardization of Indicators We apply microenterprise credit data from 2010 to 2015 from a commercialbank in Inner Mongolia western China The 68 indicatorsremaining after the initial selection are shown in column (b)numbered from 1 to 68 in Table 2 the standardized valueof each indicator is obtained by instituting the raw dataand materials of indicators into Formulas (1)ndash(3a) (3b) and(3c) and Table 1 according to the type of indicators amongwhich the standardization values of qualitative indicators aredetermined by the professionals of universities and commu-nity The micro enterprisesrsquo true credit status (0 representingnondefault and 1 representing default) and other relatedinformation are shown in Table 2

42 The First Round of Indicator Selection Based on SVM

(1) Classification of Micro Enterprise Samples The 68 indica-tors of micro enterprises remaining after the initial selection

Mathematical Problems in Engineering 7

Table 3 The division of micro enterprise samples

Nondefault samples Default samples TotalTraining set 664 24 688Test set 166 6 172Total 830 30 860

Table 4 The results of first round of indicator selection based on SVM

Serialnumber

(a)Criteria layer

(b)Indicator name

(1)119860119895119860 ()

(2)119889119895 ()

(3)Selection results

0 mdash All indicators 8303 mdash mdash1

Internal financial factorsQuick ratio 9137 837 Delete

sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot35 The ratio of EBITDA and total debt 8303 000 Delete36

Nonfinancial factors withinthe enterprise

The years of employment in relevant industry 7470 minus833 Retainsdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot62 Gender 8303 000 Delete63

External macroenvironmental factors

The growth rate of GDP 8303 000 Deletesdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot68 Pledge score 7470 minus833 Retain

for the first round are filtered using classification and predic-tion of SVM so as to pick out the indicators that can identifythe credit status of micro enterprises The division of microenterprise samples is shown in Table 3

(2) Determination of Optimal Parameters It is necessary todetermine the penalty coefficient 119888 and the Gaussian radialbasis function parameter 119892 by using SVMrsquos classification andprediction to calculate 1199101015840119894 in formula (4) and 1199101198951015840119894 after deletingthe 119895th indicator MATLAB software and LIBSVM toolboxare used to determine the penalty coefficient c and theGaussian radial basis function parameter g c is selected insteps of 05 between 2minus4 and 26 and 119892 is selected in stepsof 05 between 2minus5 and 25 the cross validation number isset to 3-fold the accuracy rate discretization display step isset to 09 then the program is run in MATLAB based onthe parameters that have been set and the training set andtest set that have been selected according to Table 2 columns(1)ndash(860) then we have that the optimal Gaussian radialbasis function parameter 119892 is 56569 and the optimal penaltycoefficient 119888 is 0125

(3) Calculation of theDegree of the Influence of Credit Indicatoron Evaluation Results The training model is established onMATLAB using the selected training set and the optimalparameters 119888 and 119892 the value of 1199101015840119894 in column (4) is obtainedby predicting the credit status of the enterprise in the test setDelete the 119895th indicator in the training set and test set at thesame time establish the training model in MATLAB basedon the optimal parameters 119888 and 119892 using the training set thathas removed the 119895th indicator the value of1199101198951015840119894 can be obtainedby predicting the credit status of the enterprise in the test setwhere the 119895th indicator has been deleted The values shownat Table 4 column (1) are obtained by substituting the two

credit status predictive values obtained above and the creditstatus true values shown at Table 2 69th row into formula(4) the degree of the influence of each credit indicator onevaluation results or 119889119895 shown at Table 4 column (2) isobtained by substituting the values shown at Table 4 column(1) into formula (5)

(4) The First Round of Credit Indicator Selection 119889119895 shown atTable 4 column (2) represents the degree of the influence ofthe 119895th credit indicator on evaluation results the selectionresults obtained according to the first round of indicatorselection criteria are shown in column (3) of Table 4 whereldquoDeleterdquo indicates that the corresponding credit indicator isdeleted and ldquoRetainrdquo indicates that the corresponding creditindicator is retained in the first round of indicator selectionbased on the SVM

After the first round of indicator selection we delete 25indicators and keep 43 indicators that can identify the creditstatus of micro enterprises

43 The Second Round of Indicator Selection Based on R-Type Clustering The second round of indicator selection forthe 43 indicators remaining after the first round of indicatorselection based on R-type clustering is to filter out theindicators with strong ability of credit qualification and deletethe redundant information indicators

(1) Determine the Number of Clusters in Each CriterionLayer Calculate the number of clusters in each criteria layeraccording to the fact that there will be 20 credit indicatorsretained in the final indicator model specifically there are43 indicators remaining after the first round of indicatorselection where there are 18 indicators remaining from thefirst criterion layer the internal financial factors and theywould be divided into (1843) times 20 asymp 8 clusters There are

8 Mathematical Problems in Engineering

20 indicators remaining from the second criterion layer theinternal nonfinancial factors keeping the indicator-collateralscore directly in order to correspond to 5C factor analysismodel and treat it alone as a cluster the remaining 19indicators are divided into (1943)times20 asymp 9 clustersThere are5 indicators remaining from the third criterion layer externalmacro environmental factors and they would be divided into(543) times 20 asymp 2 clusters

(2) Clustering the Indicators within the Criteria Layer Theindicators in the first criterion layer financial internal factorsare used as an example for clustering the other two criterionlayers do similar processing

Firstly make all the indicators marked ldquoRetainrdquo inTable 4 column (3) numbers 1ndash35 from the first criterialayer the internal financial factors into a cluster respectivelywhich is formed into 18 clusters then cluster any two clustersof indicators into a new cluster which clusters the indicatorswithin the first criteria layer into 17 clusters adding up to 119862218= 153 clustering schemes Substitute the standardized valuesof the indicators of each clustering scheme into formula (6) tocalculate each clustering schemersquos deviation squared sum theclustering scheme with the smallest deviation squared sumis chosen and then the first round of clustering is completedContinue clustering in this way until the number of clustersin the first criteria layer reaches the preset quantity 8 Theclustering results of all the indicators are shown in Table 4column (1)

(3) The Test of the Rationality of the Number of ClustersCluster the 43 credit indicators marked ldquoRetainrdquo shown inTable 4 column (3) within the criteria layer based on R-type hierarchical clustering according to the principle ofminimum sum of deviation squares and the clustering resultsare shown in Table 5 column (1) in order to avoid some ofthe indicators misinterpreted in the second round of R-typeclustering because of the significant difference between theevaluation indicators within the cluster in this paper use themethod of 119870-119882 test in SAS software for the clustered creditindicators to complete the significant test at a significancelevel of 001 (except for the cluster with only one indicator)and the 119870-119882 test sig values for each cluster are shown inTable 5 column (2) according to the criterion of test 20clusters of indicators are clustered as reasonable so there isno need to reset the number of clusters

(4) The Calculation of 119882 Value Substitute the standardizedvalues of the 43 indicators marked rdquoRetainrdquo in column (3) ofTable 4 into formula (7) to calculate the 119882 values of the 43indicators and they are shown in Table 5 column (3)

(5)The Second Round of Credit Indicator SelectionThe secondround of indicator selection is achieved by keeping theindicator of the largest 119882 value in each cluster accordingto the clustering results shown in Table 5 column (1) theresults of selection are shown in Table 5 column (4) in whichthe indicators marked rdquoDeleterdquo are deleted and the indicatorsmarked rdquoRetainrdquo are retained in the second round of indicatorselection based on R-type clustering

After the second round of indicator selection we delete23 indicators and keep 20 indicators that can significantlyidentify the credit status of enterprises and do not containredundant information indicators

44 Contrast with the 5C Model Comparatively analyze theconstructedmicro enterprisesrsquo credit indicator model and 5Cfactor analysis model the results are shown in column (1) ofTable 6 in which legal representativersquos loan default recordsand four other evaluation indicators reflect the moral qualityof the 5C elements the cash recovery rate of all assets and 11other evaluation indicators reflect the repayment ability of the5C elements the fixed rate of capital and 2 other evaluationindicators reflect the capital strength of the 5C elementsthe collateral score reflects the secured collateral of the 5Celements the industry sentiment indicator and the Engelcoefficient reflect the operating environment conditions ofthe 5C elements

45 The Validity Test of Credit Indicators and the Final Indica-tor System After the pretreatment of micro enterprisersquo creditindicator and two rounds of indicator selection the paperconstructs a credit indicator system of micro enterprises with20 credit indicators shown in column (b) of Table 5

For the standardized values of the 20 credit indicatorsshown in column (b) of Table 6 remaining after the finalselection use the ROC curve in SPSS software to test thevalidity of the indicators in the constructed micro enterprisecredit indicator system the ROC curve of each indicator isshown in Figure 4 the AUC of each indicator is shown incolumn (2) of Table 6 As shown in column (2) of Table 6the AUC values of the 20 credit indicators remaining after thefinal selection are all greater than the critical value of 05 asshown in column (3) of Table 5 the results of the validity testof the credit indicators show that all the indicators remainedafter the final selection has passed the validity test

5 Conclusions

(1) In this paper the micro enterprise credit indicator modelis constructed through the double combination selectionmodel based on SVM and R-type clustering where internalfinancial factors nonfinancial factors and external macroenvironmental factors are criteria layers and the cash recov-ery rate of all assets and 20 other credit indicators areindicators layers

(2) Compared with the 5C element model the resultsshow that in this paper all the credit indicators of themicro enterprise credit indicator model can be related to theelements in the 5C element model so the information of theconstructed micro enterprise credit indicator model coversall the elements of the 5C element model

(3)Theresults of the validity test of the credit indicators ofmicro enterprise based on ROC curve show that all the creditindicators of the micro enterprise credit indicator modelconstructed in this paper pass the validity test so all theindicators in the micro enterprise credit indicator model arevalid

Mathematical Problems in Engineering 9

Table5Th

esecon

droun

dof

indicatorsele

ctionbasedon

R-type

cluste

ring

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Clusters

(2)Sigvalueo

f119870-119882

test

(3) 119882119895

(4)Selection

results

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

The1stclu

ster

02698

25820

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

4Netcash

flowfro

mop

eratingactiv

ities

10259

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot17

Ther

atio

ofshareholdersrsquoequ

ityTh

e8th

cluste

r00535

1653

3Re

tain

18Th

eratio

ofassetsandliabilities

16464

Dele

te

19

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

The9

thclu

ster

02161

8227

Retain

20Th

erange

ofprod

uctsales

4726

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot36

Thec

reditsitu

ationof

enterpris

einthelastthree

years

The18thclu

ster

00357

48551

Retain

37Th

elevelof

enterpris

ersquosin

placer

egistered

capital

11510

Delete

39Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

The19thclu

ster

mdash3324

Retain

40En

gelcoefficient

The2

0thclu

ster

08550

81689

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

43Perc

apita

disposableincomeo

furban

resid

ents

80611

Dele

te

10 Mathematical Problems in Engineering

Table6Micro

enterpris

esrsquocreditevaluationindicatorsystem

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Con

trastw

ith5C

elem

ents

(2)AU

Cvalue

(3)Va

lidity

test

Quality

Ability

Capital

Guarantee

Environm

ent

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

radic0630

Pass

2Netcash

flowratio

forn

onperfo

rmingliabilities

operatingactiv

ities

radic0571

3Th

egrowth

rateof

retained

earnings

radic0678

4Ca

shratio

ofmainbu

sinessincom

eradic

0689

5Th

eratio

ofshareholdersrsquoequ

ityradic

0689

6Netprofi

tradic

0752

7Fixedrateof

capital

radic0745

8Th

eratio

ofcurrentliabilitiestoEB

ITradic

0710

9

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

radic0704

Pass

10Th

elevelof

brandedprod

ucts

radic0564

11Th

eyearsof

employmentinrelated

indu

stry

radic0769

12Legalrepresentativersquos

loan

defaultrecord

radic0733

13Th

eyearsto

hold

thep

ost

radic0748

14Living

cond

ition

radic0724

15Th

ecreditsitu

ationof

enterpris

esin

recent

three

years

radic0757

16Th

esitu

ationof

enterpris

ersquoslaw-abiding

operation

radic0703

17Th

elegaldisputes

ituationof

enterpris

eradic

0764

18Pledge

score

radic0725

19Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

radic0578

Pass

20En

gelcoefficient

radic0855

Mathematical Problems in Engineering 11

Sens

itivi

ty

10

08

06

04

02

00

ROC curve

1 minus Mpecificity00 02 04 06 08 10

Curve sourceCashRatioOfMainBusinessIncomeeRatioOfCurrentLiabilitiesToEBITCashRecoveryRateOfAllAssetseEquitRatioOfShareholdersFixedRateOfCapitalNetCashFlowRatioForNonperformaingLiabilitiesOperatingActivitiesNetProfit

eGrowthRateOfRetainedEarningseYearsOfEmploymentInRelatedIndustryeLevelOfBrandedProductsRatioOfeMoneyWithdrawnByeEnterpriserougheBank

LoanDefaultRecordOfLegalRresentative

LivingConditioneYearsToHoldePost

eCreditSituationOfEnterprisesInRecentreeYearseLegalDisputeSituationOfEnterpriseeLawAbidingOperationSituationOfEnterpriseIndustrySentimentIndex

PledgeScoreEngelCoefficient

Reference Line

Figure 4 Validity test of credit evaluation indicator of micro enterprise

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Thiswork is supported by the Key Project of National NaturalScience Foundation of China (71731003) China PostdoctoralScience Foundation (2015M582746XB) and Natural ScienceFoundation of InnerMongolia Autonomous Region of China(2016MS0714)

References

[1] L Zhanjiang ldquoEstablishment of Evaluation indicator System ofCredit State of Micro Enterprisesrdquo Technology Economics vol36 no 02 pp 109ndash116 2017

[2] C Guotai Z Yajing and S Baofeng ldquoThe Debt Rating ForSmall Enterprises Based on Probit Regressionrdquo Journal of Man-agement Sciences in China vol 19 pp 136ndash156 2016

[3] W Zhang J Lu and Y Zhang ldquoComprehensive EvaluationIndex System of Low Carbon Road Transport Based on FuzzyEvaluation Methodrdquo in Proceedings of the Green IntelligentTransportation System and Safety GITSS 2015 pp 659ndash668China

[4] CHonghai ldquoStudy of Evaluation Indicators Screening Based onInformation Substitutabilityrdquo Statistics amp Information Forumvol 31 no 10 pp 17ndash22 2016

[5] L Youxi ldquoA Summary of Comprehensive Evaluation MethodsrdquoMarket Modernization vol 02 pp 254-255 2016

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Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

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Nature and SocietyHindawiwwwhindawicom Volume 2018

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Dierential EquationsInternational Journal of

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Page 7: Establishment of the Credit Indicator System of Micro ...downloads.hindawi.com/journals/mpe/2018/6390720.pdf · ResearchArticle Establishment of the Credit Indicator System of Micro

Mathematical Problems in Engineering 7

Table 3 The division of micro enterprise samples

Nondefault samples Default samples TotalTraining set 664 24 688Test set 166 6 172Total 830 30 860

Table 4 The results of first round of indicator selection based on SVM

Serialnumber

(a)Criteria layer

(b)Indicator name

(1)119860119895119860 ()

(2)119889119895 ()

(3)Selection results

0 mdash All indicators 8303 mdash mdash1

Internal financial factorsQuick ratio 9137 837 Delete

sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot35 The ratio of EBITDA and total debt 8303 000 Delete36

Nonfinancial factors withinthe enterprise

The years of employment in relevant industry 7470 minus833 Retainsdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot62 Gender 8303 000 Delete63

External macroenvironmental factors

The growth rate of GDP 8303 000 Deletesdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot68 Pledge score 7470 minus833 Retain

for the first round are filtered using classification and predic-tion of SVM so as to pick out the indicators that can identifythe credit status of micro enterprises The division of microenterprise samples is shown in Table 3

(2) Determination of Optimal Parameters It is necessary todetermine the penalty coefficient 119888 and the Gaussian radialbasis function parameter 119892 by using SVMrsquos classification andprediction to calculate 1199101015840119894 in formula (4) and 1199101198951015840119894 after deletingthe 119895th indicator MATLAB software and LIBSVM toolboxare used to determine the penalty coefficient c and theGaussian radial basis function parameter g c is selected insteps of 05 between 2minus4 and 26 and 119892 is selected in stepsof 05 between 2minus5 and 25 the cross validation number isset to 3-fold the accuracy rate discretization display step isset to 09 then the program is run in MATLAB based onthe parameters that have been set and the training set andtest set that have been selected according to Table 2 columns(1)ndash(860) then we have that the optimal Gaussian radialbasis function parameter 119892 is 56569 and the optimal penaltycoefficient 119888 is 0125

(3) Calculation of theDegree of the Influence of Credit Indicatoron Evaluation Results The training model is established onMATLAB using the selected training set and the optimalparameters 119888 and 119892 the value of 1199101015840119894 in column (4) is obtainedby predicting the credit status of the enterprise in the test setDelete the 119895th indicator in the training set and test set at thesame time establish the training model in MATLAB basedon the optimal parameters 119888 and 119892 using the training set thathas removed the 119895th indicator the value of1199101198951015840119894 can be obtainedby predicting the credit status of the enterprise in the test setwhere the 119895th indicator has been deleted The values shownat Table 4 column (1) are obtained by substituting the two

credit status predictive values obtained above and the creditstatus true values shown at Table 2 69th row into formula(4) the degree of the influence of each credit indicator onevaluation results or 119889119895 shown at Table 4 column (2) isobtained by substituting the values shown at Table 4 column(1) into formula (5)

(4) The First Round of Credit Indicator Selection 119889119895 shown atTable 4 column (2) represents the degree of the influence ofthe 119895th credit indicator on evaluation results the selectionresults obtained according to the first round of indicatorselection criteria are shown in column (3) of Table 4 whereldquoDeleterdquo indicates that the corresponding credit indicator isdeleted and ldquoRetainrdquo indicates that the corresponding creditindicator is retained in the first round of indicator selectionbased on the SVM

After the first round of indicator selection we delete 25indicators and keep 43 indicators that can identify the creditstatus of micro enterprises

43 The Second Round of Indicator Selection Based on R-Type Clustering The second round of indicator selection forthe 43 indicators remaining after the first round of indicatorselection based on R-type clustering is to filter out theindicators with strong ability of credit qualification and deletethe redundant information indicators

(1) Determine the Number of Clusters in Each CriterionLayer Calculate the number of clusters in each criteria layeraccording to the fact that there will be 20 credit indicatorsretained in the final indicator model specifically there are43 indicators remaining after the first round of indicatorselection where there are 18 indicators remaining from thefirst criterion layer the internal financial factors and theywould be divided into (1843) times 20 asymp 8 clusters There are

8 Mathematical Problems in Engineering

20 indicators remaining from the second criterion layer theinternal nonfinancial factors keeping the indicator-collateralscore directly in order to correspond to 5C factor analysismodel and treat it alone as a cluster the remaining 19indicators are divided into (1943)times20 asymp 9 clustersThere are5 indicators remaining from the third criterion layer externalmacro environmental factors and they would be divided into(543) times 20 asymp 2 clusters

(2) Clustering the Indicators within the Criteria Layer Theindicators in the first criterion layer financial internal factorsare used as an example for clustering the other two criterionlayers do similar processing

Firstly make all the indicators marked ldquoRetainrdquo inTable 4 column (3) numbers 1ndash35 from the first criterialayer the internal financial factors into a cluster respectivelywhich is formed into 18 clusters then cluster any two clustersof indicators into a new cluster which clusters the indicatorswithin the first criteria layer into 17 clusters adding up to 119862218= 153 clustering schemes Substitute the standardized valuesof the indicators of each clustering scheme into formula (6) tocalculate each clustering schemersquos deviation squared sum theclustering scheme with the smallest deviation squared sumis chosen and then the first round of clustering is completedContinue clustering in this way until the number of clustersin the first criteria layer reaches the preset quantity 8 Theclustering results of all the indicators are shown in Table 4column (1)

(3) The Test of the Rationality of the Number of ClustersCluster the 43 credit indicators marked ldquoRetainrdquo shown inTable 4 column (3) within the criteria layer based on R-type hierarchical clustering according to the principle ofminimum sum of deviation squares and the clustering resultsare shown in Table 5 column (1) in order to avoid some ofthe indicators misinterpreted in the second round of R-typeclustering because of the significant difference between theevaluation indicators within the cluster in this paper use themethod of 119870-119882 test in SAS software for the clustered creditindicators to complete the significant test at a significancelevel of 001 (except for the cluster with only one indicator)and the 119870-119882 test sig values for each cluster are shown inTable 5 column (2) according to the criterion of test 20clusters of indicators are clustered as reasonable so there isno need to reset the number of clusters

(4) The Calculation of 119882 Value Substitute the standardizedvalues of the 43 indicators marked rdquoRetainrdquo in column (3) ofTable 4 into formula (7) to calculate the 119882 values of the 43indicators and they are shown in Table 5 column (3)

(5)The Second Round of Credit Indicator SelectionThe secondround of indicator selection is achieved by keeping theindicator of the largest 119882 value in each cluster accordingto the clustering results shown in Table 5 column (1) theresults of selection are shown in Table 5 column (4) in whichthe indicators marked rdquoDeleterdquo are deleted and the indicatorsmarked rdquoRetainrdquo are retained in the second round of indicatorselection based on R-type clustering

After the second round of indicator selection we delete23 indicators and keep 20 indicators that can significantlyidentify the credit status of enterprises and do not containredundant information indicators

44 Contrast with the 5C Model Comparatively analyze theconstructedmicro enterprisesrsquo credit indicator model and 5Cfactor analysis model the results are shown in column (1) ofTable 6 in which legal representativersquos loan default recordsand four other evaluation indicators reflect the moral qualityof the 5C elements the cash recovery rate of all assets and 11other evaluation indicators reflect the repayment ability of the5C elements the fixed rate of capital and 2 other evaluationindicators reflect the capital strength of the 5C elementsthe collateral score reflects the secured collateral of the 5Celements the industry sentiment indicator and the Engelcoefficient reflect the operating environment conditions ofthe 5C elements

45 The Validity Test of Credit Indicators and the Final Indica-tor System After the pretreatment of micro enterprisersquo creditindicator and two rounds of indicator selection the paperconstructs a credit indicator system of micro enterprises with20 credit indicators shown in column (b) of Table 5

For the standardized values of the 20 credit indicatorsshown in column (b) of Table 6 remaining after the finalselection use the ROC curve in SPSS software to test thevalidity of the indicators in the constructed micro enterprisecredit indicator system the ROC curve of each indicator isshown in Figure 4 the AUC of each indicator is shown incolumn (2) of Table 6 As shown in column (2) of Table 6the AUC values of the 20 credit indicators remaining after thefinal selection are all greater than the critical value of 05 asshown in column (3) of Table 5 the results of the validity testof the credit indicators show that all the indicators remainedafter the final selection has passed the validity test

5 Conclusions

(1) In this paper the micro enterprise credit indicator modelis constructed through the double combination selectionmodel based on SVM and R-type clustering where internalfinancial factors nonfinancial factors and external macroenvironmental factors are criteria layers and the cash recov-ery rate of all assets and 20 other credit indicators areindicators layers

(2) Compared with the 5C element model the resultsshow that in this paper all the credit indicators of themicro enterprise credit indicator model can be related to theelements in the 5C element model so the information of theconstructed micro enterprise credit indicator model coversall the elements of the 5C element model

(3)Theresults of the validity test of the credit indicators ofmicro enterprise based on ROC curve show that all the creditindicators of the micro enterprise credit indicator modelconstructed in this paper pass the validity test so all theindicators in the micro enterprise credit indicator model arevalid

Mathematical Problems in Engineering 9

Table5Th

esecon

droun

dof

indicatorsele

ctionbasedon

R-type

cluste

ring

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Clusters

(2)Sigvalueo

f119870-119882

test

(3) 119882119895

(4)Selection

results

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

The1stclu

ster

02698

25820

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

4Netcash

flowfro

mop

eratingactiv

ities

10259

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot17

Ther

atio

ofshareholdersrsquoequ

ityTh

e8th

cluste

r00535

1653

3Re

tain

18Th

eratio

ofassetsandliabilities

16464

Dele

te

19

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

The9

thclu

ster

02161

8227

Retain

20Th

erange

ofprod

uctsales

4726

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot36

Thec

reditsitu

ationof

enterpris

einthelastthree

years

The18thclu

ster

00357

48551

Retain

37Th

elevelof

enterpris

ersquosin

placer

egistered

capital

11510

Delete

39Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

The19thclu

ster

mdash3324

Retain

40En

gelcoefficient

The2

0thclu

ster

08550

81689

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

43Perc

apita

disposableincomeo

furban

resid

ents

80611

Dele

te

10 Mathematical Problems in Engineering

Table6Micro

enterpris

esrsquocreditevaluationindicatorsystem

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Con

trastw

ith5C

elem

ents

(2)AU

Cvalue

(3)Va

lidity

test

Quality

Ability

Capital

Guarantee

Environm

ent

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

radic0630

Pass

2Netcash

flowratio

forn

onperfo

rmingliabilities

operatingactiv

ities

radic0571

3Th

egrowth

rateof

retained

earnings

radic0678

4Ca

shratio

ofmainbu

sinessincom

eradic

0689

5Th

eratio

ofshareholdersrsquoequ

ityradic

0689

6Netprofi

tradic

0752

7Fixedrateof

capital

radic0745

8Th

eratio

ofcurrentliabilitiestoEB

ITradic

0710

9

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

radic0704

Pass

10Th

elevelof

brandedprod

ucts

radic0564

11Th

eyearsof

employmentinrelated

indu

stry

radic0769

12Legalrepresentativersquos

loan

defaultrecord

radic0733

13Th

eyearsto

hold

thep

ost

radic0748

14Living

cond

ition

radic0724

15Th

ecreditsitu

ationof

enterpris

esin

recent

three

years

radic0757

16Th

esitu

ationof

enterpris

ersquoslaw-abiding

operation

radic0703

17Th

elegaldisputes

ituationof

enterpris

eradic

0764

18Pledge

score

radic0725

19Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

radic0578

Pass

20En

gelcoefficient

radic0855

Mathematical Problems in Engineering 11

Sens

itivi

ty

10

08

06

04

02

00

ROC curve

1 minus Mpecificity00 02 04 06 08 10

Curve sourceCashRatioOfMainBusinessIncomeeRatioOfCurrentLiabilitiesToEBITCashRecoveryRateOfAllAssetseEquitRatioOfShareholdersFixedRateOfCapitalNetCashFlowRatioForNonperformaingLiabilitiesOperatingActivitiesNetProfit

eGrowthRateOfRetainedEarningseYearsOfEmploymentInRelatedIndustryeLevelOfBrandedProductsRatioOfeMoneyWithdrawnByeEnterpriserougheBank

LoanDefaultRecordOfLegalRresentative

LivingConditioneYearsToHoldePost

eCreditSituationOfEnterprisesInRecentreeYearseLegalDisputeSituationOfEnterpriseeLawAbidingOperationSituationOfEnterpriseIndustrySentimentIndex

PledgeScoreEngelCoefficient

Reference Line

Figure 4 Validity test of credit evaluation indicator of micro enterprise

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Thiswork is supported by the Key Project of National NaturalScience Foundation of China (71731003) China PostdoctoralScience Foundation (2015M582746XB) and Natural ScienceFoundation of InnerMongolia Autonomous Region of China(2016MS0714)

References

[1] L Zhanjiang ldquoEstablishment of Evaluation indicator System ofCredit State of Micro Enterprisesrdquo Technology Economics vol36 no 02 pp 109ndash116 2017

[2] C Guotai Z Yajing and S Baofeng ldquoThe Debt Rating ForSmall Enterprises Based on Probit Regressionrdquo Journal of Man-agement Sciences in China vol 19 pp 136ndash156 2016

[3] W Zhang J Lu and Y Zhang ldquoComprehensive EvaluationIndex System of Low Carbon Road Transport Based on FuzzyEvaluation Methodrdquo in Proceedings of the Green IntelligentTransportation System and Safety GITSS 2015 pp 659ndash668China

[4] CHonghai ldquoStudy of Evaluation Indicators Screening Based onInformation Substitutabilityrdquo Statistics amp Information Forumvol 31 no 10 pp 17ndash22 2016

[5] L Youxi ldquoA Summary of Comprehensive Evaluation MethodsrdquoMarket Modernization vol 02 pp 254-255 2016

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Page 8: Establishment of the Credit Indicator System of Micro ...downloads.hindawi.com/journals/mpe/2018/6390720.pdf · ResearchArticle Establishment of the Credit Indicator System of Micro

8 Mathematical Problems in Engineering

20 indicators remaining from the second criterion layer theinternal nonfinancial factors keeping the indicator-collateralscore directly in order to correspond to 5C factor analysismodel and treat it alone as a cluster the remaining 19indicators are divided into (1943)times20 asymp 9 clustersThere are5 indicators remaining from the third criterion layer externalmacro environmental factors and they would be divided into(543) times 20 asymp 2 clusters

(2) Clustering the Indicators within the Criteria Layer Theindicators in the first criterion layer financial internal factorsare used as an example for clustering the other two criterionlayers do similar processing

Firstly make all the indicators marked ldquoRetainrdquo inTable 4 column (3) numbers 1ndash35 from the first criterialayer the internal financial factors into a cluster respectivelywhich is formed into 18 clusters then cluster any two clustersof indicators into a new cluster which clusters the indicatorswithin the first criteria layer into 17 clusters adding up to 119862218= 153 clustering schemes Substitute the standardized valuesof the indicators of each clustering scheme into formula (6) tocalculate each clustering schemersquos deviation squared sum theclustering scheme with the smallest deviation squared sumis chosen and then the first round of clustering is completedContinue clustering in this way until the number of clustersin the first criteria layer reaches the preset quantity 8 Theclustering results of all the indicators are shown in Table 4column (1)

(3) The Test of the Rationality of the Number of ClustersCluster the 43 credit indicators marked ldquoRetainrdquo shown inTable 4 column (3) within the criteria layer based on R-type hierarchical clustering according to the principle ofminimum sum of deviation squares and the clustering resultsare shown in Table 5 column (1) in order to avoid some ofthe indicators misinterpreted in the second round of R-typeclustering because of the significant difference between theevaluation indicators within the cluster in this paper use themethod of 119870-119882 test in SAS software for the clustered creditindicators to complete the significant test at a significancelevel of 001 (except for the cluster with only one indicator)and the 119870-119882 test sig values for each cluster are shown inTable 5 column (2) according to the criterion of test 20clusters of indicators are clustered as reasonable so there isno need to reset the number of clusters

(4) The Calculation of 119882 Value Substitute the standardizedvalues of the 43 indicators marked rdquoRetainrdquo in column (3) ofTable 4 into formula (7) to calculate the 119882 values of the 43indicators and they are shown in Table 5 column (3)

(5)The Second Round of Credit Indicator SelectionThe secondround of indicator selection is achieved by keeping theindicator of the largest 119882 value in each cluster accordingto the clustering results shown in Table 5 column (1) theresults of selection are shown in Table 5 column (4) in whichthe indicators marked rdquoDeleterdquo are deleted and the indicatorsmarked rdquoRetainrdquo are retained in the second round of indicatorselection based on R-type clustering

After the second round of indicator selection we delete23 indicators and keep 20 indicators that can significantlyidentify the credit status of enterprises and do not containredundant information indicators

44 Contrast with the 5C Model Comparatively analyze theconstructedmicro enterprisesrsquo credit indicator model and 5Cfactor analysis model the results are shown in column (1) ofTable 6 in which legal representativersquos loan default recordsand four other evaluation indicators reflect the moral qualityof the 5C elements the cash recovery rate of all assets and 11other evaluation indicators reflect the repayment ability of the5C elements the fixed rate of capital and 2 other evaluationindicators reflect the capital strength of the 5C elementsthe collateral score reflects the secured collateral of the 5Celements the industry sentiment indicator and the Engelcoefficient reflect the operating environment conditions ofthe 5C elements

45 The Validity Test of Credit Indicators and the Final Indica-tor System After the pretreatment of micro enterprisersquo creditindicator and two rounds of indicator selection the paperconstructs a credit indicator system of micro enterprises with20 credit indicators shown in column (b) of Table 5

For the standardized values of the 20 credit indicatorsshown in column (b) of Table 6 remaining after the finalselection use the ROC curve in SPSS software to test thevalidity of the indicators in the constructed micro enterprisecredit indicator system the ROC curve of each indicator isshown in Figure 4 the AUC of each indicator is shown incolumn (2) of Table 6 As shown in column (2) of Table 6the AUC values of the 20 credit indicators remaining after thefinal selection are all greater than the critical value of 05 asshown in column (3) of Table 5 the results of the validity testof the credit indicators show that all the indicators remainedafter the final selection has passed the validity test

5 Conclusions

(1) In this paper the micro enterprise credit indicator modelis constructed through the double combination selectionmodel based on SVM and R-type clustering where internalfinancial factors nonfinancial factors and external macroenvironmental factors are criteria layers and the cash recov-ery rate of all assets and 20 other credit indicators areindicators layers

(2) Compared with the 5C element model the resultsshow that in this paper all the credit indicators of themicro enterprise credit indicator model can be related to theelements in the 5C element model so the information of theconstructed micro enterprise credit indicator model coversall the elements of the 5C element model

(3)Theresults of the validity test of the credit indicators ofmicro enterprise based on ROC curve show that all the creditindicators of the micro enterprise credit indicator modelconstructed in this paper pass the validity test so all theindicators in the micro enterprise credit indicator model arevalid

Mathematical Problems in Engineering 9

Table5Th

esecon

droun

dof

indicatorsele

ctionbasedon

R-type

cluste

ring

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Clusters

(2)Sigvalueo

f119870-119882

test

(3) 119882119895

(4)Selection

results

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

The1stclu

ster

02698

25820

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

4Netcash

flowfro

mop

eratingactiv

ities

10259

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot17

Ther

atio

ofshareholdersrsquoequ

ityTh

e8th

cluste

r00535

1653

3Re

tain

18Th

eratio

ofassetsandliabilities

16464

Dele

te

19

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

The9

thclu

ster

02161

8227

Retain

20Th

erange

ofprod

uctsales

4726

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot36

Thec

reditsitu

ationof

enterpris

einthelastthree

years

The18thclu

ster

00357

48551

Retain

37Th

elevelof

enterpris

ersquosin

placer

egistered

capital

11510

Delete

39Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

The19thclu

ster

mdash3324

Retain

40En

gelcoefficient

The2

0thclu

ster

08550

81689

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

43Perc

apita

disposableincomeo

furban

resid

ents

80611

Dele

te

10 Mathematical Problems in Engineering

Table6Micro

enterpris

esrsquocreditevaluationindicatorsystem

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Con

trastw

ith5C

elem

ents

(2)AU

Cvalue

(3)Va

lidity

test

Quality

Ability

Capital

Guarantee

Environm

ent

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

radic0630

Pass

2Netcash

flowratio

forn

onperfo

rmingliabilities

operatingactiv

ities

radic0571

3Th

egrowth

rateof

retained

earnings

radic0678

4Ca

shratio

ofmainbu

sinessincom

eradic

0689

5Th

eratio

ofshareholdersrsquoequ

ityradic

0689

6Netprofi

tradic

0752

7Fixedrateof

capital

radic0745

8Th

eratio

ofcurrentliabilitiestoEB

ITradic

0710

9

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

radic0704

Pass

10Th

elevelof

brandedprod

ucts

radic0564

11Th

eyearsof

employmentinrelated

indu

stry

radic0769

12Legalrepresentativersquos

loan

defaultrecord

radic0733

13Th

eyearsto

hold

thep

ost

radic0748

14Living

cond

ition

radic0724

15Th

ecreditsitu

ationof

enterpris

esin

recent

three

years

radic0757

16Th

esitu

ationof

enterpris

ersquoslaw-abiding

operation

radic0703

17Th

elegaldisputes

ituationof

enterpris

eradic

0764

18Pledge

score

radic0725

19Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

radic0578

Pass

20En

gelcoefficient

radic0855

Mathematical Problems in Engineering 11

Sens

itivi

ty

10

08

06

04

02

00

ROC curve

1 minus Mpecificity00 02 04 06 08 10

Curve sourceCashRatioOfMainBusinessIncomeeRatioOfCurrentLiabilitiesToEBITCashRecoveryRateOfAllAssetseEquitRatioOfShareholdersFixedRateOfCapitalNetCashFlowRatioForNonperformaingLiabilitiesOperatingActivitiesNetProfit

eGrowthRateOfRetainedEarningseYearsOfEmploymentInRelatedIndustryeLevelOfBrandedProductsRatioOfeMoneyWithdrawnByeEnterpriserougheBank

LoanDefaultRecordOfLegalRresentative

LivingConditioneYearsToHoldePost

eCreditSituationOfEnterprisesInRecentreeYearseLegalDisputeSituationOfEnterpriseeLawAbidingOperationSituationOfEnterpriseIndustrySentimentIndex

PledgeScoreEngelCoefficient

Reference Line

Figure 4 Validity test of credit evaluation indicator of micro enterprise

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Thiswork is supported by the Key Project of National NaturalScience Foundation of China (71731003) China PostdoctoralScience Foundation (2015M582746XB) and Natural ScienceFoundation of InnerMongolia Autonomous Region of China(2016MS0714)

References

[1] L Zhanjiang ldquoEstablishment of Evaluation indicator System ofCredit State of Micro Enterprisesrdquo Technology Economics vol36 no 02 pp 109ndash116 2017

[2] C Guotai Z Yajing and S Baofeng ldquoThe Debt Rating ForSmall Enterprises Based on Probit Regressionrdquo Journal of Man-agement Sciences in China vol 19 pp 136ndash156 2016

[3] W Zhang J Lu and Y Zhang ldquoComprehensive EvaluationIndex System of Low Carbon Road Transport Based on FuzzyEvaluation Methodrdquo in Proceedings of the Green IntelligentTransportation System and Safety GITSS 2015 pp 659ndash668China

[4] CHonghai ldquoStudy of Evaluation Indicators Screening Based onInformation Substitutabilityrdquo Statistics amp Information Forumvol 31 no 10 pp 17ndash22 2016

[5] L Youxi ldquoA Summary of Comprehensive Evaluation MethodsrdquoMarket Modernization vol 02 pp 254-255 2016

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Page 9: Establishment of the Credit Indicator System of Micro ...downloads.hindawi.com/journals/mpe/2018/6390720.pdf · ResearchArticle Establishment of the Credit Indicator System of Micro

Mathematical Problems in Engineering 9

Table5Th

esecon

droun

dof

indicatorsele

ctionbasedon

R-type

cluste

ring

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Clusters

(2)Sigvalueo

f119870-119882

test

(3) 119882119895

(4)Selection

results

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

The1stclu

ster

02698

25820

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

4Netcash

flowfro

mop

eratingactiv

ities

10259

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot17

Ther

atio

ofshareholdersrsquoequ

ityTh

e8th

cluste

r00535

1653

3Re

tain

18Th

eratio

ofassetsandliabilities

16464

Dele

te

19

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

The9

thclu

ster

02161

8227

Retain

20Th

erange

ofprod

uctsales

4726

Dele

tesdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

sdotsdotsdot36

Thec

reditsitu

ationof

enterpris

einthelastthree

years

The18thclu

ster

00357

48551

Retain

37Th

elevelof

enterpris

ersquosin

placer

egistered

capital

11510

Delete

39Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

The19thclu

ster

mdash3324

Retain

40En

gelcoefficient

The2

0thclu

ster

08550

81689

Retain

sdotsdotsdotsdotsdotsdot

sdotsdotsdotsdotsdotsdot

43Perc

apita

disposableincomeo

furban

resid

ents

80611

Dele

te

10 Mathematical Problems in Engineering

Table6Micro

enterpris

esrsquocreditevaluationindicatorsystem

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Con

trastw

ith5C

elem

ents

(2)AU

Cvalue

(3)Va

lidity

test

Quality

Ability

Capital

Guarantee

Environm

ent

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

radic0630

Pass

2Netcash

flowratio

forn

onperfo

rmingliabilities

operatingactiv

ities

radic0571

3Th

egrowth

rateof

retained

earnings

radic0678

4Ca

shratio

ofmainbu

sinessincom

eradic

0689

5Th

eratio

ofshareholdersrsquoequ

ityradic

0689

6Netprofi

tradic

0752

7Fixedrateof

capital

radic0745

8Th

eratio

ofcurrentliabilitiestoEB

ITradic

0710

9

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

radic0704

Pass

10Th

elevelof

brandedprod

ucts

radic0564

11Th

eyearsof

employmentinrelated

indu

stry

radic0769

12Legalrepresentativersquos

loan

defaultrecord

radic0733

13Th

eyearsto

hold

thep

ost

radic0748

14Living

cond

ition

radic0724

15Th

ecreditsitu

ationof

enterpris

esin

recent

three

years

radic0757

16Th

esitu

ationof

enterpris

ersquoslaw-abiding

operation

radic0703

17Th

elegaldisputes

ituationof

enterpris

eradic

0764

18Pledge

score

radic0725

19Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

radic0578

Pass

20En

gelcoefficient

radic0855

Mathematical Problems in Engineering 11

Sens

itivi

ty

10

08

06

04

02

00

ROC curve

1 minus Mpecificity00 02 04 06 08 10

Curve sourceCashRatioOfMainBusinessIncomeeRatioOfCurrentLiabilitiesToEBITCashRecoveryRateOfAllAssetseEquitRatioOfShareholdersFixedRateOfCapitalNetCashFlowRatioForNonperformaingLiabilitiesOperatingActivitiesNetProfit

eGrowthRateOfRetainedEarningseYearsOfEmploymentInRelatedIndustryeLevelOfBrandedProductsRatioOfeMoneyWithdrawnByeEnterpriserougheBank

LoanDefaultRecordOfLegalRresentative

LivingConditioneYearsToHoldePost

eCreditSituationOfEnterprisesInRecentreeYearseLegalDisputeSituationOfEnterpriseeLawAbidingOperationSituationOfEnterpriseIndustrySentimentIndex

PledgeScoreEngelCoefficient

Reference Line

Figure 4 Validity test of credit evaluation indicator of micro enterprise

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Thiswork is supported by the Key Project of National NaturalScience Foundation of China (71731003) China PostdoctoralScience Foundation (2015M582746XB) and Natural ScienceFoundation of InnerMongolia Autonomous Region of China(2016MS0714)

References

[1] L Zhanjiang ldquoEstablishment of Evaluation indicator System ofCredit State of Micro Enterprisesrdquo Technology Economics vol36 no 02 pp 109ndash116 2017

[2] C Guotai Z Yajing and S Baofeng ldquoThe Debt Rating ForSmall Enterprises Based on Probit Regressionrdquo Journal of Man-agement Sciences in China vol 19 pp 136ndash156 2016

[3] W Zhang J Lu and Y Zhang ldquoComprehensive EvaluationIndex System of Low Carbon Road Transport Based on FuzzyEvaluation Methodrdquo in Proceedings of the Green IntelligentTransportation System and Safety GITSS 2015 pp 659ndash668China

[4] CHonghai ldquoStudy of Evaluation Indicators Screening Based onInformation Substitutabilityrdquo Statistics amp Information Forumvol 31 no 10 pp 17ndash22 2016

[5] L Youxi ldquoA Summary of Comprehensive Evaluation MethodsrdquoMarket Modernization vol 02 pp 254-255 2016

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Page 10: Establishment of the Credit Indicator System of Micro ...downloads.hindawi.com/journals/mpe/2018/6390720.pdf · ResearchArticle Establishment of the Credit Indicator System of Micro

10 Mathematical Problems in Engineering

Table6Micro

enterpris

esrsquocreditevaluationindicatorsystem

Seria

lnu

mber

(a)

Criteria

layer

(b)

Indicatorn

ame

(1)Con

trastw

ith5C

elem

ents

(2)AU

Cvalue

(3)Va

lidity

test

Quality

Ability

Capital

Guarantee

Environm

ent

1

Internalfin

ancialfactors

Cash

recovery

rateof

allassets

radic0630

Pass

2Netcash

flowratio

forn

onperfo

rmingliabilities

operatingactiv

ities

radic0571

3Th

egrowth

rateof

retained

earnings

radic0678

4Ca

shratio

ofmainbu

sinessincom

eradic

0689

5Th

eratio

ofshareholdersrsquoequ

ityradic

0689

6Netprofi

tradic

0752

7Fixedrateof

capital

radic0745

8Th

eratio

ofcurrentliabilitiestoEB

ITradic

0710

9

Non

financialfactorsw

ithin

thee

nterprise

Thep

ropo

rtionof

thetotalam

ount

ofmon

eywith

draw

nby

thee

nterprise

throug

htheb

ank

radic0704

Pass

10Th

elevelof

brandedprod

ucts

radic0564

11Th

eyearsof

employmentinrelated

indu

stry

radic0769

12Legalrepresentativersquos

loan

defaultrecord

radic0733

13Th

eyearsto

hold

thep

ost

radic0748

14Living

cond

ition

radic0724

15Th

ecreditsitu

ationof

enterpris

esin

recent

three

years

radic0757

16Th

esitu

ationof

enterpris

ersquoslaw-abiding

operation

radic0703

17Th

elegaldisputes

ituationof

enterpris

eradic

0764

18Pledge

score

radic0725

19Ex

ternalmacro

environm

entalfactors

Indu

stry

sentim

entind

icator

radic0578

Pass

20En

gelcoefficient

radic0855

Mathematical Problems in Engineering 11

Sens

itivi

ty

10

08

06

04

02

00

ROC curve

1 minus Mpecificity00 02 04 06 08 10

Curve sourceCashRatioOfMainBusinessIncomeeRatioOfCurrentLiabilitiesToEBITCashRecoveryRateOfAllAssetseEquitRatioOfShareholdersFixedRateOfCapitalNetCashFlowRatioForNonperformaingLiabilitiesOperatingActivitiesNetProfit

eGrowthRateOfRetainedEarningseYearsOfEmploymentInRelatedIndustryeLevelOfBrandedProductsRatioOfeMoneyWithdrawnByeEnterpriserougheBank

LoanDefaultRecordOfLegalRresentative

LivingConditioneYearsToHoldePost

eCreditSituationOfEnterprisesInRecentreeYearseLegalDisputeSituationOfEnterpriseeLawAbidingOperationSituationOfEnterpriseIndustrySentimentIndex

PledgeScoreEngelCoefficient

Reference Line

Figure 4 Validity test of credit evaluation indicator of micro enterprise

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Thiswork is supported by the Key Project of National NaturalScience Foundation of China (71731003) China PostdoctoralScience Foundation (2015M582746XB) and Natural ScienceFoundation of InnerMongolia Autonomous Region of China(2016MS0714)

References

[1] L Zhanjiang ldquoEstablishment of Evaluation indicator System ofCredit State of Micro Enterprisesrdquo Technology Economics vol36 no 02 pp 109ndash116 2017

[2] C Guotai Z Yajing and S Baofeng ldquoThe Debt Rating ForSmall Enterprises Based on Probit Regressionrdquo Journal of Man-agement Sciences in China vol 19 pp 136ndash156 2016

[3] W Zhang J Lu and Y Zhang ldquoComprehensive EvaluationIndex System of Low Carbon Road Transport Based on FuzzyEvaluation Methodrdquo in Proceedings of the Green IntelligentTransportation System and Safety GITSS 2015 pp 659ndash668China

[4] CHonghai ldquoStudy of Evaluation Indicators Screening Based onInformation Substitutabilityrdquo Statistics amp Information Forumvol 31 no 10 pp 17ndash22 2016

[5] L Youxi ldquoA Summary of Comprehensive Evaluation MethodsrdquoMarket Modernization vol 02 pp 254-255 2016

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Page 11: Establishment of the Credit Indicator System of Micro ...downloads.hindawi.com/journals/mpe/2018/6390720.pdf · ResearchArticle Establishment of the Credit Indicator System of Micro

Mathematical Problems in Engineering 11

Sens

itivi

ty

10

08

06

04

02

00

ROC curve

1 minus Mpecificity00 02 04 06 08 10

Curve sourceCashRatioOfMainBusinessIncomeeRatioOfCurrentLiabilitiesToEBITCashRecoveryRateOfAllAssetseEquitRatioOfShareholdersFixedRateOfCapitalNetCashFlowRatioForNonperformaingLiabilitiesOperatingActivitiesNetProfit

eGrowthRateOfRetainedEarningseYearsOfEmploymentInRelatedIndustryeLevelOfBrandedProductsRatioOfeMoneyWithdrawnByeEnterpriserougheBank

LoanDefaultRecordOfLegalRresentative

LivingConditioneYearsToHoldePost

eCreditSituationOfEnterprisesInRecentreeYearseLegalDisputeSituationOfEnterpriseeLawAbidingOperationSituationOfEnterpriseIndustrySentimentIndex

PledgeScoreEngelCoefficient

Reference Line

Figure 4 Validity test of credit evaluation indicator of micro enterprise

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Thiswork is supported by the Key Project of National NaturalScience Foundation of China (71731003) China PostdoctoralScience Foundation (2015M582746XB) and Natural ScienceFoundation of InnerMongolia Autonomous Region of China(2016MS0714)

References

[1] L Zhanjiang ldquoEstablishment of Evaluation indicator System ofCredit State of Micro Enterprisesrdquo Technology Economics vol36 no 02 pp 109ndash116 2017

[2] C Guotai Z Yajing and S Baofeng ldquoThe Debt Rating ForSmall Enterprises Based on Probit Regressionrdquo Journal of Man-agement Sciences in China vol 19 pp 136ndash156 2016

[3] W Zhang J Lu and Y Zhang ldquoComprehensive EvaluationIndex System of Low Carbon Road Transport Based on FuzzyEvaluation Methodrdquo in Proceedings of the Green IntelligentTransportation System and Safety GITSS 2015 pp 659ndash668China

[4] CHonghai ldquoStudy of Evaluation Indicators Screening Based onInformation Substitutabilityrdquo Statistics amp Information Forumvol 31 no 10 pp 17ndash22 2016

[5] L Youxi ldquoA Summary of Comprehensive Evaluation MethodsrdquoMarket Modernization vol 02 pp 254-255 2016

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Page 12: Establishment of the Credit Indicator System of Micro ...downloads.hindawi.com/journals/mpe/2018/6390720.pdf · ResearchArticle Establishment of the Credit Indicator System of Micro

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom