Analysis of the Mass Appraisal Model - Real Estate … of the Mass Appraisal Model ... The paper begins with a review of some papers using neural network models in property valuation

Using Artificial Neural Network in Kaohsiung City 1

Analysis of the Mass Appraisal Model

Using Artificial Neural Network in Kaohsiung City

by Pi-ying Lai, Associate Professor, National Pingtung Institute of Commerce (Taiwan)

Introduction

Multiple regression models are predominantly used in housing price model and forecasting. One problem

with the regression method is that it relies on functional assumptions to ascribe a form to fit the

relationships of the variables. The artificial neural network (ANN) technique is a method designed to

capture functional forms automatically, allowing hidden nonlinear relationships between the modeling

variables to be uncovered. Use of the ANN technique has increased rapidly in the past few years, especially

in the information area, and its performance has been outstanding. The study of artificial neural networks is

a sub-field of computer science concerned with the use of computers in tasks that are normally considered

to require knowledge, perception, reasoning, learning, understanding and similar cognitive abilities

(Gevarter,1985) ANNs, which require high-speed computation, an understanding of tolerance, and

nonlinear processing ability, have been applied to property price forecasting in recent years.

This paper applies ANN technology to real estate appraisal in Kaohsiung City market. The authors have

attempted to develop a predictive model of the housing price using back-propagation in an artificial neural

network. The so-called back-propagation (BP) model has been the most popular and most widely

implemented of all the neural network paradigms. The BP is the multi-layer feed-forward neural networks

which consist of a series of simple interconnected neurons, or nodes, between input and output vectors. The

nodes are connected by weights and outputs signals, which are functions of the sum of the inputs to the

node modified by an activation function. The output of a node is scaled by the connecting weight and fed

forward to be an input to the nodes in the next layer of network (Ge, et al., 2001). It is assumed to be a fully

connected feed-forward network, which means activation travels in a direction from the input layer to the

output layer, and the units in one layer are connected to every other unit in the next layer up (Callan, 1999).

Recurrent connection of back propagation is an extension of the BP model in which the network combines

feedback and feed-forward mechanisms. This means that there is a single time-step delay through the

network, with the output feeding back to the neurons at the same time as external inputs (Chester, 1993).

We will investigate several aspects of the use of neural networks as a tool for predicting residential

property values. The paper begins with a review of some papers using neural network models in property

valuation. Then, housing prices in Kaohsiung’s real estate market are analyzed using a neural network

model and a multiple regression model. Finally, the results of the analysis are presented along with some

concluding remarks.


Literature Review

Most housing price forecasting models have used multiple regression analysis (MRA) methodologies

(Reichert, 1990; Ho & Ganesan, 1998). The problem with this method is that it has involves human

judgment because it relies on functional assumptions to ascribe a form to fit the relationships of the

variables. The application of multiple regression to real estate appraisal has often produced serious

problems primarily because of multicolinearity issues in the independent variables and the inclusion of

“outlier” properties in the sample. It is difficult to map multi-attribute nonlinear relationships using

regression analysis, which makes multiple regression an inadequate model for a market that requires

precise and fast responses (Brunson et al., 1994; Do and Grudnitski, 1992). ANNs could overcome these

problems because they have the ability to learn by themselves, to generalize solutions, and to respond

adequately to highly correlated, incomplete, or previously unknown data (Shaw, 1992).

Property appraisals are often required for asset valuation, property tax and/or insurance estimations, sales

transactions, and land planning. The sales comparison approach is widely considered the most appropriate

approach for valuing residential real estate. Traditionally, the sales comparison method has been used in the

sales comparison approach to justify the property value. More recently, hedonic pricing models have also

been used to identify the real estate price.

Tay and Ho (1991) have used the BP model in estimating sale prices of apartments and compared this

method with a traditional multiple regression analysis (MRA) model. It is important to note that the Do and

Grudnitski (1992) neural network model resulted in almost twice as many predicted values within 5% of

the actual sale price than the regression model had predicted—i.e., 40% vs. 20% on a test sample of 105

houses. They concluded that the neural network model performs better than a multiple regression model for

estimating the value of U.S. residential property. Eight attributes were used as independent variables (age,

number of bedrooms, number of bathrooms, total square footage, number of garages, number of fireplaces,

number of stories, and lot size) and the selling price was used as the dependent variable. Their neural

network model was formed with three nodes in the hidden layer. W.J.McCluskey, K. Dyson, S. Anand, and

D. McFall (1997) also found that neural networks provide superior predicative ability in comparison to the

multiple regression in Northern Ireland. Results of their research are summarized in Table 1 (p. 3).

Evans et al. (1991) tested neural networks for accuracy in valuation when estimating residential property

prices in England and Wales. They investigated the effects on the average prediction error when outliers in

both the training data and the test data were removed. They concluded that when outliers are removed from

the data sets, neural network models work well to value property. The average absolute error for their

neural network models ranged between 5% and 7%.

Not all studies have reported successful or favorable results from the use of neural networks. Allen and

Zumwalt (1994) review a number of these studies and present an example of what can occur when different

neural network models are used for predicting stock price movements. They conclude that optimal neural

network models depend upon the specific data sets and time periods involved. In addition, they found that

the same data combined with different model settings (e.g., model tolerance, number of hidden nodes,

number of hidden layers,) can produce opposite results. Thus, they strongly recommend caution during the

development and use of neural network models in finance-related fields.


Table 1. Summary of Literature Results

Authors Sample Time/Country Sample Results (MAPE)

Do & Grudnitsk 1992/U.S. 105 residential

properties

1. ANN (6.9%)

2. MRA (11.3%)

Tay & Ho 1997 1991/Singapore Training Sample 833

Test Sample 222

Total 1055

1. ANN (3.9%)

2. MRA (7.5%)

Evans 1992/England & Wales 34 ANN1 3.48%

ANN2 5.03%

McCluskey 1997/Norehern Irland Training Sample 378

Test Sample 138

Total 416

1992-1994

ANN1 15. 7%

ANN2 7.75%

McGreal, Adair,

McBurney &

Patterson 1998

1992-1993/England 1026 ANN 10%

ANN 15%

Lenk at al. 1997/ ANN 15%

Worzala (1995) 1993-1994/US Training ample 217

Test Sample 71

Total 288

ANN 13.2%

Borst 1992 1992/US Training Sample 137

Test Sample 43

Total 180

ANN1 8.7%

ANN2 12.4%

Din, Hoesli & Bender

(2001)

1978-1992/Switzerland 285 ANN1 11%

ANN2 15%

Runeson, Lam, Ge 1981-2001 Training Sample 54 Forecasting

Runeson, Lam Hong Kong Test Sample 17

Forecast 17

Total 88

Error (26%, 59%,61%)

Note: ANN means artificial neural network, MRA means multiple regression analysis


Methodology

Data

This research is based on statistics on housing price obtained from the land administration bureau in

Kaohsiung City. Table 2 defines the variables used in the model.

Table 2. Variables Description

Variables

Priori

hypothesis Definition Units

LOCATION _ The administration district, 1 if the

house is located in Yancheng

District ,Gushan District , Sanmin

District ,Sinsing District ,Cianjin

District,Lingya District , Cianjhen

District, 0 if is located in Zuoying

District, Nanzih District, Cijin

District ,Siaogang District

Dummy

variables

ROADW _ Road width Meters

ROADS _ The location of Land, 1 if the land is

located in Corner lot, near street, not

near street lo, 0 if the land is located

in the lot of over lot line.

Dummy

variables

TYPE _ Type of house, 1 if the house is

single house & apartment 0

otherwise

Dummy

variables

STRUCT _ Structure material of house, 1 if the

material is RC, SRC, 0 if material is

bricks

Dummy

variables

AGE _ Age of the house years

TOTFLOR _ Total floor of the house floors

ZONING _ Land zoning, 1 if the land zoning is

commercial, 0 residential

Dummy

variables

BUILAREA _ Building floor area Square meters


Hedonic Price Model

The hedonic model involves regressing the property attributes transferred against those attributes of a house

hypothesized to be determinants of the transaction price in Kaohsiung City. Attributes hypothesized to

contribute to the price of the house include the location (the administration district), road width (in meters),

the location of land (near street situation), type of house, structural material of house, house age (in years),

total floors of the house (in floors), land zoning, and building floor area (in square meters). Implicitly, the

model for hedonic price function is specified as:

Figure 1. Geographical Distributition of 2,471 real estate transactition cases in Kaohsiung City

Artificial Neural Network Model

A neural network system is an artificial intelligence model that replicates the human brain’s learning

process. The brain’s neurons are the basic processing units that receive signs from and send signals to many

nervous system channels throughout the human body. When the body senses an input experience, the

nervous system carries many messages describing the input to the brain. The brain’s neurons interpret the

information form these input signals by passing the information through synapses that combine and

transform the data. A response is ultimately created when the information processing is complete. Through

repetition of stimuli and feedback of responses, the brain learns the optimal processing and response to the

stimuli. The brain’s actual leaning path is still somewhat of a chemical mystery; what is known is that

learning does occur and reoccur through the repetition of the input stimuli and the output response.


Artificial neural networks were developed utilizing this “black box” concept. Just as a human brain learns

with repetition of similar stimuli, a neural network trains itself with historical pairs of input and output data.

Neural networks usually operate without an a priori theory that guides or restricts the relationship between

the inputs and the outputs. The ultimate accuracy of the predicted output response, rather than the

description of the specific path or relationship between the inputs and the output response, is the goal of the

model. The typical topology of three-layer, recurrent back-propagation is illustrated in Figure 2.

Figure 2 shows the three layers of nodes: the input layer, the hidden layer, and the output layer. The input

layer contains data from the measures of explanatory or independent variables. The data is passed through

the nodes of the hidden layers to the output layer, which represents the dependent variables. A nonlinear

transfer function assigns weights to the information as it passes through the hidden layer nodes, mimicking

the transformation of information as it passes through the brain’s synapses. The goal of the artificial neural

network model is to show the relationship that really exists between the input, independent variables and

the output, or dependent, variables.

Figure 2. Processing Element of Artificial Neuron

Performance of Model

The method of error correction used in the model is usually referred to as back-propagation. The objective

of the neural network is to find a set of weights for the explanatory variables and minimize the error

between the neural network output and the actual data (Allen and Zumwalt, 1994).

Two criteria were used to compare the performance of the different models: (1) the mean absolute error

between the predicted and actual selling price of the samples, including: RMSE and MAPE and (2) the Hit

Ratio in the sample between the predated and selling price of the sample. The best model for predicting

actual sales prices was determined to be the one that resulted in the lowest mean absolute percentage error

and/or the highest percentage of predicted sale price with an absolute error below 5% of the actual sale

price.


The data model with a smaller MAPE is deemed superior. This error measurement attempts to produce a

single number that represents the total error for all properties. This error measurement fails, however, to

provide information as to how the error differs between the properties. For example, if a model provides

extremely accurate results for 90% of the properties tested while providing horribly inaccurate results for

10% of the properties tested, the MAPE value for this model may be comparable to another model with

unacceptable results (i.e., a large standard deviation in error, but with a comparable MAPE).The MAPE is

defined in the second formula shown below.

1. Root Mean Squared Errors (RMSE) is defined as:

2. Mean Absolute Percentage Errors (MAPE) is defined as:

3. Hit Ratio is defined as:

Y_Selling Price of sample __confidence level at 5__10__20_

n_No. of Hit Ratio N_Total sample

Empirical Results

Forecasting Result of MRA Model

The statistical analysis was carried out using the regression procedure. The results of the MRA revealed

that all the variables entered were statistically significant at the 5% significance level, and the R-square

value obtained was 69.4%. The results of the analysis are shown in the Table.3. Among all the variables,

the ones with positive signs of coefficient were Location for properties; ROADW; ROADR; AGE for

building ; Total floor; Zoning for land; BUILAREA for building floor area. Those with negative signs

were: Type for building use; STRUC for building. According to economic theory, age is expected to have

an inverse relationship with housing price, but the reverse was indicated by the analysis. This departure

from theory may be justifiable in the case of Kaohsiung City as it was observed that the age for buildings

increased even with soaring housing prices. In Kaohsiung City, the housing prices were affected by land

prices and the real estate market , not by age. Besides, the old buildings were located in the traditional

downtown and the prices of those properties were even higher than the new buildings in the suburban

district. This may also help to account for the inverse relationship obtained for age of building.


Table 3. Estimated MRA model for Housing Prices in Kaohsiung City

Forecasting Results of ANN Model

The ANN model was developed from a set of data. For a particular input, an output (housing price) is

produced from the model. Then, the model compares the model output to the actual housing price. The

accuracy of the value is determined by the total mean square error. Then back-propagation is used to

attempt to reduce prediction errors, which is done by adjusting the connection weights. The performance of

the network can be influenced by the number of hidden layers and the number of nodes that are included in

each hidden layer. The trial-and error process is applied to find the optimal artificial neural network

model.(See Figure 3.) We used the Alyuda software to construct the artificial neural network model. In

accordance to standard analytical practice, the sample size was divided on a random basis into two sets,

namely the training set and the test set. The training set and test set contain 70% and 30% of the total

sample, respectively. (See Figure 4.) The input importance of all variables in the best artificial neural

networks is shown in Figure 5. Figure 5 shows that building floor area and where the land is located in the

street are important factors that determine the housing price.


Figure 3. ANN Training Error graph

Note: Iterations trained: 5136


Figure 4. Actual and Forecast Price in ANN model

Figure 5. Input Importance of Variables in ANN model

Results of Comparative Study with MRA and ANN Models

The results of the comparative study are given in Table 5. As shown in Table 5, the R-square from the

neural network model is higher than the R-square from MRA model. The results imply that the neural

network model can estimate the housing price more accurately than the MRA model.

As shown in Table 5, the MAPE of the forecast generated by the ANN model was 19.02; for the MRA

model, the MAPE was 23.71%. Thirty-five percent of hit ratios of the predicated price are within 10% of

the actual price and 62 % are within 20% of the actual price in the ANN model. Compared to the MRA

model, the ANN model performs better.


Conclusion

This study employs a recurrent back-propagation neural network to produce housing price models for

Kaohsiung city. From our empirical study, we found that an ANN model will generate more forecasting

error than the MRA model. This is due to the nature of neural network model. The model are designed to

capture the non-linear relationship between the input and output variables automatically, without having to

specify the non-linear terms to fit the data. This research investigated the merits of applying neural network

technology to the problem of real estate appraisal.

Furthermore, the results found in this research could be a function of the specific data characteristics of the

sample used. It may be possible that neural networks will do a much better job than multiple regression if

the nonlinear relationships between the variables are greater. despite the RMSE, MAPE, & Hit Ratio, the

performance of the ANN model is better than the MRA model in Kaohsiung City.

As we mentioned in the literature review, our results are similar to the empirical results of McGreal, Adair,

McBurney and Patterson (1998); Din, Hoesli, and Bender (2001) ; and Wong, So, and Hung (2001).

Finally, the software randomly generates the input importance for each of the nodes in the hidden layer.

Hence, the ANN is recommended when there is a sufficient sample data set or when there is no theoretical

basis for the data specification. Continued research in this area is important and necessary before the final

verdict on the use of neural networks in real estate appraisal can be decided.


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Analysis of the Mass Appraisal Model - Real Estate … of the Mass Appraisal Model ... The paper begins with a review of some papers using neural network models in property valuation