Saiyidi Mat Roni - 2014 - Partial Least Square in a Nutshell

1 Partial least square in a nutshell | Saiyidi MAT RONI 1 November 2014

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S a i y i d i M A T R O N I

2 Partial least square in a nutshell | Saiyidi MAT RONI 1 November 2014

1 Partial least square in a nutshell

Partial least square (PLS) a robust structural equation modelling (SEM) approach. It is

sometimes referred as component-based SEM or simply PLS-SEM. PLS-SEM is a causal

modelling statistical approach with an aim to maximise explained variance of dependent

latent variables (Chin, 1998b; Hair, Ringle, & Sarstedt, 2011).

Unlike covariance-based SEM, e.g. provided by AMOS and LISREL, PLS-SEM does

not put emphasis on normality of data distribution (Ringle, Sarstedt, & Straub, 2012), which

allows researchers to use their raw data in the analysis without having to transform their data

to make it at least, approximate normally distributed, prior to running SEM. Although some

studies suggest choosing PLS-SEM over covariance-based SEM on a basis of non-normal

data distribution is a weak argument, the fact that violation of normality assumption can

produce unintended biases in the final statistical result (or no solution at all), it is prudent to

opt for PLS-SEM to alleviate two serious issues with covariance-based SEM: improper

solutions where solution is beyond what is gauged by parameters, and factor indeterminacy

(Fornell & Bookstein, 1982).

For more in-depth review of PLS-SEM features Hair et al. (2011), Chin (1998b), Wold

(1985) and Hair Jr, Sarstedt, Hopkins, and Kuppelwieser (2014) are good references to begin

with.

3 Approach to structural equation modelling (SEM) | Saiyidi MAT RONI 1 November 2014

Screen data •Delete monotones

Missing value analysis •Choose MI or EM

Check outliers •Trim or Winsor

Check normality •transform if necessary

Run factor analysis •Extraction: PCA, PAF or ML •Rotation: Orthogonal or oblique

Reliability & validity •Cronbach's alpha • AVE

Address biases •CMB -> Harman's single factor score •NRB -> split half, then test means difference

2 Approach to structural equation modelling (SEM)

2.1 Preliminary data analysis

As in most cases, before an actual analysis can be performed, it is advisable to run

preliminary data analysis (PDA). PDA is recommended to ensure the dataset is ‘cleaned’ and

‘cleansed’ of substantial noise that attract biases in the final results of the actual analysis. The

following diagram illustrates a common approach to PDA.

AVE = average variance extracted CMB = common method bias EM = Expected maximisation MI = Multiple imputations ML = Maximum likelihood NRB = Non-response bias PAF = Principal axis factoring PCA = Principal component analysis


2.2 Measurement model

Once PDA is done, the next step to make before the interpretation of the output of a

structural model, is to look at the measurement model. Assessments of measurement model

than later interpret the result of the structural model are two-stage SEM approach suggested

by Anderson and Gerbing (1988) and Hair et al. (2011). Measurement model stage involves

an assessment of model parameters which included reliability test using Cronbach’s alpha

and composite reliability (Kock, 2013; Urbach & Ahlemann, 2010), validity analyses through

average variance extracted (AVE) and standardised factor loadings and cross-loadings

(Fornell & Larcker, 1981; Hair, Black, Babin, & Anderson, 2010; Kline, 2010; Schumacker

& Lomax, 2012), and also an assessment to determine the nature of construct being a

formative or reflective (Chin, 1998a). The quality of the measurement model is further

assessed on lateral and vertical collinearity using variance inflation factor (VIF) (Kock &

Lynn, 2012). The criteria for the assessment is summarised in Table 1 below.

Table 1: Measurement model assessment criteria.

Assessment Criterion Note Reference Item reliability Individual item standardised

loading on parent factor. Min. of .50 Hair et al. (2010)

Convergent validity

Individual item standardised loading on parent factor, and Loadings with sig. p-value

Min. of .50 p < .05

Hair et al. (2010) Gefen and Straub (2005)

Composite reliability > .70 Fornell and Larcker (1981) Nunnally and Bernstein (1994) Hair et al. (2010)

Average variance extracted (AVE)

> .50 Hair et al. (2010) Urbach and Ahlemann (2010)

Discriminant validity

Square-root of AVE More than the correlations of the latent variables.

Hair et al. (2010)


Reliability Cronbach’s alpha

> .70

Nunnally and Bernstein (1994) Urbach and Ahlemann (2010) Hair et al. (2010)

Variance inflation factor (VIF) < 10 < 5

Hair et al. (2010) Kock and Lynn (2012)

Nature of construct

Formative / reflective: Chin (1998a) Coltman, Devinney, Midgley, and Veniak (2008)


2.3 Structural model

After measurement model is found to be satisfactory, structural model parameter

estimates then can be used for analyses and interpretation. The structural model is evaluated

through coefficient of determination, R2(Chin, 1998a, 1998b), predictive relevance, Q2

(Geisser, 1975; Stone, 1974), effect size, f2 (Cohen, 2013), and path coefficients (see Hair et

al., 2011; Mohamadali, 2012). These criteria are summarised in Table 2 below.

Table 2: Structural model criteria.

Criterion Note Reference Coefficient of determination, R2 .67 substantial

.33 average

.19 weak

Chin (1998a)

Predictive relevance, Q2 > 0 Stone-Geisser test

Geisser (1975) Stone (1974)

Effect size, f 2 .02 small .15 medium .35 large

Cohen (2013)

Path coefficient Magnitude Sign p-value

Hair et al. (2010)

7 WarpPLS | Saiyidi MAT RONI 1 November 2014

3 WarpPLS

3.1 Start WarpPLS Double-click on the icon > Proceed to use software


3.2 Transfer data set from Excel to WarpPLS readable format Data file: PLS.FullData.xlsx If your dataset is in SPSS format (.sav): File > Save As > Type in file name > Save as type: > select Excel 2007 through 2010 (*.xlsx) > Save.

Open PLS.FullData.xlsx > Your data should look like this:


On WarpPLS: Proceed to Step 1 > Create project file > File name > Type BasicModel > Save.

Proceed to Step 2 > Read from file > Files of type: > (*.xlsx) > Select PLS.FullData > Open.


Your data preview should look like this. Next > Finish > Check your data set > OK > Yes.

Proceed to Step 3 > Pre-process data > OK.


Check your data > Yes.

On main window: Project > Save Project.

12 Basic model | Saiyidi MAT RONI 1 November 2014

4 Basic model

Data file: BasicModel.prj

3 Predictors (independent variables) and 1 criterion (dependent variable).

4.1 Create latent variables Proceed to Step 4 > Define SEM Model > Latent variable options > Create latent variable > Click anywhere on the canvas (white area).


Latent variable name: > type EASE > Add indicators: Click PEOU1 > Add. Repeat the Add indicators steps for PEOU2, …, PEOU6 > Save > Save latent variable settings > OK.


4.2 Create direct links among latent variables Proceed to Step 4 > Define SEM Model > Direct link options > Create direct link. Click EASE > Click INTENT > WarpPLS creates the line in the model. Repeat the process for USEFUL-INTENT and ATTITUDE-INTENT.

Model options > Save model and close > OK. Proceed to Step 5 > Perform SEM analysis > your result should look like this.


4.3 Measurement model On main window > View/save analysis results.

Examine the value of each criterion and compare them against the thresholds listed in

the table below.

Assessment Criterion Note Steps Item reliability Individual item standardised

loading on parent factor. Min. of .50 View > View indicator

loadings and cross-loadings > View combined loadings and cross-loadings.

Convergent validity

Individual item standardised loading on parent factor. Loadings with sig. p-value

Min. of .50 < .05

View > View indicator loadings and cross-loadings > View combined loadings and cross-loadings

Composite reliability

> .70

View > View latent variable coefficients.

Average variance extracted (AVE)

> .50


Discriminant validity

Square-root of AVE More than the correlations of the latent variables.

View > View correlations among latent variables and errors > View correlations among latent variables with sq. rts. of AVEs.

Reliability Cronbach’s alpha > .70 View > View latent variable coefficients.

Variance inflation factor (VIF)

< .50 View > View latent variable coefficients.


Nature of construct

Formative / reflective: Look for Simpson’s paradox indication

View > View causality assessment coefficients > View path-correlation sign

4.4 Structural model On main window > View/save analysis results.

Examine the value of each criterion and compare them against the thresholds listed in

the table below.

Criterion Note Steps Coefficient of determination, R2 .67 substantial

.33 average

.19 weak


Predictive relevance, Q2 > 0 Stone-Geisser test


Effect size, f 2 .02 small .15 medium .35 large

View > View standard errors and effect sizes for path coefficients.

Path coefficient Magnitude Sign p-value

From the main structural model, or View > View path coefficients and P values.

17 Model with moderating variable | Saiyidi MAT RONI 1 November 2014

5 Model with moderating variable

Data file: ModeratingVariable.prj

Moderating

variables

18 Model with mediator variable | Saiyidi MAT RONI 1 November 2014

6 Model with mediator variable

Data file: MediatingVariable.prj

Mediating variable

19 Model with second-order factor | Saiyidi MAT RONI 1 November 2014

7 Model with second-order factor

Data file: SecondOrderFactor.prj .

Proceed to Step 5 > Perform SEM analysis > Close window.

On the main window > Modify > Add one or more latent variable…

Second-order factor comprises of identify and identity latent variables.

Moderating variable.

20 Model with second-order factor | Saiyidi MAT RONI 1 November 2014

Latent variable to be added: > select internal > Add > OK.

> select identify > Add > OK > Close.

Proceed to Step 4 > Yes > Define SEM model.

Latent variable name: > Type SOCIAL > Add indicators: > choose lv_internal > Add > choose lv_identify > Add.

Save > Save latent variable settings.

21 Model with control variable | Saiyidi MAT RONI 1 November 2014

8 Model with control variable

Data file: ControlVariable.prj

Control variable

Moderating variable

22 References | Saiyidi MAT RONI 1 November 2014

9 References

Anderson, J. C., & Gerbing, D. W. (1988). Structural equation modeling in practice: A

review and recommended two-step approach. Psychological Bulletin, 103(3), 411-

423. doi: 10.1037/0033-2909.103.3.411

Chin, W. W. (1998a). Issues and opinion on structural equation modeling. MIS Quarterly,

22(1), VII-XVI.

Chin, W. W. (1998b). The partial least squares approach to structural equation modelling. In

G. A. Marcoulides (Ed.), Modern methods for business research (pp. 295-336).

Mahwah, New Jersey: Lawrence Erlbaum Associates.

Cohen, J. (2013). Statistical Power Analysis for the Behavioral Sciences (2 ed.). Hoboken:

Taylor and Francis.

Coltman, T., Devinney, T. M., Midgley, D. F., & Veniak, S. (2008). Formative versus

reflective measurement models: Two applications of formative measurement. Journal

of Business Research, 61(12), 1250-1262.

Fornell, C., & Bookstein, F. (1982). Two structural equation models: LISREL and PLS

applied to consumer exit-voice theory. Journal of Marketing Research, 19, 440-452.

Fornell, C., & Larcker, D. F. (1981). Evaluating Structural Equation Models with

Unobservable Variables and Measurement Error. JMR, Journal of Marketing

Research, 18(1), 39.

Gefen, D., & Straub, D. (2005). A practical guide to factorial validity using PLS-graph:

Tutorial and annotated example. Communications of the Association for Information

Systems, 16, 91-109.

Geisser, S. (1975). The Predictive Sample Reuse Method with Applications. Journal of the

American Statistical Association, 70(350), 320-328. doi:

10.1080/01621459.1975.10479865

Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2010). Multivariate data analysis

(7 ed.). Upper Saddle River, NJ, USA: Prentice-Hall, Inc.

Hair, J. F., Ringle, C. M., & Sarstedt, M. (2011). PLS-SEM: Indeed a silver bullet. Journal of

Marketing Theory and Practice, 19(2), 139-151. doi: 10.273/MTP1069-6679190202

Hair Jr, J. F., Sarstedt, M., Hopkins, L., & Kuppelwieser, V. G. (2014). Partial least squares

structural equation modeling (PLS-SEM). European Business Review, 26(2), 106-121.

doi: doi:10.1108/EBR-10-2013-0128

23 References | Saiyidi MAT RONI 1 November 2014

Kline, R. B. (2010). Principles and Practice of Structural Equation Modeling, Third Edition

(3 ed.). New York: Guilford Publications.

Kock, N. (2013). WarpPLS 4.0 User Manual. Loredo, Texas: ScriptWarp Systems.

Kock, N., & Lynn, G. S. (2012). Lateral Collinearity and Misleading Results in Variance-

Based SEM: An Illustration and Recommendations. Journal of the Association for

Information Systems, 13(7), 546-580.

Mohamadali, N. A. K. (2012). Exploring new factors and the question of ‘which’ in user

acceptance studies of healthcare software. (Doctor of Philosophy), University of

Nottingham, Nottingham. Retrieved from

Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory. New York: McGraw Hill.

Ringle, C. M., Sarstedt, M., & Straub, D. W. (2012). Editor's comments: a critical look at the

use of PLS-SEM in MIS quarterly. MIS Quarterly, 36(1), iii-xiv.

Schumacker, R. E., & Lomax, R. G. (2012). A Beginner's Guide to Structural Equation

Modeling : Third Edition (3 ed.). Hoboken: Taylor and Francis.

Stone, M. (1974). Cross-Validatory Choice and Assessment of Statistical Predictions. Journal

of the Royal Statistical Society. Series B (Methodological), 36(2), 111-147. doi:

10.2307/2984809

Urbach, N., & Ahlemann, F. (2010). Structural Equation Modeling in Information Systems

Research Using Partial Least Squares. Journal of Information Technology Theory and

Application, 11(2), 5-40.

Wold, H. (1985). Partial least square. In S. Kotz & N. L. Johnson (Eds.), Encyclopedia of

statistical sciences (Vol. 6, pp. 581-591). New York: Wiley.

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Saiyidi Mat Roni - 2014 - Partial Least Square in a Nutshell