STRUCTURE EQUATION MODELLING ---WITH PLS

SEM

1. Structural Equation Modeling (SEM): By ADANCO & SmartPLS Organised By: Prof. Seetharaman, Dean (Academics) and Dr. K. Maddulety, Deputy Director S P Jain School of Global Management Dubai • Mumbai • Singapore • Sydney   www.spjain.org

2. Organization of Multivariate Methods

3. Key Characteristics of PLS-SEM

4. Key Characteristics of PLS-SEM

5. Key Characteristics of PLS-SEM

6. Key Characteristics of PLS-SEM

7. Rules of Thumb for Choosing Between PLS-SEM and CB-SEM Use PLS-SEM when • The goal is predicting key target constructs or identifying key "driver" constructs. • Formatively measured constructs are part of the structural model. Note that formative measures can also be used with CB-SEM, but doing so requires construct specification modifications (e.g., the construct must include both formative and reflective indicators to meet identification requirements). • The structural model is complex (many constructs and many indicators). • The sample size is small and/or the data are non-normally distributed. • The plan is to use latent variable scores in subsequent analyses. Use CB-SEM when • The goal is theory testing, theory confirmation, or the comparison of alternative theories. • Error terms require additional specification, such as the covariation . • The structural model has non-recursive relationships. • The research requires a global goodness-of-fit criterion

8. Model Considerations When Choosing PLS-SEM • Measurement model requirements are quite flexible. PLS-SEM can handle reflective and formative measurement models as well as single-item measures without additional requirements or constraints. • Model complexity is generally not an issue for PLS-SEM. As long as appropriate data meet minimum sample size requirements, the complexity of the structural model is virtually unrestricted.

9. A Systematic Procedure for Applying PLS-SEM

10. Guidelines for Choosing the Measurement Model Mode

11. Guidelines for Single-Item Use

12. Systematic Evaluation of PLS-SEM Results

13. Comparing Reliability and Validity

14. Outer Loading Relevance Testing

15. Rules of Thumb for Evaluating Reflective Measurement Models Internal consistency reliability : composite reliability should be higher than 0.708 (in exploratory research, 0.60 to 0.70 is considered acceptable). Consider Cronbach's alpha as a conservative measure of internal consistency reliability. • Indicator reliability : the indicator's outer loadings should be higher than 0.708. Indicators with outer loadings between 0.40 and 0.70 should be considered for removal only if the deletion leads to an increase in composite reliability and AVE above the suggested threshold value. • Convergent validity : the AVE should be higher than 0.50. • Discriminant validity : An indicator's outer loadings on a construct should be higher than all its cross loadings with other constructs. The square root of the AVE of each construct should be higher than its highest correlation with any other construct ( Fornell Larcker criterion).

16. Formative Measurement Models Assessment Procedure

17. Collinearity Assessment in Formative Measurement Models Using the VIF

18. Decision-Making Process for Keeping or Deleting Formative Indicators Continued on next slide

19. Decision-Making Process for Keeping or Deleting Formative Indicators

20. Rules of Thumb for the Evaluation of Formative Measurement Indicators • Assess the formative construct's convergent validity by examining its correlation with an alternative measure of the construct, using reflective measures or a global single item (redundancy analysis). The correlation between the constructs should be 0.80 or higher. • Collinearity of indicators: Each indicator's tolerance (VIF) value should be higher than 0.20 (lower than 5). Otherwise, consider eliminating indicators, merging indicators into a single index, or creating higher-order constructs to treat collinearity problems. Continued on next slide

21. Rules of Thumb for the Evaluation of Formative Measurement Indicators • Examine each indicator's outer weight (relative importance) and outer loading (absolute importance) and use bootstrapping to assess their significance. • When an indicator's weight is significant, there is empirical support to retain the indicator. • When an indicator's weight is not significant but the corresponding item loading is relatively high (i.e., > 0.50), the indicator should generally be retained. • If both the outer weight and outer loading are nonsignificant , there is no empirical support to retain the indicator and it should be removed from the model.

22. Recommended Use of Bootstrap Sign Change Options Continued on next slide

23. Recommended Use of Bootstrap Sign Change Options

24. Indicators of the Formative Measurement Models

25. Indicators of the Formative Measurement Models

26. Indicators of the Formative Measurement Models

27. Indicators of the Formative Measurement Models

28. Structural Model Assessment Procedu re

29. Rules of Thumb for Structural Model Evaluation Examine each set of predictors in the structural model for collinearity . Each predictor construct's tolerance (VIF) value should be higher than 0.20 (lower than 5). Otherwise, consider eliminating constructs, merging predictors into a single construct, or creating higher-order constructs to treat collinearity problems. Use bootstrapping to assess the significance of path coefficients. The minimum number of bootstrap samples must be at least as large as the number of valid observations but should be 5,000. The number of cases should be equal to the number of valid observations in the original sample. Critical values for a two-tailed test are 1.65 (significance level = 10%), 1.96 (significance level = 5%), and 2.57 (significance level = 1 %). In applications, you should usually consider path coefficients with a 5% or less probability of error as significant.

30. Rules of Thumb for Structural Model Evaluation PLS-SEM aims at maximizing the R-square values of the endogenous latent variable(s) in the path model. Thus, the objective is high R-square values. While the exact interpretation of the R-square value level depends on the particular model and research discipline, in general, R-square values of 0.75, 0.50, or 0.25 for the endogenous constructs can be described as respectively substantial, moderate, and weak. • Use the R-square- adj when comparing models with different exogenous constructs and/or different numbers of observations.

31. Rules of Thumb for Structural Model Evaluation The effect size f-square allows assessing an exogenous construct's contribution to an endogenous latent variable's R-square value. The f-square values of 0.02, 0.15, and 0.35 indicate an exogenous construct's small, medium, or large effect, respectively, on an endogenous construct. Predictive relevance: Use blindfolding to obtain cross-validated redundancy measures for each endogenous construct. Make sure the number of observations used in the model estimation divided by the omission distance D is not an integer. Choose D values between 5 and 10. The resulting Q2 values larger than 0 indicate that the exogenous constructs have predictive relevance for the endogenous construct under consideration.

32. Rules of Thumb for Structural Model Evaluation As a relative measure of predictive relevance (q2), values of 0.02, 0.15, and 0.35 respectively indicate that an exogenous construct has a small, medium, or large predictive relevance for a certain endogenous construct Do not use the GoF . Heterogeneity : If theory supports the existence of alternative subgroups of data, carry out PLS-SEM multigroup or moderator analyses. If no theory or information is available about the underlying groups of data, an assessment should be conducted to identify unobserved heterogeneity.