Question
Asked 18th Jan, 2021

Two-stage disjoint approach PLS-SEM. Do considering the overall model fit (SRMR, NFI, RMS_theta) still make sense?

Kind colleagues,
I am running a PLS-SEM on SmartPls 3.0. I specified the model as with two higher orderd formative components (HOCs). The lower order construcst instead have reflective causality (it's a reflective-formative HCM). To estimate it I tried with the repeated indicators approach and calculate the internal, convergent and discriminant validity statistics for HOCs by hand. Everything works fine except the overall model fit (which I know to be a very debated topic) that gives me SRMR above 0.11 and an infinite Chi-square (which I interpret as too many degrees of freedom and too tiny sample - 260). By using the disjoint two-stage approach instead, my model works perfectly. Not only the path coefficients are all significant, but also the overall model fit is amazing (SRMR below 0.06). My question is: does it make sense to consider these overall fit measure in the two stages approach? I mean, is it even comperable to a specification estimated with the repeated indicators approach? How should I choose the best model?
I need the help of the community!
Thanks everyone

All Answers (3)

22nd Jan, 2021
Mehmet Mehmetoglu
Norwegian University of Science and Technology
Giacomo Buzzao, I am not using SmartPls, but I think, in general, estimating higher-order constructs using the two-stage approach seems reasonable due to complexity involved. What the two-stage approach does in your case is that it creates component scores for the first-order constructs using the PLS-SEM algorithm and then uses these component scores as the manifest variables of the formative constructs which themselves are also component scores. Another way of saying this is that your first-order constructs are predicting your second-order construct. PLS-SEM itself is a two-stage algorithm. Following this reasoning then, any fit measures or alike provided by software based on PLS-SEM algorithm can also be used for evaluating higher-order component models.
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22nd Jan, 2021
Imran Anwar
Chandigarh University
Credé, M., & Harms, P. D. (2015). 25 years of higher-order confirmatory factor analysis in the organizational sciences: A critical review and development of reporting recommendations. Journal of
Organizational Behavior, 36(6), 845-872.
Jackson, D. L., Gillaspy, J. A., & Purc-Stephenson, R. (2009).
Reporting practices in confirmatory factor
analysis: an overview and some recommendations. Psychological methods, 14(1), 6-23.
Hopefully these papers will help your query.
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