Endogeneity in PLS-SEM

Questions about the implementation and application of the PLS-SEM method, that are not related to the usage of the SmartPLS software.
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Kv_HH
PLS Junior User
Posts: 2
Joined: Fri Jun 11, 2021 1:27 pm
Real name and title: Kyra, Student

Endogeneity in PLS-SEM

Post by Kv_HH »

Hello everyone,

I'm trying to use the Gaussian copula approach to detect endogeneity issues. I followed Hult, G. T. M., Hair Jr, J. F., Proksch, D., Sarstedt, M., Pinkwart, A., & Ringle, C. M. (2018). Addressing endogeneity in international marketing applications of partial least squares structural equation modeling. Journal of International Marketing, 26(3), 1-21.
My model has multiple endogenous variables. I read Park, Sungho, and Sachin Gupta (2012), “Handling Endogenous Regressors by Joint Estimation Using Copulas,” Marketing Science, 31 (4), pp. 567–86. with the consequence that I know that it is required to create the copula for each individual endogenous variable and adding all copulas to the original model. Unlike the example of Hult, et al. 2018 my research model contains 6 variables. Four of them are antecedents with each one arrow to either of the two mediator variables (full mediation). This means only the two mediator variables have arrows to the to target variables. But now my problem:
Do I have over 20 copulars or just 3? (Please compare the CUSL, COMP, CUSA, LIKE example to understand how I counted over 20 copluars for the whole model or just 3 if only the mediators and endogenous variables are relevant for the endogeneity test).

I would appreciate help with this baseline problem, thanks!
jmbecker
SmartPLS Developer
Posts: 1282
Joined: Tue Mar 28, 2006 11:09 am
Real name and title: Dr. Jan-Michael Becker

Re: Endogeneity in PLS-SEM

Post by jmbecker »

Generally, you should include all relevant copulas at the same time. However, adding copula terms for all predictor variables might not be very efficient and the results are not very trustworthy, because you need very large datasets to reliably estimate such models. Thus, I would first think about which variables have a potential endogeneity problem and then add copula terms only for these specific variables. I would try to avoid adding more than two or three copula terms in one model unless you have very large datasets (>10,000).

In general, copula models need much larger datasets than initially though and the non-normality needs to be sufficiently strong to make the copula approach work reliably. Please see our recent paper on this topic: Becker, JM., Proksch, D. & Ringle, C.M. (2022). Revisiting Gaussian copulas to handle endogenous regressors. Journal of the Academy of Marketing Science, 50, 46–66. https://doi.org/10.1007/s11747-021-00805-y
Dr. Jan-Michael Becker, BI Norwegian Business School, SmartPLS Developer
Researchgate: https://www.researchgate.net/profile/Jan_Michael_Becker
GoogleScholar: http://scholar.google.de/citations?user ... AAAJ&hl=de
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