Endogeneity testing with Gaussian copula

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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JuliaSophie
PLS Junior User
Posts: 1
Joined: Mon Mar 28, 2022 8:41 am
Real name and title: Julia Sophie Gießler-Havemann

Endogeneity testing with Gaussian copula

Post by JuliaSophie »

Hi everyone,

I am in the middle of executing the Gaussian copula approach to address potential endogeneity issues in my data (N=1193). I am doing MGAs on the UTAUT2, which means that I have 7 hopefully exogenous constructs, 1 endogenous mediator and 1 endogenous dependent variable where all arrows end, all measured reflectively with established scales. Because my focus is on explaining group differences rather than predicting, I followed the guidelines from https://www.pls-sem.net/downloads/gauss ... ula-files/, extracted the latent variable scores, verified their non-normality and used the REndo package in R to create the copulas and test for their significance. (My standard regression equation uses zero as intercept.) First, I included each of the 8 copulas separately and found significant results in 2 of my 7 antecedent construct copulas. This result is the same when I include all copulas at the same time. When I add established control variables and repeat the process anew, I only find additional significant copulas for the control variables themselves. :(

So, I have three main questions:

1. Do I still have to repeat the analysis for all several hundred possible combinations of copula inclusions or is the simultaneous inclusion of all copulas sufficient? From jmbecker’s recent forum reply (https://forum.smartpls.com/viewtopic.ph ... ity#p71812) , I understand that even a selective inclusion of copulas could be reasonable, but I am still not sure if one-time simultaneous inclusion of all selected copulas into one big regression equation is enough or whether all copula inclusion combinations have to be tested separately.

2. More generally speaking, would it be fair to say that the Gaussian copula approach, if executed correctly in terms of distributional assumptions, regression equation formulation with/without intercept, and sample size (Becker, Proksch & Ringle, 2022), is the most sensitive approach to detect endogeneity, because by its mathematical nature, it creates a copula with the maximum possible correlation with the error term, whereas other, instrumental variables might include additional, opposing variance sources that could cancel out some of the variance that should actually also be attributed to the effects captured in the error term?

3. My model is fairly well established in the literature, but I have not found any publications that explicitly test for endogeneity like I do right now. All other structural and measurement model quality criteria in my data are fine, particularly also the inner VIFs (all < 3) that would otherwise suggest common method variance. If I understand the literature correctly, the likely source of endogeneity in my case would therefore probably be an omitted variable in the model. So, I was wondering if I could still proceed with my MGAs with the data as it is and deal with the endogeneity by a) simply highlight this potential issue as an indication that the established model could use some future refinements beyond the existing control variables (which did not help) and b) by of course interpreting those results of the MGAs that include significant effects in the two potentially affected variables extra carefully (or basically just not interpreting them with reference to the potential issue), but still working “normally” with the rest?

I would be extremely grateful for any tip or hint!

Thank you so much in advance and warm regards,

Julia
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