Hausman test for endogeneity in SEM m... PreviousNext
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 Hilco posted on Thursday, November 10, 2011 - 2:54 am
I've searched the internet and textbooks, but cannot find an answer to this question. Please help me out! It's a final step in my thesis.

I have a SEM path model, consisting of all direct effects, and one mediator path. This mediator path is included in my SEM to control for the simultaneous estimation of X and Y.

My thesis supervisor told me to run an additional endogeneity test, preferably a Hausman test. This Hausman works perfectly fine, indicating no endogeneity problem. But Hausman tests whether the OLS (!) coefficients are unbiased, while my theory is a SEM-like path model. Can I use this test?

By the way, if I run an OLS regression model of my theory (i.e., without the mediating-path), I get both qualitatively and quantitatively similar results.
 Tihomir Asparouhov posted on Thursday, November 10, 2011 - 3:06 pm
I don't see any problems in principle using Hausman test for endogeneity in SEM but you should still be comparing the ML estimate with the IV estimates.
 Hilco posted on Friday, November 11, 2011 - 12:34 am
That shoul'dn't be a problem, since these results are similar. do you perhaps have a citation that I could use to substatiate this argument? That would really help me out.
 Tihomir Asparouhov posted on Friday, November 11, 2011 - 11:35 am
This is probably a good starting point and the reference there
 Tihomir Asparouhov posted on Friday, November 11, 2011 - 11:37 am
Also this one

Kirby, J. and K.A. Bollen. 2009. “Using Instrumental Variable (IV) Tests to Evaluate Model Specification in Latent Variable Structural Equation Models.” Sociological Methodology 39: 327-355.
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