I have a question concerning structural equation modeling: If the overall fit of my model is very good like in the following model, do I still have to test whether the fit of each measurement model is good as well? And if yes, why is that? And what can I do if my whole model includes measuresment models, that just cannot be tested separately because there are only 2 indicators for each latent variable?

Thank you in advance for your help!



1 Answer 1


I would say just leave it as is. You are right that each model per se is not identified as covariance factor analysis model with two indicators per variable, so you cannot get much done, anyway -- at least in the mainstream covariance testing paradigm. Ken Bollen, Shawn Bauldry and myself have a forthcoming paper in Psychometrika where we show how to test such measurement models using instrumental variables technique, but I can't see a test like ours to find any issues with this model.

Mind you, you probably don't have a terrific model, but only a small sample size, so whatever's wrong with your model just does not show up :).


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