I understand that it is not meaningful to consider the model fit of a just-identified model (say, a path model), because the df is zero. But I haven't read a lot of discussion about the coefficients of just-identified models. 1) Can the path coefficients of this just-identified model be trusted? 2) Is achieving over-identification the top priority, i.e.,if this just-identified path model is what I am interested in, should I sacrifice some parameters(e.g., constrain some path coefficients to be equal or set a nonsig. one to be zero), in order to obtain an over-identified model?
1. Yes. 2. The left-out paths should be based on the theory you are testing.
K Wilkins posted on Sunday, January 27, 2013 - 3:44 pm
Hi Dr. Muthen,
I had a related question. I know that model fit indices such as chi-square are not calculated when analyzing a just-identified model. It seems AIC and BIC are calculated when I run my model, I was curious if I am able to report these?
Q1: No. In fact, adding other model parts, that factor model will have testable implications because the correlations with variables in other model parts have to be explainable via that factor. So for instance, if the factor predicts an observed Y, you will have a testable model.
To follow-up and assure my understanding - does this then mean that I can move past the measurement model (of this latent factor, it is the only one in the model) and run the structural piece with the latent construct in it, and see if the latent factor fits, in addition to fit of overall model (with predictors and outcomes)?