Comparison of Student t and Gaussian ... PreviousNext
Mplus Discussion > Latent Variable Mixture Modeling >
 Albert Burgess-Hull posted on Saturday, June 08, 2019 - 10:35 am
I'm wondering if it is appropriate to compare the fit of a Student t latent profile model to the fit of a normal (Gaussian) latent profile model with a log-likelihood ratio test? Both models are fit with the same indicator variables and have the same number of classes. I am under the impression that this should be appropriate given that the normal distribution is a special case of the student t-distribution as the degrees of freedom parameter approaches infinity, but I’m not positive. The potential of using a log-likelihood test to compare the fit of a Skew-t mixture model to a normal mixture model was suggested in “Structural Equation Models and Mixture Models with Continuous Non-Normal Skewed Distributions“ (Asparouhov & Muthen, 2014); however, there wasn’t explicit mention of whether one could compare a Student t model to a normal (Gaussian) model.

Thanks for your help.
 Tihomir Asparouhov posted on Monday, June 10, 2019 - 8:31 am
This is correct. The models are nested and you can use the LRT test for comparison.
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