Mplus FAQ How can I compute a chi-squared test for nested models with the MLR or MLM estimators?
Chi-squared difference tests are frequently used to test differences between nested models in confirmatory factor, path, and structural equation modeling. Nested models are two models (or more if one is fitting a series of models) that are identical except that one of the models constrains some of the parameters (the null model) and one does not have those constraints (the alternative model). Examples of this include the introduction of a set of dichotomous predictors representing a single nominal (categorical) variable to the model, or a test for differences across groups in a multiple group model. Typically a chi-squared difference test involves calculating the difference between the chi-squared statistic for the null and alternative models, the resulting statistic is distributed chi-squared with degrees of freedom equal to the difference in the degrees of freedom between the two models. However, when a model is run in Mplus using the MLM or MLR estimators, the following warning mess
