An extended model comparison framework for covariance and mean structure models, accommodating multiple groups and latent mixtures

The model comparison framework of Levy and Hancock for covariance and mean structure models is extended to treat multiple-group models, both in cases in which group membership is known and in those in which it is unknown (i.e., finite mixtures). The framework addresses questions of distinguishability as well as difference in fit of the models with respect to data, first by determining the nature of the models' relation in terms of the families of distributions that constitute the models and then by conducting the appropriate statistical tests. In the case of latent mixtures of groups, the standard likelihood ratio theory does not apply, and a bootstrapping approach is used to facilitate the tests. Illustrations demonstrate the procedures.