Model selection and evaluation in factor mixture modeling using a two-stage ML approach

Finite factor mixture modeling is used to model the covariation between observed variables within component. Major issues involved with factor mixture modeling include determining the number of components in a mixture, and evaluating the overall model. However, problems arise when using the conventional single-stage ML approach to fit a factor mixture model. In particular, the determination of the number of components is confounded with model misspecification. Besides, the single-stage ML approach only allows relative model fit indices such as AIC and BIC, which do not support tests of model evaluation, hence tests for factorial invariance across components are not available. To circumvent these problems, this paper studies behavior of a newly-proposed two-stage ML approach in model selection, and provided several fit indices for evaluating the overall model. Results suggest that (1) The two-stage approach identifies the model with the correct number of components more frequently when the model is misspecified or when the distribution assumption is violated; (2) Even when the model and distribution are both correctly specified, the classification-based criteria perform better with the two-stage approach when all components share the same factor loadings; (3) Most provided fit indices for overall model evaluation perform well, while the conventional chi-square difference test statistics associated with either ML or GLS methods rejects the correct models too frequently and can not be trusted.