Model Selection in Finite Mixture Models: A k -Fold Cross-Validation Approach

Finite mixture models, whether latent class models, growth mixture models, latent profile models, or factor mixture models, have become an important statistical tool in social science research. One of the biggest and most debated challenges in mixture modeling is the evaluation of model fit and model comparison. In the application of mixture models, researchers often fit a collection of models and then decide on a single optimal model based on a variety of model fit information. We propose a k-fold cross-validation procedure to model selection whereby the model is repeatedly fit to k−1 different partitions of the data set, the resulting model is then applied to kth partition of the sample, and the distribution of fit indexes is examined. This method is illustrated with growth mixture models fit to longitudinal data on reading ability collected as part of the Early Childhood Longitudinal Study–Kindergarten Cohort.