Power and type I error of local fit statistics in multilevel latent class analysis

In the social and behavioral sciences, variables are often categorical and people are often nested in groups. Models for such data, such as multilevel logistic regression or the multilevel latent class model, should account for not only the categorical nature of the variables, but also the nested structure of the persons. To assess whether the model accomplishes this goal adequately, local fit measures for multilevel categorical data were recently introduced by Nagelkerke, Oberski, and Vermunt (2015). The BVR-group evaluates the variable–group fit, and the BVR-pair evaluates the person–person fit within groups. In this article, we evaluate the performance of these 2 measures for the multilevel latent class model (Vermunt, 2003). An extensive simulation study indicates that whenever multilevel latent class modeling itself is viable, Type I error is controlled and power is adequate for both fit statistics. Thus, the BVR-group and BVR-pair are useful measures to locate important sources of misfit in multilevel latent class analysis.