Power and Type I Error of Local Fit Statistics in Multilevel Latent Class Analysis

Erwin Nagelkerke,Daniel L Oberski,Jeroen K Vermunt

doi:10.1080/10705511.2016.1250639

Abstract

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.

Highlights

In the social and behavioral sciences, variables are often categorical and people are often nested in groups
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

Summary

Introduction

In the social and behavioral sciences, variables are often categorical and people are often nested in groups. Maybe more important, it does solve the statistical problem of dependent observations, but it substantively allows observed groups to be classified On the lower level the assumption is that all dependence between items is captured by the latent variable, assuming conditional independence of the indicators given the LC variable. This assumption is identical to that of a regular LC model. On the higher level a similar assumption is made, where the observed group members are assumed conditionally independent given the higher level latent variable

Methods

Results

Conclusion