Can a Normed Fit Index Assist with Model Selection in Latent Class Analysis with Large Samples? A Preliminary Investigation

Abstract

Latent class analysis (LCA) is a popular method in the social and behavioral sciences for identifying subgroups of individuals characterized by unique patterns of behaviors. A pragmatic challenge is selection of the optimal number of latent classes, and it is often necessary to take a data-driven approach. With large sample sizes, penalized fit criteria and likelihood ratio-based significance testing can suggest impractically large numbers of classes. Analogues of the normed fit index (NFI), non-normed fit index (NNFI), and root mean square error of approximation (RMSEA) from the structural equation modeling literature were considered for use with LCA. Potential advantages and limitations of these fit indices were examined through two real-world data examples and a small simulation study. Results suggested that traditional cutoffs for the NFI/NNFI may not be equally useful for LCA and that the RMSEA may have quite limited usefulness for LCA