Generalized Confirmatory Factor Mixture Modeling: A Tool for Assessing Factorial Invariance Across Unspecified Populations

Abstract

Mixture modeling is an increasingly popular analysis in applied research settings. Confirmatory factor mixture modeling can be used to test for the presence of multiple populations that differ on one or more parameters of a factor model in a sample lacking a priori information about population membership. There have, however, been considerable difficulties regarding convergence and parameter recovery in confirmatory factor mixture models. The present study uses a Monte Carlo simulation design to expand upon a previous study by Lubke, Muthén, & Larsen (2002) which investigated the effects on convergence and bias of introducing intercept heterogeneity across latent classes, a break from the standard approach of intercept invariance in confirmatory factor modeling when the mean structure is modeled.

Using convergence rates and percent bias as outcome measures, eight design characteristics of confirmatory factor mixture models were manipulated to investigate their effects on model performance: N; mixing proportion; number of indicators; factor saturation; number of heterogeneous intercepts, location of intercept heterogeneity, magnitude of intercept heterogeneity, and the difference between the latent means (Δκ) of the two modeled latent classes. A small portion of the present study examined another break from standard practice by having models with noninvariant factor loadings.

Higher rates of convergence and lower bias in the parameter estimates were found for models with intercept and/or factor loading noninvariance than for models that were completely invariant. All manipulated model conditions affected convergence and bias, often in the form of interaction effects, with the most influential facets after the presence of heterogeneity being N and Δκ, both having a direct relation with convergence rates and an inverse relation with bias magnitude. The findings of the present study can be used to some extent to inform design decisions by applied researchers, but breadth of conditions was prioritized over depth, so the results are better suited to guiding future methodological research into confirmatory factor mixture models. Such research might consider the effects of larger Ns in models with complete invariance of intercepts and factor loadings, smaller values of Δκ in the presence of noninvariance, and additional levels of loading heterogeneity within latent classes.