Evaluating latent variable interactions with structural equation mixture models.

摘要

Interactions are commonly hypothesized in psychological research. Methods exist for estimating interactions with observed variables, but problems with small effect sizes, measurement error, predictor distributions, and the unknown nature of the relationships among the variables of interest make it difficult to detect interactions. Latent variable approaches were proposed to remedy some problems with observed variables, however these methods require a priori specification of the functional form of the interaction. The present work evaluates an approach using structural equation mixture models (SEMMs) to estimate interactions among latent variables without specifying a functional form in advance. Results indicate that the approach can approximate a variety of latent variable relationships. Larger sample sizes and areas with more observations were associated with better SEMM performance. Typically, SEMMs with additional classes had less bias. It is recommended that researchers examine predicted value plots for several SEMMs to evaluate the relationships among the latent variables.