title: Regression Mixture Models: Does Modeling the Covariance Between Independent Variables and Latent Classes Improve the Results?
abstract: Regression mixture models are increasingly used as an exploratory approach to identify heterogeneity in the effects of a predictor on an outcome. In this simulation study, we tested the effects of violating an implicit assumption often made in these models; that is, independent variables in the model are not directly related to latent classes. Results indicate that the major risk of failing to model the relationship between predictor and latent class was an increase in the probability of selecting additional latent classes and biased class proportions. In addition, we tested whether regression mixture models can detect a piecewise relationship between a predictor and outcome. Results suggest that these models are able to detect piecewise relations but only when the relationship between the latent class and the predictor is included in model estimation. We illustrate the implications of making this assumption through a reanalysis of applied data examining heterogeneity in the effects of family resources on academic achievement. We compare previous results (which assumed no relation between independent variables and latent class) to the model where this assumption is lifted. Implications and analytic suggestions for conducting regression mixture based on these findings are noted.
authors.affiliation: a Department of Psychology , University of South Carolina.
authors.forename: Andrea E
authors.initials: AE
authors.lastname: Lamont
authors.affiliation: b Department of Methodology and Statistics , Tilburg University.
authors.forename: Jeroen K
authors.initials: JK
authors.lastname: Vermunt
authors.affiliation: c Department of Individual, Family and Community Education , University of New Mexico.
authors.forename: M Lee
authors.initials: ML
authors.lastname: Van Horn
mesh_terms: D002648:Child; D003198:Computer Simulation; D003430:Cross-Sectional Studies; D003627:Data Interpretation, Statistical; D004522:Educational Status; D005190:Family / Q000523:psychology; D005260:Female; D006801:Humans; D008137:Longitudinal Studies; D008297:Male; D015233:Models, Statistical; D009010:Monte Carlo Method; D012044:Regression Analysis
keywords: Regression mixture models; finite mixture models; latent class regression; simulation