Not quite normal: Consequences of violating the assumption of normality with regression mixture models

Van Horn, M. Lee and Smith, Jessalyn and Fagan, Abigail and Jaki, Thomas and Maysn, Katherine and Hawkins, D. and Feaster, Daniel and Howe, George (2012) Not quite normal: Consequences of violating the assumption of normality with regression mixture models. Structural Equation Modeling, 19 (2). pp. 227-249. ISSN 1070-5511

Abstract

Regression mixture models, which have only recently begun to be used in applied research, are a new approach for finding differential effects. This approach comes at the cost of the assumption that error terms are normally distributed within classes. This study uses Monte Carlo simulations to explore the effects of relatively minor violations of this assumption. The use of an ordered polytomous outcome is then examined as an alternative that makes somewhat weaker assumptions, and finally both approaches are demonstrated with an applied example looking at differences in the effects of family management on the highly skewed outcome of drug use. Results show that violating the assumption of normal errors results in systematic bias in both latent class enumeration and parameter estimates. Additional classes that reflect violations of distributional assumptions are found. Under some conditions it is possible to come to conclusions that are consistent with the effects in the population, but when errors are skewed in both classes the results typically no longer reflect even the pattern of effects in the population. The polytomous regression model performs better under all scenarios examined and comes to reasonable results with the highly skewed outcome in the applied example. We recommend that careful evaluation of model sensitivity to distributional assumptions be the norm when conducting regression mixture models.