title: Impact of an equality constraint on the class-specific residual variances in regression mixtures: A Monte Carlo simulation study.
abstract: Regression mixture models are a novel approach to modeling the heterogeneous effects of predictors on an outcome. In the model-building process, often residual variances are disregarded and simplifying assumptions are made without thorough examination of the consequences. In this simulation study, we investigated the impact of an equality constraint on the residual variances across latent classes. We examined the consequences of constraining the residual variances on class enumeration (finding the true number of latent classes) and on the parameter estimates, under a number of different simulation conditions meant to reflect the types of heterogeneity likely to exist in applied analyses. The results showed that bias in class enumeration increased as the difference in residual variances between the classes increased. Also, an inappropriate equality constraint on the residual variances greatly impacted on the estimated class sizes and showed the potential to greatly affect the parameter estimates in each class. These results suggest that it is important to make assumptions about residual variances with care and to carefully report what assumptions are made.
authors.affiliation: Department of Psychology, University of Alabama, Tuscaloosa, AL, USA. mjkim.epsy@gmail.com.
authors.forename: Minjung
authors.initials: M
authors.lastname: Kim
authors.affiliation: Department of Psychology, University of South Carolina, Columbia, South Carolina, USA.
authors.forename: Andrea E
authors.initials: AE
authors.lastname: Lamont
authors.affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster, UK.
authors.forename: Thomas
authors.initials: T
authors.lastname: Jaki
authors.affiliation: Department of Epidemiology and Public Health, University of Miami, Miami, FL, USA.
authors.forename: Daniel
authors.initials: D
authors.lastname: Feaster
authors.affiliation: Department of Psychology, George Washington University, Washington, DC, USA.
authors.forename: George
authors.initials: G
authors.lastname: Howe
authors.affiliation: Department of Individual, Family, & Community Education, University of New Mexico, Albuquerque, NM, 87131, USA. MLVH@unm.edu.
authors.forename: M Lee
authors.initials: ML
authors.lastname: Van Horn
mesh_terms: D001499:Bayes Theorem; D003198:Computer Simulation; D006801:Humans; D015233:Models, Statistical; D009010:Monte Carlo Method; D012044:Regression Analysis
keywords: Differential effects; Effect heterogeneity; Regression mixture; Residual variances