Finite mixtures for simultaneously modelling differential effects and non-normal distributions

George, Melissa and Yang, Na and Jaki, Thomas and Feaster, Daniel and Lamont, Andrea E. and Van Horn, M. Lee and Wilson, Dawn K. (2013) Finite mixtures for simultaneously modelling differential effects and non-normal distributions. Multivariate Behavioral Research, 48 (6). pp. 816-844. ISSN 0027-3171

Abstract

Regression mixture models have been increasingly applied in the social and behavioral sciences as a method for identifying differential effects of predictors on outcomes. Although the typical specification of this approach is sensitive to violations of distributional assumptions, alternative methods for capturing the number of differential effects have been shown to be robust. Yet, there is still a need to better describe differential effects that exist when using regression mixture models. This study tests a new approach that uses sets of classes (called differential effects sets) to simultaneously model differential effects and account for nonnormal error distributions. Monte Carlo simulations are used to examine the performance of the approach. The number of classes needed to represent departures from normality is shown to be dependent on the degree of skew. The use of differential effects sets reduced bias in parameter estimates. Applied analyses demonstrated the implementation of the approach for describing differential effects of parental health problems on adolescent body mass index using differential effects sets approach. Findings support the usefulness of the approach, which overcomes the limitations of previous approaches for handling nonnormal errors.