Using regression mixture models with non-normal data: examining an ordered polytomous approach

George, Melissa and Yang, Na and Van Horn, M. Lee and Smith, Jessalyn and Jaki, Thomas and Feaster, Daniel and Maysn, Katherine and Howe, George (2013) Using regression mixture models with non-normal data: examining an ordered polytomous approach. Journal of Statistical Computation and Simulation, 83 (4). pp. 757-770. ISSN 1563-5163

Abstract

Mild to moderate skew in errors can substantially impact regression mixture model results; one approach for overcoming this includes transforming the outcome into an ordered categorical variable and using a polytomous regression mixture model. This is effective for retaining differential effects in the population; however, bias in parameter estimates and model fit warrant further examination of this approach at higher levels of skew. The current study used Monte Carlo simulations; 3000 observations were drawn from each of two subpopulations differing in the effect of X on Y. Five hundred simulations were performed in each of the 10 scenarios varying in levels of skew in one or both classes. Model comparison criteria supported the accurate two-class model, preserving the differential effects, while parameter estimates were notably biased. The appropriate number of effects can be captured with this approach but we suggest caution when interpreting the magnitude of the effects.