A Skew-Normal Mixture Regression Model

Abstract

A challenge associated with traditional mixture regression models (MRMs), which rest on the assumption of normally distributed errors, is determining the number of unobserved groups. Specifically, even slight deviations from normality can lead to the detection of spurious classes. The current work aims to (a) examine how sensitive the commonly used model selection indices are in class enumeration of MRMs with nonnormal errors, (b) investigate whether a skew-normal MRM can accommodate nonnormality, and (c) illustrate the potential of this model with a real data analysis. Simulation results indicate that model information criteria are not useful for class determination in MRMs unless errors follow a perfect normal distribution. The skew-normal MRM can accurately identify the number of latent classes in the presence of normal or mildly skewed errors, but fails to do so in severely skewed conditions. Furthermore, across the experimental conditions it is seen that some parameter estimates provided by the skew-normal MRM become more biased as skewness increases whereas others remain unbiased. Discussion of these results in the context of the applicability of skew-normal MRMs is provided.