Mixture of regression models with latent variables and sparse coefficient parameters.

Abstract

Mixture models have been widely used in marketing research and epidemiology to capture heterogeneity in endogenous latent variables among individuals. However, when collinearity between endogenous latent variables at the component level is present, some componentspecific path coefficients will be zero. In this paper, a systematic computational algorithm is developed to identify parameters that need to be constrained to be zero and to address other issues including the initialization procedure, the provision of standard errors of estimates, and the method to determine the number of components. The proposed algorithm is illustrated using simulated data and a real data set concerning emotional behaviour of preschool children.