Determining the number of components in mixtures of linear models

Abstract

Methods for determining the number of components in normal mixtures are extended to mixtures of linear regression models. This simulation study evaluates the influence of component separation and mixing proportions on the performance of 22 approximations of measures for determining the number of components in mixtures of linear regression models. Estimated measures based on the maximized log likelihood of the observed data are compared to estimated measures based on the maximized log likelihood of the complete data. Approximations of measures which previously required the convergence rate of the EM algorithm are presented which have no such restriction for their implementation. As an alternative to the EM algorithm, which is known to be sensitive to starting values, differential evolution was the implemented optimization algorithm. This study is further set apart in that the performances of the approximated component measures are explored without assuming the mixing proportions to be equal or assuming equal component variances. Based on the results of the k=1 and 2 component model simulations, the minimum description length, MDL, is the recommended criterion for choosing between one and two component mixtures of linear regression models.