Department of Statistics, The Ohio State University
Statistics and Biostatistics Colloquium Series

Finite mixture models provide a flexible tool for modeling data that arise from a heterogeneous population. When a random variable with a finite mixture distribution depends on certain covariates, we obtain a finite mixture of regression (FMR) model. In the applications of FMR models, such as in biology, genetics, engineering, and marketing, often many covariates are of initial interest and their contributions to the response variable vary from one component to another of the FMR model. This creates a complex variable selection problem. Existing methods, such as AIC and BIC, are computationally expensive as the number of covariates and components in the mixture model increases. In this paper, we introduce a penalized likelihood approach for variable selection in FMR models. The new method introduces penalties that depend on the size of the regression coefficients and the mixture structure. The new method is shown to have the desired sparsity property. A data-adaptive method for selecting tuning parameters and an EM-algorithm for efficient numerical computations are developed. Simulations show that the method performs very well and requires much less computing power. The new method is illustrated by analyzing two real data sets.

Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.