Componentwise variable selection in finite mixture regression

摘要

The finite mixture regression is a method to account for heterogeneity in relationship between the response variable and the predictor variables. The goal of this research is to investigate the variable selection issue within each component in the finite mixture regression. This has not been studied much in the literature from a Bayesian perspective. We propose an approach by embedding variable selection into the data augmentation method that iteratively updates estimation in two steps: estimate parameters for each component and determine the latent membership of each observation. Componentwise variable selection is realized by imposing special priors or procedures designed for parsimony in the first step. Due to separation of the two steps, our approach provides a freedom to choose from a wide variety of variable selection techniques. In particular, we illustrate how two popular variable selection techniques can be embedded in the proposed approach: $g$-prior and Stochastic Search Variable Selection. A simulation study is conducted to assess performance of the proposed approach under a variety of scenarios through investigating accuracy of variable selection and clustering. Results show that the proposed approach successfully identifies important variables even in noisy scenarios. The proposed approach is also applied to a real data set from bioinformatics and the results provide evidence to an existing hypothesis.