A Hierarchical Bayesian Approach for Finite Mixture of Mode Regression Model Using Skew-Normal Distribution

Abstract

Many data that exhibit asymmetrical behavior can be well modeled with skew-normal random errors. Moreover, data that arise from a heterogeneous population can be efficiently analyzed by a finite mixture of regression models. These observations motivate us to propose a novel finite mixture of mode regression model based on a mixture of the skew-normal distributions to explore asymmetrical data from several subpopulations. Thanks to the stochastic representation of the skew-normal distribution, we construct a Bayesian hierarchical modeling framework and then develop an efficient Markov chain Monte Carlo sampling algorithm to generate posterior samples for obtaining the Bayesian estimates of the unknown parameters and their corresponding standard errors. Simulation studies and a real-data example are presented to illustrate the performance of the proposed Bayesian methodology.

Keywords

Bayesian analysis / Mode regression / Heterogeneous data / Skew-normal distribution / Markov chain Monte Carlo

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