Variable selection for varying dispersion beta regression model

Abstract

The beta regression models are commonly used by practitioners to model variables that assume values in the standard unit interval (0, 1). In this paper, we consider the issue of variable selection for beta regression models with varying dispersion (VBRM), in which both the mean and the dispersion depend upon predictor variables. Based on a penalized likelihood method, the consistency and the oracle property of the penalized estimators are established. Following the coordinate descent algorithm idea of generalized linear models, we develop new variable selection procedure for the VBRM, which can efficiently simultaneously estimate and select important variables in both mean model and dispersion model. Simulation studies and body fat data analysis are presented to illustrate the proposed methods.

Keywords:

• beta regression
• varying dispersion
• variable selection
• coordinate descent algorithm
• BIC

AMS 2000 Subject Classifications:

• Primary: 62G10
• Secondary: 62G08

Acknowledgements

The authors are grateful to the editors and the reviewers for their insightful comments and suggestions, which have greatly improved this paper. The research was supported in part by National Natural Science Foundation of China (11171112, 11101114, 11201190), National Statistical Science Research Major Program of China (2011LZ051), The Natural Science Project of Jiangsu Province Education Department (13KJB110024) and the Natural Science Foundation of Zhejiang Province Education Department (Y201121276).