A New Semiparametric Approach to Finite Mixture of Regressions Using Penalized Regression via Fusion

• Activity Number: 610
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Erin Austin*+ and Wei Pan and Xiaotong Shen
• Companies: University of Minnesota and University of Minnesota and University of Minnesota
• Keywords: FMR ; Group LASSO ; Group TLP ; Semiparametric

Abstract

For some modeling problems a population may be better assessed as an aggregate of unknown subpopulations, each with a distinct relationship between a response and associated variables. The finite mixture of regressions (FMR) model, where an outcome is derived from one of a finite number of linear regression models, is a natural tool in this setting. In this article we first propose a novel penalized regression approach, then we demonstrate how it can, in some types of problems, better identify subpopulations and their corresponding models than a semiparametric FMR method. Our new method fits models for each person via grouping pursuit, utilizing a new group truncated L1-penalty (gTLP) that shrinks differences between estimated parameter vectors. The methodology causes the individuals' regression coefficients to cluster into a few common models, in turn revealing previously unknown subpopulations. In fact, by varying the penalty strength, the new method can reveal a hierarchical structure among the subpopulations that can be useful in exploratory analysis. Real data analysis shows the performance of the method is promising.