Categorical Predictors and Pairwise Comparisons in Logistic Regression via Penalization and Bregman Methods

• Activity Number: 257
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section for Statistical Programmers and Analysts
• Author(s): Tian Chen*+ and Howard Bondell
• Companies: North Carolina State University and NC State University
• Keywords: pairwise comparison ; logistic regression ; categorical predictors ; penalization ; Bregman iteration

Abstract

Logistic regression is widely used to study the relationship between a binary response and a set of covariates. When the covariates in the logistic regression are categorical, two goals are determining the important factors, and detecting differences among the levels of these important categorical factors. In this paper, we propose a penalization based approach to conduct these pairwise comparisons among the levels. Within a single procedure, the irrelevant factors can be removed, while the levels within the important factors can be collapsed into groups. We propose an algorithm based on Bregman iterations, which transforms the constrained problem into a series of simple unconstrained problems. The utility of the method itself, as well as the computational approach, are examined via both theory and simulation.