Variable Selection Algorithms for the Proportional Odds Model

• Activity Number: 401
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Xizhen Cai*+ and David Hunter
• Companies: Penn State University and Penn State University
• Keywords: penalized profile likelihood ; consistency ; MM algorithms ; ICM algorithms

Abstract

Variable selection via a penalized likelihood approach has been used for generalized linear models, and corresponding estimates enjoy an oracle property (Fan and Li, 2001). We discuss the problem of variable selection for a sparse proportional odds model, which is a semi-parametric model, and penalized profile likelihood is maximized to estimate and select variables simultaneously. We show under certain regularity conditions that the estimates for nonzero coefficients are normally distributed, while those for zero coefficients are nearly n-consistent. These results are derived using an expansion for the profile likelihood function by Murphy and Van der Vaart (2000), so they can be easily generalized to a much broader range of semi-parametric models. We also provide a further condition on the smoothness of the profile likelihood functions that guarantees sparse estimates. In addition, various algorithms to maximize the penalized likelihood estimator are proposed based on MM algorithm framework.