On Optimized Shrinkage Variable Selection in Generalized Linear Models

• Activity Number: 178
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Erin Melcon*+
• Companies: University of California at Davis
• Keywords: Adaptive Lasso ; Bootstrap ; Generalized Linear Models ; Lasso

Abstract

The lasso (Tibshirani, 1996) and adaptive lasso (Zou, 2006) have become popular methods of model selection in linear models (LMs). Recently, Hastie and Park (2006) extended the lasso and adaptive lasso into generalized linear models. Both of these methods involve penalizing the regression coefficients, and shrinking a subset of them to zero. This has made the lasso and adaptive lasso popular for model selection. A difficulty for any penalization procedure is the amount of shrinkage to apply to the coefficients, or in other words, what is the ``best'' value of the penalization parameter. Current methods for selecting the penalty parameter in GLMs are cross validation and information criteria. In this paper, we extend the idea of the fence method (Jiang et. al) to GLMs, and show that the proposed bootstrap method outperforms cross validation and the information criteria.