Variable Selection of Spatial Generalized Linear Models: A Penalized Quasi-Likelihood Approach

• Activity Number: 176
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Wenning Feng*+ and Chae Young Lim and Tapabrata Maiti
• Companies: Michigan State University and Michigan State and Michigan State University
• Keywords: Generalized linear model ; Spatial statistics ; Variable selection ; Penalized Quasi-likelihood ; Increasing domain asymptotic ; Spatial binary data

Abstract

The penalized likelihood approach is one of the most popular variable selection methods for high-dimensional statistical modeling. In the spatial statistics literature, the corresponding adaption under the spatial linear model has been developed in several pieces of work recently. However, few contributions are made under the spatial generalized linear model. The main challenges are the spatial correlation structure and the difficulty in deriving the likelihood. In this paper, we propose a penalized quasi-likelihood approach to perform the variable selection in spatial generalized linear models. A computationally efficient algorithm is developed to obtain the approximate penalized quasi-likelihood estimates. Under the increasing domain design, we establish the consistency, asymptotic distribution and oracle properties of the variable selection estimation in the spatial logistic regression model, which differs from the existing theory of variable selection. The effectiveness of our approach is demonstrated in a number of simulation studies. As an application, we apply our method in a Michigan lung cancer data set.