Variable Selection in Linear Regression Models for Incomplete Dataset

• Activity Number: 106
• Type: Contributed
• Date/Time: Monday, August 12, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Stat. Sciences*
• Author(s): Xiaowei Yang*+ and John Boscardin and Thomas Belin
• Affiliation(s): University of California, Los Angeles and University of California, Los Angeles and University of California, Los Angeles
• Keywords: Bayesian Variable Selection ; Missing Data ; Linear Regression Models ; Multiple Imputation

Abstract

When analyzing incomplete datasets using linear regression models, most popular soft packages discard the incomplete cases from consideration. A better solution is via Multiple Imputation, but for the task of variable selection it faces difficulty. Standard variable selection methods, such as stepwise, usually result in models with different selected predictors for each of the imputed datasets; thus, they cannot be simply merged into one final single model. Bayesian variable selection offers a solution to the difficulty by giving posterior selection probabilities of all possible models for each imputed dataset. Two strategies are proposed in this paper: "Impute Then Select" (ITS) and "Simultaneously Impute And Select" (SIAS). Both are generic frameworks that allow different Bayesian variable selection algorithms. ITS first does Multiple Imputation, then applies Bayesian variable selection to the multiple imputed datasets and, finally, combines the posterior selection probabilities. SIAS does Bayesian variable selection and missing data imputation simultaneously within one Gibbs Sampling process. Preliminary studies show that both of them are promising in application.