Resampling Methods for Variable Selection in the Presence of Missing Data for Small- and Large-Scale Problems

• Activity Number: 208
• Type: Invited
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Qi Long*+ and Brent A. Johnson
• Companies: Emory University and Emory University
• Keywords: Bootstrap imputation ; Missing data; ; Resampling ; Stability selection; ; Variable selection

Abstract

In the presence of missing data, variable selection procedures need to be tailored to missing data mechanisms and statistical approaches that are used for handling missing data.We focus on the mechanism of missing at random (MAR) and variable selection procedures that can be combined with imputation methods. We investigate a general resampling approach (BI-SS) that combines bootstrap imputation (Efron, 1994) and stability selection (Meinshausen and Buhlmann, 2010), a subsampling/resampling approach for variable selection developed for fully observed data. As a result of drawing strength from these two seminal works, our proposed approach achieves good performance in variable selection for both small-scale and large-scale problems and for general missing data patterns. In particular, it is not sensitive to the values of two tuning parameters, namely, the amount of regularization and the threshold for selection. For comparison, we also investigate an alternative approach that combines bootstrap imputation with Bolasso (Bach, 2008), another recently proposed variable selection procedure based on resampling. This alternative approach is shown to be inferior to BI-SS, and in particular,