Variable selection in the presence of missing data: resampling and imputation

In the presence of missing data, variable selection methods need to be tailored to missing data mechanisms and statistical approaches used for handling missing data. We focus on the mechanism of missing at random and variable selection methods that can be combined with imputation. We investigate a general resampling approach (BI-SS) that combines bootstrap imputation and stability selection, the latter of which was developed for fully observed data. The proposed approach is general and can be applied to a wide range of settings. Our extensive simulation studies demonstrate that the performance of BI-SS is the best or close to the best and is relatively insensitive to tuning parameter values in terms of variable selection, compared with several existing methods for both low-dimensional and high-dimensional problems. The proposed approach is further illustrated using two applications, one for a low-dimensional problem and the other for a high-dimensional problem.