Variable selection for high-dimensional incomplete data using horseshoe estimation with data augmentation

Bayesian shrinkage methods have been widely employed to perform variable selection with high-dimensional data. However, the presence of missing data hinders the implementation of these methods. Since complete case analyses can lead to biased estimates, applicable and efficient methods of variable selection with imputation are needed to obtain valid results. In order to address this issue, we propose an algorithm that employs the horseshoe shrinkage prior for shrinkage and multiple imputation for missing data in high-dimensional settings with a practical suggestion on model selection decision strategy. Simulation studies and real data analyses are presented and compared with those of other possible approaches. The simulation results suggest that the proposed algorithm can be considered as a general strategy for model selection of incomplete continuous data.