High-dimensional linear mixed model selection by partial correlation

We wish to perform variable selection in high-dimensional linear mixed models where the number of the potential covariates is much larger than the sample size and where the random effects are utilized to describe correlated observations. We propose a variable selection procedure based on the Thresholded Partial Correlation (TPC) algorithm (Li, Liu, and Lou 2017) to conduct variable selection using the partial correlation between the covariates and the response variable conditional on the random effects, and this procedure is called the conditional Thresholded Partial Correlation, denoted by TPCc. This TPCc approach is able to select the fixed effects in high-dimensional data when the covariates are highly correlated. We investigate the performance of the proposed method (TPCc) in a variety of simulated high-dimensional data sets. The simulation results show that the TPCc outperforms the TPC in selecting the most appropriate model among the candidate pool in the mixed modeling setting. We also apply the proposed method to a real high-dimensional data set in the production of riboflavin.