MI- Random rPQL : A Variable Selection Method for Linear Mixed Models with Missing Data

Variable selection, a statistical approach for identifying important predictors of an outcome, becomes particularly challenging when data are both clustered and incomplete. Despite the widespread use of linear mixed models (LMMs) in social and behavioral research, limited work has addressed variable selection in LMMs with incomplete data. Missing data can reduce estimation precision and distort the relationships between predictors and outcomes. Although multiple imputation (MI) is commonly used to handle missing data in clustered settings, aggregating variable selection results across imputed datasets, especially for both fixed and random effects, remains a methodological challenge. This issue is further compounded in high-dimensional contexts, where the number of predictors equals or exceeds the number of within-cluster observations. To address these limitations, we propose MI-random rPQL, a regularization-based method for variable selection in LMMs with incomplete clustered data. The method integrates multiple imputation with random rPQL to jointly identify important fixed and random effects. A simulation study was conducted to evaluate its performance. The results show that MI-random rPQL effectively selects important predictors even under substantial missingness, offering a flexible and robust solution for variable selection in high-dimensional, clustered datasets with incomplete data.