Joint variable selection in generalized linear mixed models with random regularized penalized quasi-likelihood technique.

Abstract

Variable selection provides a pathway toward preventing generalized linear mixed models from encountering issues of model overfitting, nonconvergence, low external validity, and estimation biases. Among the various selection approaches, the methods of regularized penalized quasi-likelihood (rPQL) show some superiority in jointly choosing both important fixed and random effects. However, three challenges limit the wider usage of the variable selection approaches in practice: the high computational cost, the outnumbered predictors problem, and multicollinearity. To overcome these challenges, the current study proposes a new algorithm, the random rPQL, that incorporates an rPQL estimation with the resampling technique. In addition, the study introduces a new selection criterion, the ranking worth estimation, to the selection process. Simulation results indicate (a) random rPQL can select fixed and random effects with high accuracy and efficiency even when the number of candidate variables exceeds within-group observations or when severe multicollinearity exists. (b) The results also show that the ranking worth estimation is more robust in the progress of regularization integrated with the resampling approach. (PsycInfo Database Record (c) 2025 APA, all rights reserved).