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

Area of Science:

• Statistics
• Computational Statistics

Background:

• Variable selection is crucial for generalized linear mixed models (GLMMs) to prevent overfitting, nonconvergence, and biases.
• Regularized penalized quasi-likelihood (rPQL) methods show promise for selecting both fixed and random effects.
• Practical application of rPQL is hindered by high computational cost, numerous predictors, and multicollinearity.

Purpose of the Study:

• To propose a novel algorithm, random rPQL, to overcome limitations of existing variable selection methods in GLMMs.
• To introduce a new selection criterion, ranking worth estimation, for enhanced regularization.
• To evaluate the accuracy and efficiency of the proposed methods under challenging conditions.

Main Methods:

• Development of the random rPQL algorithm, integrating rPQL estimation with resampling techniques.
• Introduction of the ranking worth estimation criterion for the variable selection process.
• Conducting simulation studies to assess performance under various scenarios, including high-dimensional data and multicollinearity.

Main Results:

• Random rPQL demonstrates high accuracy and efficiency in selecting fixed and random effects.
• The proposed method effectively handles situations where the number of predictors exceeds observations.
• The ranking worth estimation proves robust when integrated with regularization and resampling.

Conclusions:

• The random rPQL algorithm offers a computationally efficient and accurate solution for variable selection in GLMMs.
• The ranking worth estimation enhances the robustness of the selection process.
• The developed approach effectively addresses multicollinearity and high-dimensional predictor issues in statistical modeling.