Variable selection in multivariate multiple regression.

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Analyzing correlated multiple responses is crucial in many fields.
• Traditional methods often struggle with mixed outcome types (binary, count, continuous) and require careful correlation modeling.
• Variable selection is essential due to the complexity of multi-response models.

Purpose of the Study:

• To develop a robust method for estimation and variable selection in multi-response regression models with correlated outcomes.
• To extend the generalized estimating equation (GEE) methodology for simultaneous analysis of diverse outcome types.
• To address the challenge of parameter estimation and variable selection in complex correlated response settings.

Main Methods:

• Utilized an extension of generalized estimating equation (GEE) methodology.
• Proposed a penalized-likelihood approach for simultaneous parameter estimation and variable selection.
• Incorporated nonlinear functions to handle diverse outcome types (binary, count, continuous).

Main Results:

• Monte Carlo simulations demonstrated the method's effectiveness across various sample sizes and numbers of response variables.
• The proposed method showed superior performance compared to treating responses as uncorrelated.
• An unstructured correlation model with Bayesian information criterion (BIC) for tuning parameter selection was recommended.

Conclusions:

• The developed penalized-likelihood approach based on extended GEEs provides a valid and efficient tool for analyzing correlated multiple responses.
• The method successfully integrates estimation and variable selection for mixed-type outcomes.
• Practical application using concrete slump test data validated the method's utility.