Regularized reduced rank regression for mixed predictor and response variables.

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• Existing regression models struggle with high-dimensional data containing mixed-type variables.
• The GMR3 model handles mixed response and predictor types but lacks regularization for high dimensionality.

Purpose of the Study:

• Introduce the Generalized Mixed Regularized Reduced Rank Regression (GMR4) model.
• Enhance regression performance in high-dimensional settings with mixed-type predictors and responses.
• Provide a method for estimating key model parameters (rank S and penalty parameter λ).

Main Methods:

• Extension of the GMR3 model incorporating regularization techniques (Ridge, Lasso, Group Lasso).
• Development of a cross-validation procedure for estimating rank (S) and penalty parameter (λ).
• Simulation studies to evaluate model performance across various data scenarios.

Main Results:

• GMR4 demonstrates suitability for datasets with numerous predictors or collinearity.
• Simulation results guide the selection of the penalty parameter (λ).
• Empirical application reveals a sparse, interpretable solution with influential predictors.

Conclusions:

• GMR4 effectively handles high-dimensional data with mixed-type predictors and responses.
• The model provides valuable insights into complex datasets, as shown in the health care application.
• Regularization and cross-validation are key to GMR4's performance in challenging statistical settings.