High-dimensional regression with ordered multiple categorical predictors

Area of Science:

• Statistics
• Machine Learning
• Data Science

Background:

• Ordered multiple categorical (OMC) response models are established, but OMC predictors in high-dimensional linear regression are under-researched.
• High-dimensional settings require methods to select relevant variables and handle pseudocategories of discrete predictors.

Purpose of the Study:

• To propose a novel method for linear regression with high-dimensional ordered multiple categorical predictors.
• To address the challenge of automatic variable selection and handling of pseudocategories in OMC predictors.

Main Methods:

• A dummy variable transformation method for OMC predictors.
• An L1 penalty regression approach applied to the transformed variables.
• Derivation of model selection consistency under high-dimensional assumptions.

Main Results:

• The proposed method demonstrates good performance in simulation studies.
• The method shows effectiveness in real data analysis.
• Successful automatic selection of pseudocategories and irrelevant explanatory variables.

Conclusions:

• The developed method offers a robust solution for high-dimensional linear regression with OMC predictors.
• The approach exhibits wide applicability in various regression analysis scenarios.
• Validates the effectiveness of dummy variable transformation and L1 penalty for this specific problem.