A model-based approach to multivariate principal component regression: Selecting principal components and estimating...

Area of Science:

• Statistics
• Machine Learning
• Data Analysis

Background:

• Principal Component Regression (PCR) is widely used but has limitations.
• Large variance principal components (PCs) may not be relevant to outcomes.
• Unstandardized regression coefficients lack standard error estimates, hindering interpretation.

Purpose of the Study:

• To address limitations in PCR by proposing a novel model-based approach.
• To enable testing the explanatory power of individual PCs.
• To enable computation of standard error estimates for unstandardized regression coefficients.

Main Methods:

• Developed a model-based approach for multivariate PCR.
• Incorporated two mean and covariance structure models.
• Estimated models to derive inferential information.

Main Results:

• The proposed approach allows for testing the relevance of individual PCs.
• Standard error estimates for unstandardized regression coefficients can be computed.
• Validation through a real-world example and simulation studies under various conditions.

Conclusions:

• The new model-based approach enhances the interpretability and inferential capabilities of PCR.
• Addresses key limitations regarding PC relevance and coefficient interpretation.
• Provides a robust method for statistical inference in PCR applications.