Reduced-rank clustered coefficient regression for addressing multicollinearity in heterogeneous coefficient...

Area of Science:

• Statistics
• Econometrics
• Machine Learning

Background:

• Clustered coefficient regression (CCR) models heterogeneous relationships between variables.
• Existing CCR methods often suffer from unstable estimation and clustering due to multicollinearity.
• Addressing multicollinearity is crucial for reliable CCR model application.

Purpose of the Study:

• To develop a more stable and robust clustered coefficient regression method.
• To introduce a penalized non-convex optimization approach for CCR.
• To improve coefficient estimation and clustering in the presence of multicollinearity.

Main Methods:

• Introduced a low-rank structure for the CCR coefficient matrix.
• Proposed a penalized non-convex optimization problem with an adaptive group fusion-type penalty.
• Developed an iterative algorithm with guaranteed convergence for solving the optimization problem.
• Derived an upper bound for coefficient estimation error.

Main Results:

• The proposed method demonstrates superior performance compared to existing CCR techniques.
• Empirical studies on simulated and real-world COVID-19 mortality data validate the method's effectiveness.
• The new approach effectively handles multicollinearity, leading to stable estimation and clustering.

Conclusions:

• The novel CCR method offers enhanced stability and accuracy in modeling heterogeneous relationships.
• The proposed penalized optimization and iterative algorithm provide a robust solution for CCR.
• This advancement has significant implications for statistical modeling in various fields, including epidemiology.