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

The article focuses on developing a reduced-rank clustered coefficient regression (CCR) model to address instability caused by multicollinearity in heterogeneous coefficient estimation. The proposed method introduces a low-rank structure in the coefficient matrix and employs a penalized non-convex optimization with an adaptive group fusion penalty, enabling stable estimation and unified clustering of observations. Theoretical properties, including an upper bound on estimation error, are established, and an iterative algorithm with guaranteed convergence is proposed. Empirical studies on simulated data and a COVID-19 mortality rate dataset across U.S. counties demonstrate the method's superior stability, interpretability, and predictive performance compared to existing CCR approaches. The model also facilitates factor analysis of heterogeneous associations, providing insights into spatial and demographic variations in COVID-19 mortality.