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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Reduced-rank clustered coefficient regression for addressing multicollinearity in heterogeneous coefficient

Yan Zhong1, Kejun He2, Gefei Li1

  • 1KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai, 200062, China.

Biometrics
|August 13, 2024
PubMed
Summary

This study introduces a novel clustered coefficient regression (CCR) method to stabilize coefficient estimation and clustering, particularly when dealing with multicollinearity in data. The new penalized non-convex optimization approach enhances model stability and accuracy for heterogeneous relationships.

Keywords:
data heterogeneitylocal multicollinearitylow-rank structuresupervised dimensionality reduction

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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.