Probability Weighted Clustered Coefficients Regression Models in Complex Survey Sampling

TL;DR

This paper introduces a new regression framework for complex survey data that effectively identifies group-specific effects and improves estimation accuracy using pairwise penalties and ADMM optimization.

Contribution

It proposes a unified group-wise covariate effect model for survey sampling, addressing variability across domains with a novel pairwise penalty approach.

Findings

The method accurately identifies groups in survey data.

It improves estimation efficiency over existing methods.

Theoretical properties are validated through numerical experiments.

Abstract

Regression analysis is commonly conducted in survey sampling. However, existing methods fail when the relationships vary across different areas or domains. In this paper, we propose a unified framework to study the group-wise covariate effect under complex survey sampling based on pairwise penalties, and the associated objective function is solved by the alternating direction method of multipliers. Theoretical properties of the proposed method are investigated under some generality conditions. Numerical experiments demonstrate the superiority of the proposed method in terms of identifying groups and estimation efficiency for both linear regression models and logistic regression models.