Probability-weighted clustered coefficient regression models in complex survey sampling

Abstract

Regression analysis is commonly conducted in survey sampling. However, existing methods fail when regression models vary across different clusters of domains. In this paper, we propose a unified framework to study the cluster-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 regularity conditions. Numerical experiments demonstrate that the proposed method outperforms its alternatives in terms of identifying the cluster structure and estimation efficiency for both linear regression and logistic regression models. American Community Survey is used as an example to illustrate the advantages of the proposed approach.