Weighted Clustered Coefficients Regression Models in Survey Sampling

Regression models are studied in survey data and are widely used to construct model-based estimators. Oftentimes, the relationships vary across different subjects or domains. Identifying a correct model structure with consideration of sampling weights is essential in making inferences and estimating population parameters. In this work, we propose the weighted clustered coefficients regression models for grouping covariate effects for survey data. The new method uses a weighted loss function and pairwise penalties on all pairs of observations. An algorithm based on the alternating direction method of multipliers algorithm is developed to obtain the estimates. We also study the theoretical properties of the estimator under the survey sampling setup. In the simulation study, the empirical performance of the proposed estimator is compared to the method without sampling weights, which suggests that sampling weights is important in identifying clusters in regression models.