  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.
