Accommodating Spatial Heterogeneity in Geographically Weighted Regression with Group Penalty

Data composed of multiple datasets, for example, survey study data collected from multiple geographic locations, has become routine and received increasing attention in recent years. Many existing strategies for analyzing such data either ignore the spatial heterogeneity across locations or are inefficient, leading to "suboptimal" estimation. Partly motivated by a Chinese social survey on pension and healthcare, we develop a geographically weighted group lasso regression (GWGPL), which can effectively accommodate spatial heterogeneity and conduct shared variable selection while promoting structural similarity across locations. Another significant development is that the selection and estimation properties for the proposed approach are rigorously proved. Simulation results demonstrate the competitive advantages of the proposed approach compared to the alternatives. Finally, we apply the proposed approach to the "One Thousand People, One Hundred Villages" social survey data to identify variables associated with inpatient treatment costs, outpatient treatment costs, and self-treatment costs, respectively. For inpatient treatment costs, the number of times receiving inpatient treatment in the past year, household expenditure, whether self-treatments were sought, mental health status, medical institution status, insurance usage, and marital status are identified to be associated variables. Compared to the alternatives, the proposed approach has a grouping structure, smoother coefficient estimation results across locations, and a better prediction performance.