Spatial Automatic Subgroup Analysis for Areal Data with Repeated Measures

• Activity Number: 220 - Frontiers of Spatio-Temporal Statistical Learning in Health Care and Environmental Science
• Type: Invited
• Date/Time: Tuesday, August 9, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Hao Helen Zhang* and Xin Wang and Zhengyuan Zhu
• Companies: University of Arizona and Miami University and Iowa State University
• Keywords: spatial regression; subgroup analysis; sparsity; ADMM; model selection; clustering

Abstract

Spatial regression is widely used for modeling s relationship between a dependent variable and explanatory covariates. Oftentimes, the linear relationships may vary across space and it is crucial to detect the dynamic variation in the model and identify the underlying location-specific model structure. We propose a new class of spatial subgroup analysis procedure procedure, Spatial Heterogeneity Automatic Detection and Estimation (SHADE), for automatically and simultaneously subgrouping and estimating covariate effects for spatial regression models. The SHADE employs a class of spatially-weighted fusion type penalty on pairwise observations, with weights constructed adaptively using spatial information, to cluster linear regression coefficients into subgroups. Under certain regularity conditions, the SHADE is shown to be able to identify the true model structure with probability approaching one and estimate the subgrouped regression coefficients consistently. A scalable alternating direction method of multiplier algorithm (ADMM)is developed to implement the procedure. We demonstrate empirical performance of the SHADE via simulations and real applications in spatial data analysis.