Developing a Locally Adaptive Spatial Multilevel Logistic Model to Analyze Ecological Effects on Health Using Individual Census Records

Geographical variable distributions often exhibit both macroscale geographic smoothness and microscale discontinuities or local step changes. Nonetheless, accounting for both effects in a unified statistical model is challenging, especially when the data under study involve a multiscale structure and non-Gaussian response variables. This study develops a locally adaptive spatial multilevel logistic model to examine binomial response variables that integrates an innovative locally adaptive spatial econometric model with a multilevel model. It takes into account global spatial autocorrelation, local step changes, and vertical dependence effects arising from the multiscale data structure. Another appealing feature is that the spatial correlation structure, implied by a spatial weights matrix, is learned along with other model parameters via an iterative estimation algorithm, rather than being presumed to be invariant. Bayesian Markov chain Monte Carlo (MCMC) samplers are derived to implement this new spatial multilevel logistic model. A data augmentation approach, drawing on recently devised Pólya-gamma distributions, is adopted to reduce computational burdens of calculating binomial likelihoods with a logit link function. The validity of the developed model is evaluated by a set of simulation experiments, before being applied to analyze self-rated health for the elderly in Shijiazhuang, the capital city of Hebei Province, China. Model estimation results highlight a nuanced geography of self-rated health and identify a range of individual- and area-level correlates of health for the elderly. Key Words: geography of health, local spatial modeling, multilevel models, spatial autocorrelation, spatial econometrics.