A Flexible Bayesian Multiscale Geographically Weighted Poisson Regression Model: Local Scales and Mixed Effects

The geographically weighted Poisson regression (GWPR) model is a discrete extension of the geographically weighted regression (GWR) model designed for count data. To relax the assumption in the conventional GWPR model that local relationships vary at the same spatial scale, we propose a multiscale GWPR model that allows for varying local scales. In addition, a Bayesian implementation of the multiscale GWPR model is developed, which offers two key advantages: (1) it enables simultaneous estimation of spatially varying coefficients and bandwidths, and (2) it provides a flexible foundation for incorporating mixed effects and nonlinear relationships. An efficient algorithm, integrated nested Laplace approximation (INLA), is employed for fast Bayesian inference. The performance of the proposed method is evaluated through a simulation study, and a premature death counts data set from the state of Georgia.