Modeling spatial variation in the relationships between violence and alcohol and drug use: A comparison of geographically weighted regression and Bayesian spatially varying coefficient process models

Previous studies consistently indicate measurable local associations between alcohol and drug usage and the incidence of violence, which reveal the importance of spatial analysis in the study of alcohol, drugs, and violence. While studies increasingly incorporate spatial correlation among model residuals to improve model performance, many analyses assume associations that are constant across a study area, an assumption that has come under scrutiny in the statistics and geography literature. In this paper, we compare and contrast two approaches for the estimation of potentially spatially varying regression effects. Specifically, we provide a comparison of a geographically weighted regression (GWR) model with a Bayesian spatially varying coefficient process model, where comparable spatial dependence functions are used. We compare the approaches with respect to conceptual structures, computational implementation, and inferential output. We apply both approaches to model the relationships of violent crime with illegal drug arrest and alcohol sales data from Houston, Texas and compare their results. We also present results of diagnostic tools for