Quantifying geographic variations in associations between alcohol distribution and violence: a comparison of geographically weighted regression and spatially varying coefficient models

Past studies consistently indicate measurable local associations between alcohol distribution and the incidence of violence. These results, coupled with measurements of spatial correlation, reveal the importance of spatial analysis in the study of the interaction of alcohol and violence. While studies increasingly incorporate spatial correlation among model residuals to improve precision and reduce bias, to date, most analyses assume associations that are constant and independent of location, an assumption coming under increasing scrutiny in the quantitative geography literature. In this paper, we review and contrast two approaches for the estimation of and inference for spatially heterogeneous effects (i.e., associative factors whose impacts on the outcome of interest vary throughout geographic space). Specifically, we provide an in-depth comparison of geographically weighted regression models (allowing covariate effects to vary in space but only allowing relatively ad hoc inference) with variable coefficient models (allowing varying effects via spatial random fields and providing model-based estimation and inference, but requiring more advanced computational techniques). We compare the approaches with respect to underlying conceptual structures, computational implementation, and inferential output. We apply both approaches to violent crime, illegal drug arrest, and alcohol distribution data from Houston, Texas and compare results in light of the differing methodological structures of the two approaches.