Slippery slopes: Stastistical methods for spatially varying associations

Regression frameworks provide the basis for many statistical modeling methods. The assumptions of independent, Gaussian errors, fixed associations across the data set, and constant variance provide a comfortable arrangement leading to many of our favorite tools for variable selection, testing, and inference. With geographically referenced data, we often want to loosen each of these restrictions allowing correlated, non-Gaussian errors, spatially varying associations, and heteroskedasticity. In this seminar, we will provide an overview of recent modeling approaches to these settings including geographically weighted regression (GWR), hierarchical modeling with random effects (random intercepts to induce spatial correlation between observations and random slopes to allow associations to vary across space). We will compare and contrast the assumptions, implementation, and inference enabled by these two approaches. We will also explore the robustness of results and assumptions required for successful implementation. We will compare results on data involving violent crime, illegal drug arrests, and alcohol sales.