Geographically Weighted Regression Modeling for Multiple Outcomes

Geographically weighted regression (GWR) has been a popular tool applied in various disciplines to explore spatial nonstationarity for georeferenced data. Such a technique, however, typically restricts the analysis to a single outcome variable and a set of explanatory variables. When analyzing multiple interrelated response variables, GWR fails to provide sufficient information about the data because it only allows separate modeling for each response variable. This study attempts to address this gap by introducing a geographically weighted multivariate multiple regression (GWMMR) technique that not only explores spatial nonstationarity but also accounts for correlations across multivariate responses. We first present the model specification of the proposed method and then draw the associated statistical inferences. Several modeling issues are discussed. We also examine finite sample properties of GWMMR using simulation. For an empirical illustration, the new technique is applied to the stop-and-frisk data published by the New York Police Department. The results demonstrate the usefulness of the GWMMR.