Visualizing and Diagnosing Coefficients from Geographically Weighted Regression Models

Abstract

Visualizing and interpreting regression coefficients from spatially varying coefficient models, such as geographically weighted regression (GWR), can be challenging, given the amount of information the models provide the spatial analyst. Adding to the visualization dilemma are various diagnostic tools for checking the coherence of the model. One such diagnostic tool is based on decomposing the regression coefficient variance matrix to test for collinearity, which is relevant because previous research has shown that collinearity in GWR can lead to estimated regression coefficients for multiple regression terms that are strongly correlated with each other. In this paper, visualization tools, such as linked scatter plots, parallel coordinate plots, and maps, are presented for diagnosing correlation in estimated regression coefficients that can be problematic for statistical inference of relationships between variables. These tools help explain patterns of dependence between regression terms apparent in scatter plots of estimated coefficients and link the structure in the scatter plots to locational information in a map. Visualization of this information should aid in the typical spatially varying coefficient model estimation process. A case study of census undercount in Franklin County, Ohio is presented as an illustrative example of applying the visual diagnostic approach in a GWR analysis.