Incorporating a local-statistics-based spatial weight matrix into a spatial regression model to predict the distribution of invasive Rosa multiflora in the Upper Midwest

In this study, we extended the spatial weight matrix defined by Getis and Aldstadt (2004) to a more general case to predict the distribution of non-native invasive Rosa multiflora among the Upper Midwest counties in a spatial lag model (SLM) context. Both the simulation study and the application to invasive Rosa multiflora data collected in 2005-2006 proved that the modified spatial weight matrix outperforms its original case in diagnostic statistics and resultant invasion maps. The geographical distribution of invasive Rosa multiflora in the Upper Midwest was significantly associated with latitude; local clusters (a group of counties) of high presence/abundance of Rosa multiflora were significantly determined by TRPF (a ratio of road density to percentage of forest cover at the county level), a variable reflecting the intensity of human disturbance. As a conclusion, the SLM model incorporating the modified spatial weight matrix has potential applications in mapping spatial data with strong clustering patterns and estimating spatial autocorrelation structure and covariate effect in ecological studies.