In this study, we extend the spatial weight matrix defined by Getis and Aldstadt (2004) to a more general case. The modified spatial weight matrix performs better than the original spatial weight matrix since the modified spatial weight matrix adjusts weights of observations based on the distance from other observations. Both the simulation study and the application to the ecological process of invasion of non-native invasive plants (NNIPs) provide evidences for the better performance of the modified spatial weight matrix. We also develop procedures that can be used to quantify the invasion stages of NNIPs. The resultant map of invasion stage on county-level provides a useful and meaningful tool for policy makers; especially, it can be used to optimize allocation of management resources. The result of simultaneous autoregressive model shows that not only the biotic and abiotic factors but also human activities play an important role in the establishment and spread of multiflora rose in the Upper Midwest. It also shows the tendency of the establishment and spread of multiflora rose (Rosa Multiflora, Thunb. ex Murr.) in the Upper Midwest.