Scale and Correlation in Multiscale Geographically Weighted Regression (MGWR)

Multiscale Geographically Weighted Regression (MGWR) is a relatively recent innovation and addition to the family of spatial regression models capable of investigating process heterogeneity. Compared with its predecessor, Geographically Weighted Regression (GWR), MGWR relaxes the assumption of a uniform spatial scale across all modeled processes. That is, MGWR allows for the possibility that some processes vary locally while others vary regionally or not at all. As a result, it provides more accurate parameter estimates. However, this relationship between scale and the correlation within and across geographically weighted regressors (i.e., spatial autocorrelation and multicollinearity) has yet to be formally investigated. This paper sheds light on this issue via two sets of controlled simulation experiments. The results suggest that both types of correlations have a negligible effect on MGWR performance until they become very strong, and their impacts are cumulative. Overall, MGWR is better at alleviating any potential local multicollinearity issues than GWR due to the varying scales estimated for different parameter surfaces. Two additional insights were obtained regarding scale. First, high levels of spatial autocorrelation may potentially contribute towards the underestimation of scale for certain processes, typically those with the lowest level of spatial heterogeneity (including the intercept), potentially falsely identifying local effects. Second, high levels of collinearity may contribute to the misidentification of anticipated scales. In some cases, when the true process is spatially varying, collinearity may lead the bandwidth to be overestimated, which can help mitigate issues associated with high collinearity but may also lead to difficulty identifying local effects. In other cases, when the true process is constant, collinearity may lead the bandwidth to be underestimated but is not problematic for accurately estimating coefficients unless collinearity becomes high. As a result, it is suggested that the optimal bandwidths estimated from MGWR be interpreted with some caution for the additional factors that may influence them. These results have important implications for empirical applications of MGWR.