Understanding and extending the geographical detector model under a linear regression framework

The Geographical Detector Model (GDM) is a popular statistical toolkit for geographical attribution analysis. Despite the striking resemblance of the q-statistic in GDM to the R-squared in linear regression models, their explicit connection has not yet been established. This study proves that the q-statistic reduces into the R-squared under a linear regression framework. Under linear regression and moderate-to-strong spatial autocorrelation, Monte Carlo simulation results show that the GDM tends to underestimate the importance of variables. In addition, an almost perfect power law relationship is present between the percentage bias and the degree of the spatial autocorrelations, indicating the presence of fast uplifting bias in response to increasing levels of spatial autocorrelations. We propose an integrated approach for variable importance quantification by bringing together the spatial econometrics model and the game theory based-Shapley value method. By applying our proposed methodology to a case study of land desertification in African, it is found human activity tends to affect land desertification both directly and indirectly. However, such effects appear to be underestimated or undistinguished in the classic GDM.