Robust geographical detector

Geographical detector (GD) is a method to measure spatial associations using a power of determinant (PD) value that compares the variance of data within spatial zones and in the whole study area. Recent studies have implemented GD in diverse fields, such as environmental and socio-economic issues. Spatial data discretization is an essential stage for determining zones using explanatory variables. However, the spatial data discretization process has been sensitive to the GD results. To address this issue, this article proposes a Robust Geographical Detector (RGD) to overcome the limitations of the sensitivity in spatial data discretization and estimate robust PD values of explanatory variables using a B-value. The RGD determines spatial zones with numerical interval breaks using an optimization algorithm of variance-based change point detection. In this study, RGD is implemented in a nationwide case study exploring potential factors of nitrogen dioxide (NO2) density in industrial regions across Australia, where data on both NO2 and potential factors are sourced from satellite images and remote sensing products using Google Earth Engine. Results show that RGD can effectively explore the maximum PD values of spatial associations between response and explanatory variables due to the optimization algorithm-based spatial zones. In addition, RGD-based PD values are generally higher, more robust, and more stable than GD-based PD values since RGD can guarantee the increment of PD values with the increase of interval numbers, which is a challenge in previous GD models. Finally, RGD could provide a more reliable interpretation of PD as RGD finds optimal intervals-based spatial zones determined by potential factors. This study demonstrates that the developed RGD model can provide robust and reliable solutions to explore spatial associations and identify geographical factors.