An optimal multivariate-stratification geographical detector model for revealing the impact of multi-factor combinations on the dependent variable

Spatial heterogeneity (SH), known as the second law of geography, has been a topic of extensive research. One common approach to analyzing SH involves comparing variances between and within strata to assess the impact of independent variables on the dependent variable. This method, known as spatial stratified heterogeneity (SSH) analysis, is often performed using the geographical detector model. Over time, several optimized versions of geographical detectors have emerged, focusing on discretizing single or dual variables. However, methods for discretizing three or more variables are still limited to the interaction detector, with research on spatial scale effects mainly focused on single factors. To overcome these limitations, an optimal multivariate-stratification geographical detector (OMGD) model has been developed. This model includes two additional modules: factor discretization optimization and scale detector. Fine-tuning factor discretization involves using five univariate and five cluster-based stratification methods to automatically explore the optimal discretization scheme for single factors or multi-factor combinations based on the Geodetector q statistics. The scale detector can then iterate through various spatial scales to identify the optimal spatial scale for SSH analysis. Furthermore, the developed OMGD model has been tested with multiple case datasets to validate its applicability and robustness. The findings demonstrate that the OMGD model can effectively extract the main attributes of single factors and multi-factor combinations, providing a better explanation for geographical phenomena. It can also automatically determine the best spatial scale for SSH analysis, thereby enhancing the overall capability of conducting SSH analysis with the geographical detector.