Geodetector

Geographic detectors are statistical methods used to detect spatial differentiation and reveal driving factors. The core idea assumes that if an independent variable affects a dependent variable, the spatial distributions of the independent and dependent variables are similar. Geographic detectors include the following four detectors:

Differentiation and factor detection: Detect the spatial differentiation of Y; And the extent to which a factor X can explain the spatial differentiation of attribute Y. Measured by q value, the expression is as follows:

where h represents the stratification of variable Y or factor X, i.e., classification or partition; Nh and N represent the number of units in layer h and the whole region, respectively; σh2 and σ2 represent the variance of layer h and the value of Y in the whole region, respectively; and SSW and SST represent the sum of variance in the layer and the total variance in the whole region, respectively. The range of q is [0,1].

Interaction detection: identify the interaction between different X factors, that is, evaluate whether the explanatory power of X1 and X2 on dependent variable Y increases or decreases, or whether the influence of these factors on Y is independent.

Risk area detection: judge whether the attribute mean value between two sub areas is significantly different, and test with t statistics:

wherein Y¯h represents the attribute mean value in sub-region h, nh represents the number of samples in sub-region h, and Var represents the variance.

Ecological test: compare whether two factors X1 and X2 have significant differences in the impact on the spatial distribution of attribute Y, and use F statistics to measure:

wherein Nx1 and Nx2 represent the sample size of the two factors, SSWX1 and SSWX2 represent the sum of the intra-layer variances of X1 and X2, respectively, and L1 and L2 represent the number of X1 and X2 layers, respectively.