2.2.4. Geogdetector

The influencing factors have spatial heterogeneity and work together to affect the temperature. Geogdetector is a set of statistical methods for detecting spatial variability and revealing forces driving the variability [32,33]. The advantages of this method are that it cannot only detect both quantitative and qualitative data, but also can detect the interaction of two factors [34]. Geogdetector contains four detectors: a risk detector, a factor detector, an ecological detector, and an interaction detector.

The risk detector can determine whether there is a significant difference in the means of attributes between two sub-regions, using the *t* statistic to test:

$$t\_{\overline{y}\_{h=1}} \overline{y}\_{h=2} = \frac{\overline{Y}\_{h=1} - \overline{Y}\_{h=2}}{\left[\frac{Var\left(\overline{Y}\_{h=1}\right)}{n\_{h=1}} + \frac{Var\left(\overline{Y}\_{h=2}\right)}{n\_{h=2}}\right]^{\frac{1}{2}'}} \tag{10}$$

where *Yh* is the attribution average in the region *h*, *nh* is the sample size of sub-region *h*, and *Var* is the variance. The statistic *t* approximates the Student's distribution, where the degree of freedom (*df*) is calculated as:

$$df = \frac{\frac{Var\left(\overline{Y}\_{h=1}\right)}{n\_{z=1}} + \frac{Var\left(\overline{Y}\_{h=2}\right)}{n\_{z=2}}}{\frac{1}{n\_{h=1} - 1} \left[\frac{Var\left(\overline{Y}\_{h=1}\right)}{n\_{h=1}}\right]^2 + \frac{1}{n\_{h=2} - 1} \left[\frac{Var\left(\overline{Y}\_{h=2}\right)}{n\_{h=2}}\right]^2}}.\tag{11}$$

Null hypothesis: *Yh*=<sup>1</sup> = *Yh*=2. If H0 is rejected at significance level α, there is a significant difference in the mean of the attributes between the two sub-regions.

The factor detector mainly detects the spatial variability of *Y* and the extent to which *X* is probed to explain the spatial differentiation of *Y*. The *q*-value was used to measure the factors:

$$q = 1 - \frac{\sum\_{h=1}^{L} N\_h \sigma\_{\text{fl}}^2}{N\sigma^2} = 1 - \frac{SSW}{SST} \,\text{\,\,\,}\tag{12}$$

$$SSW = \sum\_{h=1}^{L} N\_h \sigma\_h^2 \, \prime \quad SST = N\sigma^2 \, \prime \tag{13}$$

where *h* = 1, ... , *L* is the stratum of *Y* or *X*, *Nh*, and *N* are the unit numbers of layer *h* and the unit numbers of the whole region, respectively, and <sup>σ</sup>*h*<sup>2</sup> and σ2 are the variances of *Y* of the layer *h* and of the whole region, respectively. *SSW* and *SST* are the sum of squares and the total sum of squares, respectively. The range of *q* is [0, 1]. The larger the value, the more obvious the spatial distribution of *Y* is. If the stratum is generated by the independent variable *X*, a larger *q* value shows stronger explanatory power of the independent variable *X* to *Y*, and a smaller *q* means weaker power. In extreme cases, a *q* value of 1 indicates that factor *X* has complete control over the spatial distribution of *Y*, and a *q* value of 0 indicates that factor *X* has no control over the spatial distribution of *Y*.

The ecological detector explores whether a geographical stratum, *C*, is more significant than another stratum, *D*, in controlling the spatial pattern, and the statistic *F* is used to measure it:

$$F = \frac{N\_{X1}(N\_{X2} - 1)SSW\_{X1}}{N\_{X2}(N\_{X1} - 1)SSW\_{X2}} \tag{14}$$

$$SSW\_X = \sum\_{h=1}^{L1} N\_h \sigma\_h^2 \text{ } \text{ } SST\_{X2} = \sum\_{h=1}^{L2} N\_h \sigma\_h^2 \text{ } \text{ } \tag{15}$$

where *Nx1* and *Nx2* are the sample sizes of factors *X1* and *X2*, respectively, and *SSWx1* and *SSWx2* are sums of the variances in the strata formed by *X1* and *X2*, respectively. *L1* and *L2* represent the number of variables in *X1* and *X2*, respectively. H0 is *SSWx1* = *SSWx2*. If H0 is rejected at the significance level of α, there is a significant difference in the spatial distribution of *Y* between *X1* and *X2*.

The interaction detector is used to evaluate whether *X1* and *X2* together will increase or decrease the explanatory power of the dependent variable *Y*, or whether the effects of these factors on *Y* are independent of each other. *q*(*X1*), *q*(*X2*), and *q*((*X1*∩*X2*) were calculated and compared the differences between *q*(*X1*), *q*(*X2*), and *q*((*X1*∩*X2*).

The Geogdetector software was used to calculate Geogdetector. First, we need to calculate the annual average of temperature, AT, NDVI, UD, GDP change rate, and NL in their respective time periods, and convert the data format to .tif format; secondly, a 0.5 × 0.5 km grid is established by ArcGIS software, and each variable is extracted by the points in the grid; next, the extracted AT, NDVI, UD, GDP change rate, and NL were classified respectively. In this study, these variables are divided into five categories according to the natural segmentation method in ArcGIS software. Finally, the processed data is imported into the Geogdetector software for calculation.
