## 3 Materials and Methods
### Multivariate Logistic Regression  
The logistic regression model is one of the classical machine learning methods and is commonly used in simulating urban expansion [39]. In comparison to the support vector machine and the neural network model, the logistic regression model has great advantages in training and recognition time [40]. The driving forces of spatial zoning were selected from previous studies that assessed the independent variables of urban expansion in the context similar to our own [39; 40; 41]. Three driving forces--the intensity of human activities, the human-environment interaction effect, and the physical geography and ecological backgrounds--are identified and indicted by four factors: NTL, \(GPP\), Road map, and \(LST\). The mathematical expression of multivariate logistic regression is as follows:  
\[\text{lg}P=Z= \alpha+\sum_{i=1}^{4}\beta_{i}X_{i} \tag{1}\]  
\[P=\frac{\text{e}^{Z}}{1+\text{e}^{Z}} \tag{2}\]  
where \(P\) is the urban spatial attribute index (USAI), \(\alpha\) represents the error value of urban spatial development probability without the selected factors, \(\beta_{i}\) is the logistic regression coefficient, and \(X_{i}\) represents independent variables. The NPP-VIIRS Nighttime Light remote sensing image dataset includes Raw Data Records (RDR), Sensor Data Records (SDR), and Environment Data Records (EDR), i.e., three levels of processing data products. The SDR product of the NPP-VIIRS monthly night light remote sensing image dataset from January 2018 to December 2018 was adopted with a spatial resolution of 500 m and sorted into the total brightness data of nighttime light in the Su-Xi-Chang region. MODIS MOD17A2 is an 8-day synthesis of \(GPP\) products. Each MOD17A2 data set represents the average of the corresponding 8-day \(GPP\) data. Therefore, the collation formula of the MOD17A2 data set from 2018 is as follows:  
\[GPP_{2018}=5\times Collect_{46}+\sum_{i=1}^{45}8\times Collect_{i} \tag{3}\]  
where \(GPP_{2018}\) is the total value of \(GPP\) from 2018 on each pixel, \(Collect_{i}\) represents the \(GPP\) value of each period from phase 1 to 45, and \(Collect_{46}\) is the \(GPP\) value for phase 46. Finally, the total value of \(GPP\) in the Su-Xi-Chang region for 365 days was calculated. Roads of various levels in the traffic network were sorted out and weighted as shown in Table 2. By using the ArcGIS linear density method, the traffic network density of the Su-Xi-Chang region was calculated as follows:  
\[\textit{RoadDensity}=\frac{L_{1}\times V_{1}+L_{2}\times V_{2}+\ldots+L_{n} \times V_{n}}{S_{circle}} \tag{4}\]  
where \(L_{1}\), \(L_{2}\), and \(L_{n}\) are the lengths of each linear element in a certain distance region of per space unit respectively. \(V_{1}\), \(V_{2}\), and \(V_{n}\) are corresponding weight values, respectively. \(S_{circle}\) represents the area of the space unit. _LST_ data were processed using the MODIS Conversion Toolkit (MCTK) by ENVI so as to carry out the coordinate system transformation and numerical sorting. Since the MYD11A2 dataset takes 8 days and each period of the MYD11A2 dataset is the average value of the _LST_ data, the collation formula of the MOD17A2 dataset from 2018 is:  
\[LST_{2018}=\frac{5\times Collect_{46}+\sum\limits_{i=1}^{45}8\times Collect_{i} }{365} \tag{5}\]  
where \(LST_{2018}\) is the average value of _LST_ from 2018 on each pixel, \(Collect_{i}\) represents the _LST_ value of each period from phase 1 to 45, \(Collect_{46}\) is the _LST_ value for phase 46. Finally, the average value of \(GPP\) in the Su-Xi-Chang region for 365 days was calculated. To obtain the model samples of multiple logistic regression analysis in the study area, the normalization results of various factors and the distribution of the urban spatial types (urban land = 1, non-urban land = 0) were taken as independent and dependent variables respectively. A total of 17,446 sample points were evenly selected with an equal distance of 500 m, and the values of each data were selected as independent variables.