## 4 Results  
### Landslide Susceptibility Map Using the Proposed Model  
Based on the hydrologic analysis tool in ArcGIS environment, we segment the topography of the study area into 55,899 slope units in total. The schematic diagram of slope units is shown in Figure 3.  
Firstly, in order to test the global multicollinearity, the variance inflation factor (VIF) value of each influencing factor is calculated (results shown in Table 2). A greater VIF value indicates a greater multicollinearity of the influencing factors. A value greater than 10 denot  
Figure 3: Schematic diagram of spatial proximity expression in slope units.  
problems may exist. In this case, elevation factor for instant, the maximum VIF value is 1.88, which is apparently lower than 10. Table 2 indicates that all of the influencing factors used in the proposed S-GWR model pass the global multicollinearity test.  
Then, the local multicollinearity problem is subsequently processed with PCA method. According to the principles of selecting principal components, four principal components are selected in our study, and the components explained 81.10% of the total variances. After the factor rotation, four new principal components were obtained. As is shown in Table 3, the accumulative loadings of four principal components decrease systematically. The first component can be interpreted as geological factor, as it has high positive loadings of distance-to-fault and lithology. The second component has high positive loadings of slope and slope height, indicating that this component represents slope shape factor. In the same way, the third and the fourth component represent hydrographic factor and aspect factor, respectively.  
The S-GWR model is constructed using the Gaussian kernel function and the AIC method. The neighbors of the model estimated by the AIC method is 1000. According to the prediction results, landslide susceptibility of Qingchuan County is mapped. The landslide susceptibility map is classified into five classes based on the natural breaks method [48], including very low, low, moderate, high, and very-high (shown in Figure 4). The landslide susceptibility map shows that the high-susceptibility area and very-high-susceptibility area are highly consistent with the actual landslide points, and very-low- to very-high-susceptibility classes occupy 46.37%, 25.67%, 17.62%, 8.69%, and 1.65% of study area.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Influencing Factors** & **VIF** \\ \hline Slope & 1.61 \\ Aspect & 1.06 \\ Elevation & 1.88 \\ Slope height & 1.52 \\ Lithology & 1.35 \\ Distance-to-fault & 1.87 \\ Distance-to-stream & 1.12 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Test results of variance inflation factor method of S-GWR.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Principal Components** & **PC1** & **PC2** & **PC3** & **PC4** \\ \hline Slope & 0.128 & 0.858 & 0.047 & 0.133 \\ Aspect & 0.038 & 0.132 & 0.055 & 0.981 \\ Elevation & 0.675 & 0.374 & 0.374 & \(-\)0.007 \\ Slope height & 0.106 & 0.861 & \(-\)0.152 & \(-\)0.010 \\ Lithology & 0.829 & \(-\)0.030 & \(-\)0.195 & 0.108 \\ Distance-to-fault & 0.860 & 0.122 & 0.110 & \(-\)0.066 \\ Distance-to-stream & 0.070 & \(-\)0.106 & 0.939 & 0.055 \\ Accumulative loadings & 2.706 & 2.211 & 1.178 & 1.194 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Rotated component loadings of the indicators on selected principal components.