# Analysis of Ground Subsidence Vulnerability in Urban Areas Using Spatial Regression Analysis
## 5 Spatial Regression Analysis
The model's explanatory power, \(\text{R}^{2}\), showed that the SLM model was 0.173390 and the SEM model was 0.174061, indicating that the explanatory power of SEM was relatively higher. To determine the fit of the model, log-likelihood, AIC, and SC were reviewed, and the log-likelihood values of SLM and SEM were \(-5046.05\) and \(-5053.52\), respectively, indicating that the value of SLM was relatively higher. Both values of AIC and SC of SLM were smaller. Thus, the overall statistics exhibited that \(\text{R}^{2}\) of SEM was higher, although the difference was minimal, while log-likelihood, AIC, and SC values of SLM were all more fit. Thus, the SLM model was finally selected as the most-fit model. The finally selected SLM model was analyzed, and the results show that the diameter and age of water pipelines; the age of sewer pipelines; the diameter of power cables; the diameter of communication pipes; the diameter of heating pipelines; the diameter, average depth, and age of gas pipes; and the density of all six types of pipes had a positive (+) effect on the occurrence of ground subsidence. On the other hand, the average depth of water pipelines, the diameter and the average depth of sewer pipelines, the average depth of \begin{table}
\begin{tabular}{c c c} \hline
**Underground Facility Information** & **Spatial Lag Model** & **Spatial Error Model** \\  & **(SLM)** & **(SEM)** \\ \hline Constant & 0.0235515 *** & \(-0.033493\) *** \\ \hline Water pipeline diameter (cm) & 0.00063 *** & 0.000071 *** \\ Water pipeline average depth (m) & \(-0.010554\) *** & \(-0.00999\) *** \\ Water pipeline age (years) & 0.000899 *** & 0.000957 *** \\ Sewer pipeline diameter (cm) & \(-0.000013\) *** & \(-0.000012\) ** \\ Sewer pipeline average depth (m) & \(-0.012026\) *** & \(-0.009926\) *** \\ Sewer pipeline age (years) & 0.000105 * & 0.000134 ** \\ Power cable diameter (cm) & 0.000644 *** & 0.000657 *** \\ Power cable average depth (m) & \(-0.021835\) *** & \(-0.015158\) *** \\ Underground facility & Power cable age (years) & \(-0.000489\) & \(-0.000689\) * \\ Information & Communication pipe diameter (cm) & 0.00038 *** & 0.000426 *** \\ Communication pipe average depth (m) & \(-0.000115\) & \(-0.000120\) \\ Communication pipe age (years) & \(-0.000039\) & \(-0.000182\) \\ Heating pipeline diameter (cm) & 0.000093 *** & 0.000100 *** \\ Heating pipeline average depth (m) & \(-0.019548\) *** & \(-0.017253\) * \\ Heating pipeline age (years) & \(-0.001199\) *** & \(-0.001354\) *** \\ Gas pipe diameter (cm) & 0.000209 *** & 0.000243 *** \\ Gas pipe average depth (m) & 0.021559 *** & 0.024353 *** \\ Gas pipe age (years) & 0.000644 *** & 0.000735 *** \\ Density of all six types & 0.114037 *** & 0.397172 *** \\ \hline Spatial dependence & Likelihood ratio & \\ \hline Spatial effect & Rho (\(\rho\)) & 0.326620 \\ Lambda (\(\lambda\)) & 0.127047 \\ \hline The explanatory power of the & \(\text{R}^{2}\) & 44.358796 *** \\ model & \(\text{log-likelihood}\) & 0.130332 \\ Fit of the model & AIC & \(-6183.22\) \\ SC & 12,406.4 \\ \hline \end{tabular}  
* \(p\) < 0.05, *** \(p\) < 0.01, and *** \(p\) < 0.001.  
\end{table} 
Table 5: Spatial regression analysis results. power cables, and the average depth and age of heating pipelines were found to have a negative (-) effect on the occurrence of ground subsidence. Additionally, the age of power cables and the average depth and age of the communication pipes were not found to be significant in terms of the occurrence of ground subsidence. Because the likelihood ratio statistic of the SLM model is significant (\(p<0.001\)), it can be concluded that the fit of the model is improved by applying spatial effects. In addition, the value of \(\rho\), the spatial effect, is 0.31534 (\(p<0.001\)). This means that the occurrence of ground subsidence in a specific area that has spatial autocorrelation is affected by about 31.5% of the occurrence of ground subsidence in the surrounding ground.