## 3 Results and Discussion
### Judment Results, Logit Regression  
The same eight factors debris-flow variables were subjected to logit regression analysis according to the following two equations:  
\[\mathrm{P}=\frac{1}{1+\mathrm{e}^{-\lambda}}, \tag{9}\]  
\[\lambda=\sum_{i=1}^{\mathrm{m}}\mathrm{W_{i}L_{i}}+\sum_{j=1}^{n}\mathrm{W_{m+ j}L_{j}}+\sum_{K=1}^{0}\mathrm{W_{m+n+k}L_{k}}+\mathrm{C}, \tag{10}\]  
in which \(\mathrm{P}\) is the likelihood that a debris flow will occur, \(\mathrm{L}\) is the debris-flow factor resulting from Equation (8), and \(\mathrm{W}\) is the regression coefficient. Table 12 shows the weight coefficients for each factor, and the polynomial resulting from the logit regression analysis is the following:  
\[\lambda=0.173\times\mathrm{L_{1}}+0.118\times\mathrm{L_{2}}-0.013\times \mathrm{L_{3}}-1.378\times\mathrm{L_{4}}-0.010\times\mathrm{L_{5}}+0.044\times \mathrm{L_{6}}-0.002\times\mathrm{L_{7}}+0.057\times\mathrm{L_{8}}-6.978 \tag{11}\]  
The likelihood value of a debris flow occurring was then obtained by substituting the results obtained from Equation (10) into Equation (8). If the value of \(\mathrm{P}\) was greater than or equal to 0.5, it indicated that that such an event had happened. If \(\mathrm{P}\) was smaller than 0.5, on the other hand, it had not happened. Table 13, which presents the researchers' logit regression findings, shows that the validation sample's interpretation accuracy rate was 83.0%, and that of the training sample was 79.7%, making for an overall interpretation-accuracy rate of 80.6%. The ratio of occurrence and non-occurrence in logit regression should ideally be 1:1, which could explain why its accuracy was not higher. Given the small number of debris-flow disasters relative to the number of rainfall events that could potentially trigger them, therefore, the difference in the parameters themselves is larger, so its correct interpretation is worse. By analyzing the slope potential factors of the Ching-Shuei River using Rogers regression, the relationship between the coefficients and landslide could be understood through \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Code Name** & **Factor** & **Coefficient** & **Coefficient Value** \\ \hline \(L_{1}\) & Total area of the catchment area & \(W_{1}\) & 0.173 \\ \(L_{2}\) & Average slope of the catchment area & \(W_{2}\) & 0.118 \\ \(L_{3}\) & Average slope of the stream bed & \(W_{3}\) & \(-0.013\) \\ \(L_{4}\) & Shape coefficient & \(W_{4}\) & \(-1.378\) \\ \(L_{5}\) & Type of stratum & \(W_{5}\) & \(-0.010\) \\ \(L_{6}\) & Distance from the fault & \(W_{6}\) & 0.044 \\ \(L_{7}\) & Maximum daily rain & \(W_{7}\) & \(-0.002\) \\ \(L_{8}\) & Maximum hourly rainfall & \(W_{8}\) & 0.057 \\  & Constant & & \(-6.978\) \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Coefficient table of the logit regression. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Classification Result**} \\  & **Category** & **0** & **1** & **Total** \\ \hline Training sample & 0 & 74 (96.1\%) & 3 (3.9\%) & 77 (100\%) \\ (118 rows) & 1 & 21 (51.2\%) & 20 (48.8\%) & 41 (100\%) \\ \multicolumn{3}{c}{Correct discrimination rate = [(74 + 20)/(77 + 41)] \(\times\) 100\% = 79.7\%} \\ Validation & 0 & 35 (89.7\%) & 4 (10.3\%) & 39 (100\%) \\ sample (47 rows) & 1 & 4 (50\%) & 4 (50\%) & 8 (100\%) \\ \multicolumn{3}{c}{Correct discrimination rate = [(35 + 4)/(39 + 8)] \(\times\) 100\% = 83.0\%} \\ Overall sample & 0 & 109 (98.4\%) & 7 (1.6\%) & 116 (100\%) \\ \multicolumn{3}{c}{(165 rows) & 1 & 25 (51.9\%) & 24 (48.1\%) & 49 (100\%) \\ \multicolumn{3}{c}{Correct discrimination rate = [(109 + 24)/(116 + 49)] \(\times\) 100\% = 80.6\%} \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Logit regression analysis and judgment results.