## 4 Results
### Validation and Comparison of Models  
The last and final step in landslide susceptibility modeling is validation of the achieved results and maps, as the results of modeling have no scientific significance without validation [64; 65]. Model performance and validation in training and testing phases were evaluated using statistical criteria (positive predictive rate (PPR), negative predictive rate (NPR), sensitivity, specificity, accuracy, kappa index, and RMSE), the results of which are shown in Tables 2 and 3. The results of the model performance evaluation shows that BKLR performed the best (PPR = 0.785) in terms of positive predictive rate, followed by SVM (PPR = 0.718) and KLR (PPR= 0.692). In the case of the negative predictive rate, BKLR (NPR = 0.777) was superior to SVM (NPR = 0.699) and KLR (NPR = 0.681). The highest sensitivity was found for BKLR (0.774), with 77.4% of the landslide positions were classified  
Figure 8: Distribution of landslide susceptibility zones.  
Figure 7: Landslide susceptibility map using the support vector machines (SVM) model.  
as landslides, followed by SVM (0.686) and KLR (0.672). BKLR had the highest specificity (0.788), followed by SVM (0.730) and KLR (0.701). The BKLR model classified 78.8% of the non-landslide locations as non-landslide classes. In terms of accuracy, BKLR (0.781) was superior to SVM (0.708) and KLR (0.686). The BKLR model correctly classified 78.1% of the landslide and non-landslide pixels. In terms of the kappa index, the BKLR model performed best (0.56), demonstrating a substantial to almost perfect agreement between prediction and observation, followed by SVM (0.41) and KLR (0.37). In terms of the RMSE, BKLR had the lowest value (0.31), followed by SVM (0.46) and KLR (0.50). Generally, the BKLR model, in terms of all criteria, had the best performance in the training phase, followed by SVM and KLR. The model evaluation in testing phase is shown in Table 3. Generally, the results show that BKLR, for both the training and testing phases, performed the best, followed by the SVM and KLR models.  
In the present research, the prediction capability of the three models and their results were also investigated using a popular technique: Receiver operating characteristics (ROC). The main advantage of this technique is that it determines the prediction power of the models quantitatively using area under the ROC curve (AUC) [66; 67]. The AUC result using the training dataset shows that all three models have good and reasonable prediction power. The BKLR model had the highest prediction power (AUC = 0.852), followed by SVM (AUC = 0.768) and KLR (AUC = 0.764) (Figure 9). As the achieved maps were built using the training dataset, the ROC result using the training dataset cannot be considered alone for comparison. The testing dataset, which was not used for model building, must be considered for model validation and comparison. The results show that BKLR (AUC = 0.770) had the highest prediction power, followed by SVM (AUC = 0.759) and KLR (AUC = 0.720) (Figure 10). According to [PERSON] [68], all the models have good and reasonable prediction power.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{3}{c}{**Model**} \\ \cline{2-4}  & **BKLR** & **KLR** & **SVM** \\ \hline True positive & 189 & 164 & 167 \\ True negative & 192 & 171 & 178 \\ False positive & 52 & 73 & 66 \\ False negative & 55 & 80 & 77 \\ Positive predictive rate (\%) & 0.785 & 0.692 & 0.718  
Figure 10: ROC curves using the validation dataset: (**a**) BKLR model, (**b**) KLR model, (**c**) SVM model.  
Figure 9: Receiver operating characteristics (ROC) curves using the training dataset: (**a**) BKLR model, (**b**) KLR model, (**c**) SVM model.