## 4 Results  
### Frequency Ratio Methods  
In this section, it is determined which of the FR calculation methods is the most effective. The degree of accuracy of the susceptibility maps produced is calculated, i.e., the probability that a pixel in the landslide susceptibility maps classified as unstable coincides with the areas defined in the inventory. In the tables included in this section we depict average values for the different methods and indices used to facilitate comparison among methods. According to [PERSON] et al. (2019) [PERSON] et al. (2019), working with ROC curves is the most suitable procedure--in which the increase in sensitivity true positive rate (TPR) is plotted with the increase in false positive rate (FPR) at various threshold settings. In these curves, one of the most used indices to determine the validity of diagnostic tests is the area under the ROC curve (AUC). This is an index that shows which test best discriminates between hits and misses. These calculations will be made on the maps of the three provinces, together with the extended inventory for the entire territory studied and all the slope values. Thus, the AUC values obtained are quite high and exceed the value of 0.841 (results shown in Table 8). The table shows that there is no significant difference when considering all the landslide susceptibility index values. Only the GFR values stand out, and these are clearly lower than the rest. This is because at low landslide susceptibility index values, the probability of landslides is low, the probability of success is high, and they represent most the pixels studied. One solution to highlight the differences would be to disregard pixels with low landslide susceptibility index values and use the cut-off points defined by one of the classifications discussed above. However, it is preferable to establish these levels by means of ROC curves in a section of the curve that reflects the most appropriate values rather than the total set. By working  
Figure 3: General methodology flowchart with the comparative analysis. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Provines** & **GFR** & **EFR** & **CFR** & **RFR** \\ \hline Castellon (CST) & 0.841 & 0.853 & 0.852 & 0.854 \\ Valencia (VLC) & 0.858 & 0.869 & 0.865 & 0.869 \\ Alicante (ALC) & 0.873 & 0.888 & 0.889 & 0.892 \\ Mean & 0.857 & 0.870 & 0.870 & 0.872 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: AUC values for the FR methods. on this selected range, a partial \"p\" AUC value (pAUC) is obtained, which is more meaningful as it does away with values that offer scarce information. Indeed, in this work, a large number of positive hits (sensitivity) is considered more important with the largest number of negative hits (specificity) in the most susceptible sections (landslide susceptibility index values). Considering the importance of specificity in landslide studies, the criterion of calculating pAUC for values greater than 60% (Spe or TNR > 0.6, or FPR < 0.4) has been adopted. Figure 4 below explains the behaviour of the ROC curves. It shows the ROC curves for the three provinces and with high values selected on the axes for clarity: Sen > 40% and Spe > 50%. Shown alongside are the pAUC evolution plots for high specificity values (Spe > 60%) with the area between the FPR level expressed in abscissa and the beginning of the ROC curve. Figure 4: Cont. According to the ROC curves in Figure 4 in areas of medium susceptibility with a hit rate for stable areas in the order of TNR = 70% (or 30% FPR), the gain in hits achieved in unstable areas (improvement in mean sensitivity) by the continuous methods (CFR and RFR) is very low (around 1-3%). With medium or low susceptibility (with TNR \(<\) 30% or FPR \(>\) 70%), no differences among methods can be seen as the curves coincide. Therefore, it does not seem worthwhile extending the zone delimited as unstable with the medium/low susceptibility zone for such a small gain (due to the increase in prevention costs that this requires).