## 3 Results
### Assessment of the Proposed Models  
The present study used five performance indices to assess the performance of the models developed. These included coefficient of determination (\(R^{2}\)), mean absolute error (MAE), root-mean-square error (RMSE), variance accounted for (VAF), and a20-index [32; 40; 41; 42; 94; 95; 96; 97]. These indices were widely used in previous studies for the performance assessment of ML models. The computation formulas are presented in Figure 5.  
This study also used a simple ranking system proposed by [PERSON] et al. [86] to rank the performance of each proposed PPV prediction model. Before the model development, the authors split the data  
Figure 4: Variable importance through the developed models. Figure 5: Performance indices for evaluating the developed machine learning (ML) models. into training (70%) and testing (30%) datasets. For each dataset, this technique assigned a rank of five to the model that had the best value for each performance index, and then assigned a rank of one to the model that had the worst value for each performance index. The total performance rating of each model was then calculated by summing up its total rank of each dataset (Equation (1)). The authors also calculated the final rank of each model by summing up the training and testing dataset total ranks of the model. Table 5 shows the results of performance evaluation and the final ranking of each proposed model. Overall, the RF model obtained the highest final rank (41) by far, followed by ANN, CHAID, and SVM. CART achieved the lowest final rank (10). RF had the highest total rank (23) for the training dataset, while SVM and ANN had the highest total rank (21) for the testing dataset. The CART model had the lowest total rank for both training and testing datasets. \[\textit{Model Total Rank}=\sum_{i=1}^{5}R_{i}, \tag{1}\]  
where \(i\) denotes the performance indices, and \(R_{i}\) is the model's ranking for each performance index. The performance of the proposed models was also evaluated using a gain chart, which is shown in Figure 6. A simple definition of gains is the proportion of total hits that occur in each percentile or increment. In the chart below, the diagonal red line denotes the at-chance model, the blue line (the higher line) denotes the perfect prediction model, and the other five lines in the middle represent the models that were developed in this study. Basically, higher lines indicate better models, specifically on the left side of the gain chart. The areas between each of the models and the red line show how much better the proposed models are compared to the at-chance model. Furthermore, the areas between each of the models and the perfect model show where the proposed models can be improved. It is worth noting that the aim of the developed models is to be as close to the perfect model as possible. The models also identified a PPV of greater than 5.59 mm/s as the best predictive value for the perfect model. For the training dataset, as we went through 40% of the data, the at-chance model indicated that we correctly identified 40% of the samples which had a PPV of greater than 5.59 mm/s. The perfect model showed that we correctly identified 100% of the samples which had a PPV of greater than 5.59 mm/s. As we went through 44% of the data, the RF model showed that we identified 100% of the samples with the probability of a PPV of greater than 5.59 mm/s. As we went through 46% of the data, the CHAID model showed that we identified 100% of the samples with the probability of a PPV of greater than 5.59 mm/s. As we went through 54% of the data, the ANN model showed that we identified 100% of the samples with the probability of a PPV of greater than 5.59 mm/s. As we went through 55% of the data, the SVM model showed that we identified 100% of the samples with the