## 3 Results
### Comparison of Predicted Demand and Available Capacity  
[PERSON] and [PERSON] (1998), showed that more than half of all trips in personal vehicles in the United States are taken in vehicles with multiple occupants and the mean vehicle occupancy rate is 1.63 persons. Based on this assumption and the fact that the dataset used in this study covers approximately 11% of the total vehicles in Florida, we can compare the actual and predicted utilization of each individual shelter for each day. The utilization rate was calculated as:  
\[Utilization\ (\%)=\frac{Demand}{\textit{ActualBates}}\times 100 \tag{12}\]  
Figure 17 shows the actual and predicted utilizations of the shelters, obtained by using Equation (10). Note that for each facility _Available Spaces_ is obtained from ([PERSON] and [PERSON], 1998) and the predicted utilization is computed using the demand prediction from the proposed GAM approach (actual utilization is computed using the observed demand). In addition, the figure shows predicted utilization for both training data (used to build the GAM model) and test data (hold-out samples not used in model building). The predictions for test data (while they are inevitably poorer than those for the training data) agree reasonably well with the observed data (as evidenced with the good Test Data performance in Tables 5 and 6) and are very useful in demonstrating the generalizability of the model in new or unseen conditions. The predicted utilization closely follows the actual utilization across most shelters, indicating a generally good model performance. However, in shelters like S1, S21, and S22, the predictions show noticeable deviations, suggesting potential underfitting or overfitting or the need for additional features to capture these fluctuations better. While the model performs well in stable demand scenarios, further refinement is needed for shelters with more volatile utilization patterns. Figure 17: Actual and Predicted Utilization of the Shelters Over Time. Shelters corresponding to the test data are indicated, while those not indicated correspond to the training data. As for the shelter analysis, the vehicle occupancy rate of 1.63 was adopted to estimate the demand at the lodging facilities. However, an additional assumption was made that each room at the lodging facilities could accommodate four people, which was used to adjust for the available capacity at the lodging facilities. While our vehicle occupancy assumption is empirically supported by literature, (see e.g., [45]), our room occupancy assumption could be refined with future research by surveying hotel/lodging data for average room occupancy during evacuations. Figure 18 compares actual and predicted utilization across multiple test lodging facilities over the period under review. These plots show that the prediction model, tested on a dataset not used during training, performs inconsistently, accurately predicting trends in some facilities but missing significantly in others. The summary statistics in Table 2 further highlight the performance of the model. For the training dataset, the RMSE (4.0368) and MAE (2.7591) indicate moderate error levels, with a MAPE of 108.76% and a correlation of 0.5485, suggesting a fair alignment between actual and predicted demand. However, for the test dataset, the RMSE (3.4211) and MAE (2.57656) are slightly lower, but the correlation drops significantly to 0.2096, reflecting weak predictive performance on unseen data. Additionally, the MAPE for the test data rises to 113.80%, indicating the model struggles to generalize well beyond the training dataset. Additionally, some days are missing from the plots for certain facilities due to the absence of available data for those periods. Facilities like L29 and L60 show relatively good model performance, while others like L4 and L3 exhibit discrepancies between actual and predicted utilization.