## 3 Results
### Effects of Data Normalization on Model Performance  
To account for differences in facility size and population across counties, we further studied the effectiveness of normalized performance metrics of demand predictions at shelters and lodging facilities. Specifically, actual and predicted vehicle counts were normalized by facility capacity (total spaces available at each facility). To compare results from different counties we computed scaled root mean square errors (SRMSE), which is defined as RMSE divided by the standard deviation. This enables us to compare the prediction accuracies in counties with varying shelter or lodging capacities on an equal basis. Equations (10) and (11) show SRMSE with actual data and normalized data based on facility capacity, respectively. \[SRMSE=\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}\frac{\left(\hat{y_{i}}-y_{i} \right)^{2}}{\text{Var}(y)}} \tag{10}\] \begin{table}
\begin{tabular}{c c c c c} \hline  & **RMSE** & **MAE** & **MAPE** & **CORR** \\ \hline Train Data & 6.7791 & 3.8745 & 79.41\% & 0.8593 (\textless{}0.001) \\ Test Data & 7.7213 & 4.4823 & 107.01\% & \(-0.0835\) (0.4087) \\ \hline \end{tabular}
\end{table} 
Table 6: GAM Summary Statistics for Shelters. \begin{table}
\begin{tabular}{c c c c c} \hline  & **RMSE** & **MAE** & **MAPE** & **CORR** \\ \hline Train Data & 4.0368 & 2.7591 & 108.76\% & 0.5485 (\textless{}0.001) \\ Test Data & 3.4211 & 2.57656 & 113.80\% & 0.2096 (0.0014) \\ \hline \end{tabular}
\end{table} 
Table 7: GAM Summary Statistics for Lodging Facilities. \[SRMSE_{Norm}=\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}\frac{\left(\hat{y}_{i}/\mathbf{C }_{i}-y_{i}/\mathbf{C}_{i}\right)^{2}}{\text{Var}(y/C)}} \tag{11}\]  
where \(y_{i}\) and \(\hat{y}_{i}\) represent the actual and predicted vehicle counts at the observation \(i\), respectively. \(\mathbf{C}_{i}\) denotes the facility capacity (total spaces available at the shelter or lodging facility) corresponding to the observation \(i\). Tables 8 and 9 show the prediction \(SRMSE\) and \(SRMSE_{Norm}\) results for shelters and lodging facilities, respectively, within the three counties, as well as the populations, available spaces in the facilities, the total counts of vehicles that visited the facilities during the study period in each county and the vehicle count per available space (Veh Ct/Av Sp). In contrast to RMSE (see Tables 6 and 7) which is higher for shelters, the SRMSE values overall are smaller for shelters than lodging facilities. This is because SRMSE measures prediction errors as a multiple of standard deviation and the shelter data has higher variability. \(SRMSE_{Norm}\) which uses predictions normalized by facility size provides further ability to compare counties with varying available spaces. as outlier mitigation, data normalization, and robust loss functions can be undertaken to reduce the impact of extreme variations and improve model resilience. Overall, the model demonstrates better predictive accuracy for lodging facilities, while the performance for shelters requires significant refinement to improve robustness and reliability. The discrepancies in testing performance, particularly for shelters, suggest the need for further model calibration or additional data to enhance predictive accuracy. Figures 5 and 6 depict the spatial distribution of the selected shelters and lodging facilities for the test and train datasets, with locations color-coded in red (test) and blue (train). Figure 5: Shelter Locations and Region Boundaries. Figure 6: Lodging Facility Locations and Region Boundaries. Figure 7a,b show actual vs. predicted vehicles for shelters and lodging facilities, respectively. The plots indicate that the model performs reasonably well for shelters and decently for lodging facilities throughout the study period, with many points lying close to the line of perfect prediction. There are instances where predictions deviate, indicating room for improvement. There seems to be a good match between actual and predicted values, especially for lower vehicle counts.