# A Cox Model-Based Workflow for Increased Accuracy in Activity-Travel Patterns Generation
## 4 Results
### Cox and Cox-Based Models Comparison  
Tables 4-7 present a comparative analysis of three Cox-based models: the simple Cox model, the Cox model with frailty (i.e., incorporating latent class heterogeneity), and the Cox-based machine learning model. Each model is evaluated for four distinct trip purposes (Work, Market, Education, and Other) using a combination of performance metrics, including C-index, MAE, and RMSE, with evaluations performed using both 80/20 train-test splits and 5-fold cross-validation. Table 4 illustrates the performance of the simple Cox model. While the model demonstrates moderate predictive accuracy for work-related and \"Other\" trips (C-index of 0.6746 and 0.8421, respectively), its performance significantly degrades for market and education trips, with C-index values near or below 0.5 (indicative of limited discriminative capability). The MAE and RMSE values are correspondingly high, particularly for the \"Other\" category in the 5-fold cross-validation scenario. Table 5 evaluates the Cox model with frailty. The inclusion of latent classes introduces the modeling of unobserved heterogeneity, slightly improving performance in some categories (e.g., Market trips), although the overall C-index values can be perceived as inconsistent for the different trip purposes. Notably, the model performs better in estimating market trip durations, with improvements in MAE and RMSE relative to the simple Cox model. However, for the \"Other\" category, performance is worse than that of the simple Cox model for both the 80/20 train/test split approach and the 5-fold cross-validation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Trip Purpose** & **Model Type** & **C-index** & **MAE** & **RMSE** \\ \hline \multirow{2}{*}{Work} & 80/20 Split & 0.6746 & 5.9995 & 6.6242 \\  & 5-Fold CV & 0.6788 & 5.9963 & 6.7622 \\ \hline \multirow{2}{*}{Market} & 80/20 Split & 0.45 & 3.72 & 4.8572 \\  & 5-Fold CV & 0.393 & 3.0232 & 3.8979 \\ \hline \multirow{2}{*}{Education} & 80/20 Split & 0.4545 & 3.7411 & 4.7305 \\  & 5-Fold CV & 0.6718 & 4.5595 & 5.3528 \\ \hline \multirow{2}{*}{Other} & 80/20 Split & 0.8421 & 3.4673 & 4.5029 \\  & 5-Fold CV & 0.7071 & 7.3472 & 12.9006 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simple Cox model evaluation results. Table 6 demonstrates the performance of the Cox-based machine learning model, which outperforms the traditional models across most trip purposes. The model exhibits higher C-index values and substantially lower error metrics, particularly for Work and Other trips. For example, the MAE for Work trips reduces to approximately 2.24 compared to approximately 6.0 in the simple Cox model. This enhanced performance highlights the machine learning model's ability to capture complex, non-linear relationships in the data. Table 7 provides a model comparison using the AIC for the simple Cox model and the WAIC for the Cox model with frailty. Across all trip purposes, the frailty-based model yields lower values (e.g., WAIC = 103.1 for Market trips vs. AIC = 285.44), indicating better model fit while accounting for unobserved heterogeneity and model complexity. These findings support the fact that incorporating latent class structures improves the model's explanatory power, although machine learning remains superior in predictive performance. However, it is important to note that AIC and WAIC are not directly comparable and should only be interpreted as rough indicators at this point of the analysis.