# A Cox Model-Based Workflow for Increased Accuracy in Activity-Travel Patterns Generation
## 4 Results
### Comparison of Synthetically Generated Data with Real-World  
Tables 8-11 assess the realism of synthetically generated activity-travel duration data compared to observed real-world survey data. Four different synthetic data configurations are evaluated per trip purpose using the K-S test, MAE, and RMSE. Regarding the first synthetic data (indicated as \"Synth. Data 1\") it corresponds to the synthetic data that are produced when input travel survey to the ABM is \"as-is\" without using any of the Cox or Cox-based models to repair its missing activity durations, or other inconsistencies as presented in Section 3. The second and third synthetic datasets, indicated as \"Synth. Data 2\" and \"Synth. Data 3\" in Tables 8-11, are the two synthetic datasets that emerge when input travel surveys to the ABM are repaired with the simple Cox model and the Cox model with two latent classes, respectively. Finally, with \"Synth. Data 4\" we denote the synthetic data that emerge when the input travel survey is repaired with the Cox-based machine learning model.  
Table 8 focuses on Work-related activities. The synthetic dataset is labeled as Synth. Data 3 demonstrates the highest fidelity to real-world data, with the lowest K-S test statistic (D = 0.20822, \(p\) < 0.001), and favorable MAE (3.66) and RMSE (4.72). This indicates strong similarity in the distribution and dispersion of durations.  
Table 9 pertains to Market trips. Again, Synth. Data 3 yields the most accurate results, with the lowest RMSE (3.59) and a significantly reduced K-S statistic (D = 0.4235), suggesting it most closely replicates the real-world distribution among all tested configurations.  
Table 10 presents results for Educational activities. All synthetic datasets exhibit similar MAE and RMSE values, with Synth. Data 3 offering marginal improvements in alignment with the real data distribution (\(p\) = 0.1031 in K-S test). Given the minimal intervention in educational trip durations, these results imply inherent stability in this activity type.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metrics** & **Synth. Data 1** & **Synth. Data 2** & **Synth. Data 3** & **Synth. Data 4** \\ \hline K–S test & 0.2939/ & 0.25486/ & 0.20822/ & 0.16116/ \\ (D/\(p\)-value) & \textless{}2.2 \(\times\) 10\({}^{-16}\) & \textless{}2.2 \(\times\) 10\({}^{-16}\) & 3.46 \(\times\) 10\({}^{-11}\) & 6.885 \(\times\) 10\({}^{-8}\) \\ \hline MAE & 4.572079 & 3.707881 & 3.664099 & 4.195042 \\ \hline RMSE & 5.609498 & 4.739945 & 4.723046 & 5.323675 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison of real vs. synthetic data for work purposes.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metrics** & **Synth. Data 1** & **Synth. Data 2** & **Synth. Data 3** & **Synth. Data 4** \\ \hline K–S test & 0.8619/ & 0.62409/ & 0.4235/ & 0.4213/ \\ (D/\(p\)-value) & 2.2 \(\times\) 10\({}^{-16}\) & 1.73 \(\times\) 10\({}^{-14}\) & 3.71 \(\times\) 10\({}^{-7}\) & 2.033 \(\times\) 10\({}^{-7}\) \\ \hline MAE & 2.685109 & 2.3248 & 2.407971 & 2.841279 \\ \hline RMSE & 3.932881 & 3.943628 & 3.591605 & 4.174001 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Comparison of real vs. synthetic data for Market purposes.  
Collectively, the analysis demonstrates that advanced Cox-based modeling approaches, particularly those that incorporate unobserved heterogeneity or leverage machine learning to capture complex, non-linear relationships, significantly improve the realism and predictive accuracy of synthetic activity-travel datasets. These enhancements are especially pronounced in more variable and complex trip categories, such as Work and Other, where conventional models often fail to capture nuanced duration patterns. By bridging model diagnostics (Section 4.1) with the validation of synthetic data (Section 4.2), the results underscore the critical role of both latent class modeling and neural network-based survival analysis in generating synthetic travel patterns that are behaviorally realistic and statistically robust.