## 4 Results
Additionally, it is worth discussing that while the improvement in model fit for models with ACMA and ANA compared with no attributes processing rules was minor, the differences across the class membership share are hugely different. Consider the standard latent class and the MM models. For those models there is almost equal spread of membership across the two classes. However, moving to the models with wrong specification of ACMA, it can be observed that spread is hugely imbalanced. Finally, the difference between a best fit model considering ANA and ACMA, and all other models is very large. In summary, the results indicated that the right application of ANA and ACMA attribute processing rules result in an overall improvement in the models' fits. Additionally, it was found that although incorporation of an extra layer of random parameters would not result in a significant enhancement of the model, significant changes could be observed for class shares. This result to some extent was confirmed with the previous studies (see [14]). The results highlight that even in light of ANA and ACMA while using the LC model, an extra layer for taste heterogeneity for improving the performance is still required. It is also worth discussing that the MM models, especially considering ANA and ACMA estimation, took hours, and they faced convergence issue many times. In summary it is worth discussion the results of a best fit model, model E. First of all, although some uncertainties could be observed in the significance of some t-ratios, those were incorporated for few reasons: first although they were not significant in some models they were significant in others so we kept them despite the uncertainty in the models' parameters estimates. Due to considering two classes, it was possible also that they were not significant in one class and they were in another class. Due to the nature of the dataset, it was challenging to consider only variables in the models that mostly being significant across all the models and across all classes. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{_Latent class, no ANA, no ACMA (A)_} \\ \hline
**Attributes** & **FAA 1** & **FAA 1** \\ \hline Weather: Sunny & \(-0.22\) (\(-0.703\)) & \(0.19\) (\(0.846\)) \\ \hline Day of a week & \(0.21\) (\(0.679\)) & \(0.63\) (\(2.14\)) \\ \hline Number of lanes & \(0.47\) (\(1.033\)) & \(0.85\) (\(1.43\)) \\ \hline Driver belt status & \(-0.51\) (\(-1.501\)) & \(0.13\) (\(0.49\)) \\ \hline Vehicle license plate registration & \(-0.75\) (\(-2.826\)) & \(-0.46\) (\(-2.54\)) \\ \hline Time of a day (\(11.30\)-\(1.30\)) & \(1.60\) (\(1.408\)) & \(-2.66\) (\(-0.88\)) \\ \hline Time of a day (\(1.30\)-\(3.30\)) & \(-1.41\) (\(-0.658\)) & \(0.28\) (\(0.526\)) \\ \hline Class probability, \(\gamma\) & & \(-0.16\) (\(-0.134\)) \\ \hline Classes share & \(54\%\) & \(46\%\) \\ \hline Log-likelihood & \(-3964\) \\ \hline AIC & \(7959\) \\ \hline \multicolumn{3}{c}{_Mixed-mixed, no ANA, no ACMA (B)_} \\ \hline
**Attributes** & **FAA 1** & **FAA 2** \\ \hline Weather: Sunny & \(84.79\) (\(1.422\)) & \(0.06\) (\(0.301\)) \\ \hline Day of a week & \(-67.71\) (\(-1.33\)) & \(-0.85\) (\(-8.168\)) \\ \hline Number of lanes & \(-106.19\) (\(-1.36\)) & \(0.44\) (\(2.844\)) \\ \hline Driver belt status & \(-27.23\) (\(-1.33\)) & \(0.33\) (\(2.542\)) \\ \hline Vehicle license plate registration & \(42.60\) (\(1.43\)) & \(0.51\) (\(3.534\)) \\ \hline Time of a day (\(11.30\)-\(1.30\)) & \(-31.37\) (\(1.35\)) & \(0.29\) (\(2.587\)) \\ \hline Time of a day (\(1.30\)-\(3.30\)) & \(133.77\) (\(0.301\)) & \(-15.46\) (\(-0.0089\)) \\ \hline SD. Driver belt status & \(91.60\) (\(1.30\)) & - \\ \hline SD. Vehicle license plate registration & \(105.1\) (\(1.37\)) & - \\ \hline SD. Time of a day (\(1.30\)-\(3.30\)) & \(32.2\) (\(1.39\)) & - \\ \hline Class probability, \(\gamma\) & & \(-0.089\) (\(-1.050\)) \\ \hline Classes share & \(52\%\) & \(48\%\) \\ \hline Log-likelihood & \(-3958.7\) & \\ \hline AIC & \(7958\) & \\ \hline \hline \end{tabular}
\end{table}