## 4 Results and Discussions
### Bayesian Logistic Ordinal Regressions  
#### 4.2.1 Results and Analysis of Experiment 1  
Due to the complex and multidimensional nature of the posterior distribution in Bayesian Logistic Ordinal Regression, it is quite difficult to obtain an analytical solution directly. To estimate the parameters effectively, researchers have applied the Markov Chain Monte Carlo (MCMC) method. MCMC is an algorithm commonly used for sampling of complex probability distributions. By calculating statistical quantities such as the mean, variance, and 95% confidence interval of the posterior distribution, the results represent estimates of the fixed effects. The model underwent a total of 12,500 MCMC iterations, with the first 2500 iterations discarded as a burn-in phase and the remaining 10,000 iterations forming the final MCMC sample set. The acceptance rate (AR) was 0.21, meaning that 21% of the 10,000 estimated parameter values were accepted. An AR of over 10% indicates that there are no problems with the convergence of the MCMC, confirming the validity of the model. \begin{table}
\begin{tabular}{c c c c c c} \hline  & \(\mathbf{p}\)**-Value of** & \(\mathbf{p}\)**-Value of** & **Position** & **Veh-Mean** & **Veh-Std.** \\ \hline \multirow{3}{*}{City Roads} & \multirow{3}{*}{0.197} & \multirow{3}{*}{0.294} & 1 & 1.391 & 0.548 \\ \cline{3-6}  & & & 2 & 1.534 & 0.424 \\ \cline{3-6}  & & & 3 & 1.344 & 0.563 \\ \hline \multirow{3}{*}{Expressway} & \multirow{3}{*}{0.014} & \multirow{3}{*}{0.02} & 1 & 1.601 & 0.395 \\ \cline{3-6}  & & & 2 & 1.684 & 0.355 \\ \cline{3-6}  & & & 3 & 1.317 & 0.597 \\ \hline \multirow{3}{*}{Right Lane Changes} & \multirow{3}{*}{0.208} & \multirow{3}{*}{0.165} & 1 & 1.418 & 0.533 \\ \cline{3-6}  & & & 2 & 1.443 & 0.464 \\ \cline{3-6}  & & & 3 & 1.191 & 0.661 \\ \hline \multirow{3}{*}{Left Lane Changes} & \multirow{3}{*}{0.012} & \multirow{3}{*}{0.082} & 1 & 1.483 & 0.478 \\ \cline{3-6}  & & & 2 & 1.725 & 0.338 \\ \cline{3-6}  & & & 3 & 1.472 & 0.494 \\ \hline \multirow{3}{*}{Low Traffic Flow} & \multirow{3}{*}{0.477} & \multirow{3}{*}{0.473} & 1 & 1.37 & 0.547 \\ \cline{3-6}  & & & 2 & 1.543 & 0.401 \\ \cline{3-6}  & & & 3 & 1.081 & 0.738 \\ \hline \multirow{3}{*}{Medium Traffic Flow} & \multirow{3}{*}{0.918} & \multirow{3}{*}{0.95} & 1 & 1.587 & 0.404 \\ \cline{3-6}  & & & 2 & 1.585 & 0.405 \\ \cline{3-6}  & & & 3 & 1.592 & 0.387 \\ \hline \multirow{3}{*}{High Traffic Flow} & \multirow{3}{*}{0.003} & \multirow{3}{*}{0.009} & 1 & 1.35 & 0.583 \\ \cline{3-6}  & & & 2 & 1.618 & 0.388 \\ \cline{3-6}  & & & 3 & 1.357 & 0.574 \\ \hline \end{tabular}
\end{table} 
Table 5: Nonparametric statistical results for different traffic scenarios of Experiment 2. In Figure 7, the sample values in the MCMC sampling trace plots fluctuate randomly without showing an upward or downward trend. Overlapping trajectories from multiple chains indicate consistent sampling results across different chains. The samples in the trace plots exhibit good mixing in the parameter space, with frequent fluctuations. The samples do not linger near a particular value for extended periods. After the warm-up phase, the trace plots display a stable distribution. The vertical axis in the figure represents the parameter value corresponding to each sample. The concentration of values above zero indicates that the respective feature factor has a positive effect on increasing the time buffer, thereby reducing the driver's cognitive load. Conversely, values distributed below zero suggest that the feature factor increases the driver's cognitive load. Based on this analysis, we can preliminarily conclude that a higher eye height, low traffic flow, medium traffic flow, and Vehicle Type 2 all contribute to reducing the driver's cognitive load. On the other hand, a longer distance and Vehicle Type 1 both increase the driver's cognitive load. Meanwhile, the effects of city roads and left lane changes are not evident. As shown in Table 6, the BLOC estimates include the posterior mean, posterior standard deviation (Std. dev.