## 4 Results and Discussions
### Bayesian Logistic Ordinal Regressions
#### 4.2.2 Results and Analysis of Experiment 2  
To avoid the problem of imbalanced data, in this section, the medium traffic flow is merged into the low-traffic-flow category for comparative analysis with the high traffic flow. The model ran a total of 12,500 MCMC iterations, with the initial 2500 iterations considered as the burn-in phase and discarded, leaving the remaining 10,000 iterations to constitute the final MCMC sample set. The acceptance rate (AR) was 0.22, indicating that 22% of the 10,000 estimated parameter values were accepted. An AR above 10% suggests that there are no issues with the convergence of MCMC, validating the model's effectiveness.  
Similar to Experiment 1, the sampling trace plots (Figure 8) in Experiment 2 exhibit random fluctuations, stable distributions, and are within a reasonable range of temporal buffer values. Upon preliminary analysis of the sampled parameter values in Figure 8, it is observed that the intervals of various feature variables all encompass the value of 0, suggesting that these variables do not exhibit a pronounced effect on the driver's cognitive load.  
As shown in Table 7, within this model, the MCSE values for all feature variables were less than 0.01, indicating a low variability in the simulated results of MCMC across different replications, thus rendering the results relatively reliable. Furthermore, the posterior means and medians of all feature variables were very close, suggesting that the posterior distributions approximated normal distributions.  
The analysis of the results is as follows:  
(1) Traffic Environment: The conclusions regarding lane-changing direction and road type align with those of Experiment 1, validating the effectiveness of the analytical results from Experiment 1.  
(2) Blind Spot Location: comparing position 1 (mean = \(-\)0.23, 95% CI \(-\)0.39 to 0.05) with the same longitudinal position but a different transverse position with position 2 (omitted), the latter shows a greater potential to reduce the cognitive load of drivers. Furthermore, when position 1 (with the above mean and confidence interval) is compared with position 3 (mean = \(-\)0.18, 95% confidence interval \(-\)0.37 to 0.01), which has the same transverse position but a different longitudinal position, position 3 shows a more pronounced effect in reducing drivers' cognitive load. However, the confidence interval of position 3 includes 0, which means that the correlation is not statistically significant. The displayed blind spot image is located near the driver's lateral distance and at the same longitudinal position. Positioning the blind spot display closer to the geometric center of the central display can reduce the driver's cognitive load more effectively.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Mean** & \
\begin{tabular}{c} **Std.** \\ **Dev.** \\ \end{tabular} & **MCSE** & **Median** &
\begin{tabular}{c} **[95\% Cred.** \\ **Interval**] \\ \end{tabular} \\ \hline Location1 & \(-\)0.234 & 0.090 & 0.010 & \(-\)0.234 & \(-\)0.398 & \(-\)0.053 \\ \hline Location3 & \(-\)0.188 & 0.095 & 0.006 & \(-\)0.189 & \(-\)0.373 & 0.007 \\ \hline Right Lane Changes & \(-\)0.254 & 0.081 & 0.009 & \(-\)0.255 & \(-\)0.405 & \(-\)0.083 \\ \hline City Roads & \(-\)0.150 & 0.091 & 0.008 & \(-\)0.149 & \(-\)0.330 & 0.033 \\ \hline Low Traffic Flow & \(-\)0.082 & 0.078 & 0.004 & \(-\)0.084 & \(-\)0.230 & 0.081 \\ \hline \hline \end{tabular} In this table, expressway, right lane changes, high traffic flow and Vehicle Type 3 are omitted.  
\end{table}
Table 7: BLOC estimation table of Experiment 2.  
Figure 8: MCMC sampling trace plots of Experiment 2.