## 6 Results and Discussions
Specifically, nine variables, including the average traffic volume of the sub-segment (\(Z_{\text{VOL}}\)), overall acceleration standard deviation (\(\text{VAs}_{\text{STD}}\)), lane-marking indicator (\(\text{L}_{\text{M}}\)), the average acceleration within 3 s (\(\text{T}_{\text{MEAAN}}\)), the average speed within 3 s (\(\text{T}_{\text{V}_{\text{MED}}}\)), the speed standard deviation of the following vehicle within 3 s (\(\text{T}_{\text{STD}}\)), the standard deviation of ETC of all vehicles in sub-segment (\(Z_{\text{STD}}\)), the mix measure of MTC and ETC vehicles (\(Z_{\text{MIX}}\)), the percentage of vehicles with ETC less than 4 s in sub-segment (\(\text{ZNP}_{\text{ETTC}}\)) are significantly associated with risk status in the toll plaza diverging area. Moreover, three variables are identified to be random parameters with heterogeneity in means (\(Z_{\text{VOL}}\), \(Z_{\text{ETD}}\), and \(\text{T}_{\text{STD}}\)). \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Variables** & **RPOL** & \multicolumn{2}{c}{**RPOLMH**} \\ \cline{2-5}  & **Coefficient** & **t-Stat** & **Coefficient** & **t-Stat** \\ \hline Nonrandom parameters & & & & \\ Threshold parameters for probabilities & 9.666 *** & 24.17 & 12.017 *** & 21.79 \\ Constant & \(-15.119\) *** & \(-16.04\) & \(-18.890\) *** & \(-15.86\) \\ L\({}_{\text{INIT}}\)2 & 0.730 *** & 3.35 & 0.820 *** & 3.35 \\ L\({}_{\text{INIT}}\)3 & 0.231 * & 8.9 & 0.541 * & 1.84 \\ L\({}_{\text{INIT}}\)4 & 1.382 *** & 3.54 & 1.564 *** & 3.56 \\ Z\({}_{\text{MIX}}\) & \(-0.682\) *** & \(-6.45\) & \(-0.814\) *** & \(-4.55\) \\ L\({}_{\text{M}}\) & \(-0.319\) *** & \(-4.36\) & \(-1.367\) *** & \(-5.54\) \\ VA\({}_{\text{MAX}}\) & \(-0.380\) *** & \(-5.11\) & \(-0.425\) *** & \(-5.05\) \\ TV\({}_{\text{MEAN}}\) & 3.653 *** & 21.47 & 4.587 *** & 20.13 \\ TA\({}_{\text{MEAN}}\) & \(-0.501\) *** & \(-6.06\) & \(-0.561\) *** & \(-5.99\) \\ ZNP\({}_{\text{ETTC}}\) & 1.176 *** & 10.24 & 1.356 *** & 10.24 \\ ZEMean & 0.592 *** & 5.42 & 0.812 *** & 6.5 \\ N\({}_{\text{LLC}}\)1 & 0.944 *** & 4.48 & 1.083 *** & 4.56 \\ NRLC1 & 0.756 *** & 3.64 & 0.695 *** & 2.98 \\ Random parameters & \(Z_{\text{VOL}}\) & \(-1.531\) *** & \(-12.79\) & \(-2.236\) *** & \(-14.28\) \\ Standard deviation for the random parameter (\(Z_{\text{VOL}}\)) & 2.337 *** & 23.37 & 3.014 *** & 21.36 \\ ZESTD & 0.335 *** & 3.88 & \(-0.228\) & \(-1.31\) \\ Standard deviation for the random parameter (\(Z_{\text{STD}}\)) & 2.090 *** & 21.03 & 2.122 *** & 19.06 \\ TVSTD & 0.454 *** & 4.97 & 1.077 *** & 7.1 \\ Standardized deviation for the random parameter (\(\text{TV}_{\text{STD}}\)) & 0.925 *** & 15.04 & 1.541 *** & 17.2 \\ Heterogeneity in the means of random parameters & & & 0.730 *** & 0.094 \\ L\({}_{\text{M}}\) & & & & 0.560 *** & 0.102 \\ ZESTD: & & & & \(-0.157\) * & 0.087 \\ L\({}_{\text{M}}\) & & & & \(-0.348\) *** & 0.087 \\ TVSTD: & & & & \(-0.614\) *** & 0.136 \\ L\({}_{\text{M}}\) & & & & & \\ Number of parameters & 20 & & & 25 \\ Number of observations & 2462 & & & 2462 \\ Log-likelihood with constants only & \(-2597.626\) & & & \(-2597.626\) \\ Log-likelihood at convergence & \(-1971.890\) & & & \(-1959.918\) \\ Akaike information criterion (AIC) & 3983.780 & & & 3969.836 \\ McFadden Pseudo R-squared & 0.241 & & 0.246 \\ \hline \hline \end{tabular} Notes: *, and *** denote the statistical significance at 0.1 and 0.01 levels, respectively.  
\end{table} 
Table 10: Parameter estimation results for MTC-ETC vehicle-following pattern.