## 6 Results and Discussions
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Variables** & **RPOL** & \multicolumn{2}{c}{**RPOLMH**} \\  & **Coefficient** & **t-Stat** & **Coefficient** & **t-Stat** \\ \hline Nonrandom parameters & & & & \\ Threshold parameters for probabilities & 3.345 *** & 67.06 & 3.478 *** & 66.63 \\ Constant & \(-\)4.448 *** & \(-\)19.48 & \(-\)4.583 *** & \(-\)15.87 \\ L\({}_{\rm{INIT}}\)2 & \(-\)0.285 *** & \(-\)3.83 & \(-\)0.606 *** & \(-\)3.29 \\ L\({}_{\rm{INIT}}\)3 & \(-\)0.709 *** & \(-\)9.34 & \(-\)0.365 ** & \(-\)2.00 \\ L\({}_{\rm{INIT}}\)4 & \(-\)0.813 *** & \(-\)9.4 & \(-\)0.255 *** & \(-\)2.411 \\ ZPCT\({}_{\rm{ETC}}\) & \(-\)0.178 *** & \(-\)7.14 & \(-\)0.176 *** & \(-\)3.14 \\ L\({}_{\rm{M}}\) & \(-\)0.176 *** & \(-\)7.08 & \(-\)0.448 *** & \(-\)6.80 \\ V\({}_{\rm{MAX}}\) & \(-\)0.144 *** & \(-\)6.24 & \(-\)0.246 *** & \(-\)4.54 \\ TV\({}_{\rm{MEAN}}\) & 0.176 *** & 6.35 & 2.146 *** & 6.05 \\ TA\({}_{\rm{MEAN}}\) & \(-\)0.396 *** & \(-\)14.64 & 1.488 *** & 46.53 \\ ZNP\({}_{\rm{ETC}}\) & 0.545 *** & 21.20 & 0.5543 *** & 21.15 \\ N\({}_{\rm{ILC}}\)1 & 0.352 ** & 4.70 & 0.315 *** & 4.12 \\ VA\({}_{\rm{STD}}\) & 0.146 *** & 6.05 & 2.146 *** & 6.05 \\ Random parameters & & & & \\ \({}_{\rm{ZVOL}}\) & \(-\)0.446 *** & \(-\)14.61 & \(-\)0.476 *** & \(-\)5.03 \\ Standard deviation for the random parameter (Z\({}_{\rm{VOL}}\) ) & 0.906 *** & 17.18 & 0.968 *** & 59.12 \\ Z\({}_{\rm{MIX}}\) & \(-\)0.286 *** & \(-\)4.12 & \(-\)0.674 *** & \(-\)6.00 \\ Standard deviation for the random parameter (Z\({}_{\rm{MIX}}\)) & 0.903 *** & 46.43 & 0.368 *** & 21.49 \\ Heterogeneity in the means of random parameters & & & \(-\)0.156 * & \(-\)1.86 \\ Z\({}_{\rm{VOL}}\): & & & & \\ L\({}_{\rm{INIT}}\)3 & & & & \\ Z\({}_{\rm{VOL}}\): & & & & \\ L\({}_{\rm{INIT}}\)4 & & & & \\ Z\({}_{\rm{VOL}}\): & & & & \\ L\({}_{\rm{M}}\) & & & & \\ L\({}_{\rm{M}}\) & & & & \\ Z\({}_{\rm{MIX}}\) & & & & \\ L\({}_{\rm{INIT}}\)2 & & & & \\ Z\({}_{\rm{MIX}}\) & & & & \\ ZPCT\({}_{\rm{ETC}}\) & & & & \\ Z\({}_{\rm{MIX}}\) & & & & \\ L\({}_{\rm{M}}\) & & & & \\ Z\({}_{\rm{MIX}}\) & & & & \\ VA\({}_{\rm{MAX}}\) & & & & \\ Number of parameters & 17 & & & 24 \\ Number of observations & 11,306 & & & 11,306 \\ Log-likelihood with constants only & \(-\)11,214.896 & & & \(-\)11,214.896 \\ Log-likelihood at convergence & \(-\)9828.941 & & & \(-\)9786.598 \\ Akaike information criterion (AIC) & 19,697.9 & 19,635.2 & & \\ \hline \hline \end{tabular} Notes: *, **, and *** denote the statistical significance at 0.1, 0.05, and 0.01 levels, respectively.  
\end{table} 
Table 7: Parameter estimation results for ETC-ETC vehicle-following pattern. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Variables** & **RPOL** & \multicolumn{2}{c}{**RPOLMH**} \\  & **Coefficient** & **t-Stat** & **Coefficient** & **t-Stat** \\ \hline Nonrandom parameters & & & \\ Threshold parameters for probabilities & 3.381 *** & 29.69 & 4.366 *** & 28.18 \\ Constant & \(-\)5.576 *** & \(-\)10.37 & \(-\)5.408 *** & \(-\)8.160 \\ L\({}_{\rm{INIT}}\)2 & 0.657 *** & 4.97 & 0.817 *** & 5.520 \\ L\({}_{\rm{INIT}}\)3 & 1.600 *** & 10.36 & 2.019 *** & 11.460 \\ L\({}_{\rm{INIT}}\)4 & 1.943 *** & 7.67 & 2.339 *** & 8.320 \\ Z\({}_{\rm{MIX}}\) & 0.211 *** & 3.19 & \(-\)0.5679 * & \(-\)0.260 \\ L\({}_{\rm{M}}\) & \(-\)0.268 *** & \(-\)4.82 & \(-\)0.294 ** & \(-\)2.220 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameter estimation results for all vehicle-following patterns.