## 6 Results and Discussions
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Variables** & **RPOL** & **RPOLMH** & \\ \cline{2-3}  & **Coefficient** & **t-Stat** & **Coefficient** & **t-Stat** \\ \hline Heterogeneity in the means of random parameters & & 0.151 *** & 0.052 \\ \(\rm{L}_{\rm{M}}\) & & 0.197 *** & 0.094 \\ \(\rm{Z}_{\rm{VOL}}\): & & 0.380 *** & 0.076 \\ \(\rm{ZV}_{\rm{TSD}}\): & & 0.186 ** & 0.072 \\ \(\rm{ZV}_{\rm{TSD}}\): & & \(-\)0.416 *** & 0.066 \\ \(\rm{Z}_{\rm{TSD}}\): & & 0.019 * & 0.106 \\ \(\rm{L}_{\rm{M}}\) & & \(-\)0.405 *** & 0.074 \\ \(\rm{Z}_{\rm{VOL}}\): & & 0.272 *** & 0.065 \\ \(\rm{Z}_{\rm{VOL}}\): & & 25 \\ \(\rm{Number\ of\ parameters}\) & & 2561 & 2561 \\ \(\rm{Log-likelihood\ with\ constants\ only}\) & \(-\)2402.155 & & \(-\)2402.155 \\ \(\rm{Log-likelihood\ at\ convergence}\) & \(-\)1776.738 & & \(-\)1751.157 \\ \(\rm{Akaike\ information\ criterion\ (AIC)}\) & 3587.5 & & 3552.3 \\ \(\rm{McFadden\ Pseudo\ R-squared}\) & 0.260 & 0.271 \\ \hline \end{tabular} Notes: *, **, and *** denote the statistical significance at 0.1, 0.05, and 0.01 levels, respectively.  
\end{table} 
Table 8: _Cont._ \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Variables** & **RPOL** & **RPOLMH** & \\ \cline{2-3}  & **Coefficient** & **t-Stat** & **Coefficient** & **t-Stat** \\ \hline Nonrandom parameters & & & \\ Threshold parameters for probabilities & 3.613 *** & 40.07 & 3.597 *** & 40.1 \\ Constant & \(-\)5.793 *** & \(-\)14.85 & \(-\)6.211 *** & \(-\)12.86 \\ \(\rm{L}_{\rm{M}}\) & \(-\)0.167 *** & 1.82 & 0.211 *** & 2.28 \\ \(\rm{L}_{\rm{M}}\) & \(-\)0.249 *** & \(-\)5.55 & \(-\)0.558 *** & \(-\)4.85 \\ \(\rm{VA}_{\rm{STD}}\) & \(-\)0.147 *** & \(-\)3.5 & \(-\)0.180 & \(-\)1.60 \\ \(\rm{ZD}_{\rm{MEAN}}\) & 0.179 *** & 4.51 & 0.176 *** & 4.40 \\ \(\rm{Z}_{\rm{M}}\) & 0.58 * & 11.4 & 0.242 * & 1.82 \\ \(\rm{TV}_{\rm{MEAN}}\) & 1.624 *** & 29.14 & 1.656 *** & 29.34 \\ \(\rm{TA}_{\rm{MEAN}}\) & \(-\)0.395 *** & \(-\)7.84 & \(-\)0.331 *** & \(-\)6.39 \\ \(\rm{Z}_{\rm{T}}\) & 0.420 *** & 9.47 & 0.264 *** & 2.44 \\ \(\rm{Z}_{\rm{ESP}}\) & 0.385 *** & 8.41 & 0.359 *** & 7.74 \\ \(\rm{N}_{\rm{HLC}}\) & 0.266 *** & 3.45 & 0.239 *** & 3.09 \\ \(\rm{Z}_{\rm{VOL}}\) & \(-\)0.672 *** & \(-\)12.08 & \(-\)1.100 *** & \(-\)9.81 \\ \(\rm{Standard\ deviation\ for\ the\ random\ parameter\ (Z_{\rm{VOL}})}\) & 0.920 *** & 34.14 & 0.916 *** & 34.10 \\ \(\rm{TV}_{\rm{STD}}\) & 0.331 *** & 6.4 & 0.954 *** & 8.58 \\ \(\rm{Standard\ deviation\ for\ the\ random\ parameter\ (TV_{\rm{STD}})}\) & 0.597 *** & 20.02 & 0.526 *** & 18.26 \\ \(\rm{H}_{\rm{M}}\) & & & 0.157 *** & 3.47 \\ \(\rm{Z}_{\rm{VOL}}\): & & & 0.177 *** & 3.76 \\ \(\rm{Z}_{\rm{VOL}}\): & & & \(-\)0.090 * & \(-\)1.69 \\ \(\rm{Z}_{\rm{VOL}}\): & & & 0.155 *** & 3.31 \\ \(\rm{Z}_{\rm{NETTIC}}\) & & & \(-\)0.241 *** & \(-\)7.02 \\ \(\rm{V}_{\rm{STD}}\): & & & \(-\)0.912 ** & \(-\)2.24 \\ \(\rm{TV}_{\rm{STD}}\): & & & \(-\)0.912 *** & \(-\)2.24 \\ \(\rm{Number\ of\ parameters}\) & 17 & 22 & & \\ \(\rm{Number\ of\ observations}\) & 3817 & 3817 & & \\ \(\rm{Log-likelihood\ with\ constants\ only}\) & \(-\)4259.636 & \(-\)4259.636 & & \\ \(\rm{Log-likelihood\ at\ convergence}\) & \(-\)3400.384 & \(-\)3229.269 & & \\ \(\rm{Akaike\ information\ criterion\ (AIC)}\) & 6834.8 & 6502.5 & & \\ \(\rm{McFadden\ Pseudo\ R-squared}\) & 0.202 & 0.242 & & \\ \hline \end{tabular} Notes: *, **, and *** denote the statistical significance at 0.1, 0.05, and 0.01 levels, respectively.  
\end{table} 
Table 9: Parameter estimation results for MTC-MTC vehicle-following pattern. For four vehicle-following patterns, the AIC values of the RPOL models are larger than those of RPOLMH, which demonstrates the RPOLMH models have better performance. The values of McFadden's pseudo R\({}^{2}\) of four RPOLMH models also indicate the same result. The number of significant variables is almost the same in models for different vehicle-following patterns (Tables 7-10).