# Driving Behavior Modeling Based on Consistent Variable Selection in a PWARX Model
## 4 Modeling Results
### Mode Segmentation
These tables show the location of each mode, therefore explaining the physical meaning of each mode. Mode 1 is in the high positive KdB, negative range rate and largely negative-acceleration (deceleration) region. On the other hand, mode 2 is at the opposite spectrum of mode 1, i.e., high negative KdB, positive range rate, and positive acceleration, whereas mode 3 is located where the KdB, range rate and acceleration are distributed uniformly between positive and negative sides. The vehicle-following task in the downtown area can be said to be a cyclic of safe-departure by the leading vehicle, cruising at desirable dynamics by the ego car and cautious approach to the leading car. Furthermore, examining the figures of the segmentation and the statistic tables, it can be concluded that amongst the input variables for modeling the vehicle-following task, KdB (\(u_{3}\)) and range rate (\(u_{2}\)) strongly affect the decision making (mode segmentation) of the driver, whereas the other variables influence the motion dynamics. Examining these mean values in Table 2 for drivers A to F, it could be seen that the values are different for all the modes from driver to driver. In addition, the variance values in Table 3 show the variation in the way the driver operates the brake and accelerator pedals. These variations (pedal behavior) in each node are also different from driver to driver. This signifies that each driver has his own unique model structure (i.e., unique decision making) for the car-following task, and thus this uniqueness can be leveraged directly to design automated systems peculiar to each driver. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Driver** & **Mode (_i_)** & \(\mathbf{u_{1}}\) & \(\mathbf{u_{2}}\) & \(\mathbf{u_{3}}\) & \(\mathbf{u_{4}}\) & \(\mathbf{u_{5}}\) & \(\mathbf{u_{6}}\) & \(\mathbf{y}\) \\ \hline \multirow{4}{*}{A} & 1 & 14.7967 & \(-\)0.7365 & 82.9239 & \(-\)0.0947 & 0.0573 & 1.6321 & 9.0802 \\  & 2 & 10.1805 & 2.5240 & \(-\)115.3931 & \(-\)0.1916 & \(-\)0.2338 & 2.4917 & 4.5813 \\  & 3 & 15.2099 & 0.9024 & \(-\)76.5456 & \(-\)0.0726 & \(-\)0.0564 & 1.7508 & 8.8569 \\ \hline \multirow{4}{*}{B} & 1 & 19.1161 & \(-\)1.0761 & 82.1025 & \(-\)0.1442 & 0.0599 & 2.8145 & 6.8006 \\  & 2 & 13.2032 & 3.0255 & \(-\)107.8165 & \(-\)0.0773 & \(-\)0.2275 & 5.1354 & 3.2444 \\  & 3 & 25.3100 & 0.9317 & \(-\)55.9455 & \(-\)0.0544 & \(-\)0.0425 & 3.5853 & 7.1059 \\ \hline \multirow{4}{*}{C} & 1 & 22.5530 & \(-\)1.0362 & 75.2793 & \(-\)0.1437 & 0.0507 & 3.1521 & 7.2707 \\  & 2 & 12.4296 & 3.0010 & \(-\)111.8950 & 0.2716 & \(-\)0.2467 & 6.1057 & 2.6634 \\  & 3 & 26.6439 & 1.7252 & \(-\)76.8184 & \(-\)0.0072 & \(-\)0.0784 & 4.7373 & 6.0309 \\  & 4 & 22.5461 & 0.7366 & \(-\)65.0536 & \(-\)0.0227 & \(-\)0.0341 & 2.9458 & 7.8383 \\ \hline \multirow{4}{*}{D} & 1 & 7.4822 & 1.4649 & \(-\)113.5721 & \(-\)0.1556 & \(-\)0.1883 & 3.9329 & 2.5935 \\  & 2 & 10.4366 & \(-\)0.6515 & 65.4002 & 0.0329 & 0.0567 & 2.4888 & 4.5814 \\  & 3 & 19.3710 & 0.7052 & \(-\)56.4716 & 0.0466 & \(-\)0.0444 & 2.6940 & 7.4533 \\ \hline \multirow{4}{*}{E} & 1 & 17.9504 & \(-\)1.0276 & 80.6962 & \(-\)0.2128 & 0.0603 & 2.3383 & 7.7231 \\  & 2 & 10.6959 & 2.2784 & \(-\)112.2794 & \(-\)0.3386 & \(-\)0.2163 & 3.3595 & 3.8392 \\  & 3 & 23.4378 & 0.8599 & \(-\)52.0313 & \(-\)0.0258 & \(-\)0.0424 & 2.9062 & 8.4229 \\ \hline \multirow{4}{*}{F} & 1 & 14.5640 & \(-\)0.7783 & 80.2988 & \(-\)0.1284 & 0.0632 & 1.6611 & 8.6957 \\  & 2 & 13.7065 & 1.2122 & \(-\)95.2759 & \(-\)0.0027 & \(-\)0.1033 & 2.0076 & 7.6085 \\  & 3 & 18.1030 & 0.2739 & \(-\)25.9114 & \(-\)0.1185 & \(-\)0.0134 & 1.8595 & 9.6969 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean values of the variables in each mode \(i\).