# Driving Behavior Modeling Based on Consistent Variable Selection in a PWARX Model
## 4 Modeling Results  
### Mode Segmentation  
The result for the estimated optimal number of modes or sub-models for drivers A-F based on consistent variable selection is shown in Table 1.  
Generally speaking, a three-mode model was identified as the optimal number of modes amongst the drivers for the car-following task in the downtown area. The mode segmentation result in the range-KdB space, range rate-range space, and acceleration-KdB are, respectively, shown in Figures 6-8 for drivers A, and B. These figures show the decision/result of the optimal number of modes or sub-models where a unique color represents a unique mode or sub-model with its own distinctive dynamical characteristics. Additionally, the boundaries of where the colors change can be regarded as the mode-switching or decision-making of the driver. In these figures, the red, green, and blue markers correspond to mode (sub-model) 1, 2, and 3, respectively, of Tables 2 and 3. In interpreting this result, mode 1, the region marked in red is characterized by high KdB, negative range rate, as well as the braking operation being activated numerous times, implying that this is the dangerous region for the driver. In mode 2, the green marked region, the KdB is negatively large, the range rate is positive, and the driver mainly operates the accelerator pedal, indicating that this is the safest region for the driver. The area marked in blue, mode 3 is characterized by both positive and negative KdB values, acceleration of this area is near zero with change fairly constant, which implies that this is the cruising region. In this mode, the driver is comfortable and tries to maintain stable dynamics, suggesting that this is the part of the vehicle-following task where the driver is least attentive. Generally speaking, the car-following driving task in the downtown area can be said to consist of three modes or sub-models, (i.e., the dangerous region, safe region and cruising region. However, the separating hyper-planes (decision boundaries) are different from one driver to another as shown in Figures 6-8. In these figures, parts (a) and (b) represent the identified modes for driver A and driver B, respectively. In comparing drivers A and B, driver A can be said to be a more conservative driver in the sense that the area of the identified dangerous region is bigger. In designing automated driving systems, for example for drivers A and B, this unique characteristic particular to each driver can be leveraged to offer a more comfortable driving experience. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Driver** & **A** & **B** & **C** & **D** & **E** & **F** \\ \hline Optimal Number of Modes & 3 & 3 & 4 & 3 & 3 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Identified number of modes from consistent variable selection for each driver. Figure 8: Mode segmentation result (optimal number of sub-models) of the car-following task in the acceleration-KdB space, where a unique color represents a unique mode (sub-model) with it’s own distinctive motion-control characteristics: (**a**) three-mode model identified for driver A; (**b**) three-mode model identified for driver B.  
Figure 6: Mode segmentation (optimal number of sub-models) result of the car-following task in the range-KdB space, where a unique color represents a unique mode (sub-model) with its own distinctive motion-control characteristics: (**a**) Three-mode model identified for driver A; (**b**) three-mode model identified for driver B.  
Figure 7: Mode segmentation result (optimal number of sub-models) of the car-following task in the range rate–range space, where a unique color represents a unique mode (sub-model) with its own distinctive motion-control characteristics: (**a**) three-mode model identified for driver A; (**b**) three-mode model identified for driver B. The mean values of the variables in each mode or sub-model for all the drivers are shown in Table 2, whereas Table 3 shows the acceleration statistics for each mode.