# Driving Behavior Modeling Based on Consistent Variable Selection in a PWARX Model
## 4 Modeling Results
### Variable Selection  
Statistical variable selection is usually carried out to identify from a list or set of variables the most influential variable or variables; therefore, variable selection was performed in each mode or sub-model to determine for each driver which variables are useful for expressing the motion dynamics of that mode/sub-model. The variable selection result and the corresponding identified parameters are shown in Table 4 for all the drivers where the 0 (zero) parameter value means that the variable was not selected. Examining the Table 4, the range \(u_{1}\) and time headway \(u_{6}\) were selected in all modes/sub-models for all the drivers. This implies that the range (\(u_{1}\)) and time headway (\(u_{6}\)) are the most influential variables for expressing the motion dynamics in the car-following driving task. The jerk, \(u_{4}\), was rarely selected across all modes amongst all drivers and, as such, is the variable with the least effect when expressing the dynamical motion characteristics of the car-following driving task. In interpreting the identified parameters of a regression model, a positive value signifies a linear proportional relationship with the output, i.e., an increase in that input variable results in some increase in the output. On the other hand, an input variable with a negatively valued parameter represents an inverse relationship with the output variable, i.e., an increase in that input variable will lead to a decrease in the output variable. Examining the values of the identified parameters in Table 4, the range \(u_{1}\) is positive in all the modes, meaning the speed increases as the range increases. However, the time headway \(u_{6}\) has negative-valued parameters, and as such the speed decreases when the time headway increases. At first glance, this might seem counterintuitive as the speed should be expected to increase when the time headway increases. However, a careful consideration shows that the time headway acts as a suppressor that brings the speed back to its maximum limit. This idea is intuitive considering that the driving experiment was performed in the downtown area and the driving speed is limited to a maximum of about 40 km/hr. The parameters of the other variables can be interpreted in the same manner where an increase in positively valued parameters causes the output (speed) to increase while an increase in the negative value parameters causes the output to decrease. Further observation shows that the combination of selected explanatory variables are different from mode (sub-model) to mode (sub-model) amongst all the drivers and are also different from one driver to another. In addition, both the signs and magnitudes of the parameters are different from one mode to the other, signifying that even the contribution or influence of a variable to the output can change from one sub-model to the other. The difference of results of the variable selection (i.e., which variables influence the output speed) from driver to driver agrees with the hypothesis of this paper about the need