TeleFOT

The first thing is to test whether there are enough observations to describe each level so that a two-level and a three-level analysis can be conducted. The number of observations per each level is presented in Table 5.16. It can be observed that there are enough events per driver and per trip to perform both two-level analyses but there are not many trips per driver, i.e. mean 1.72 from 1 to 3 trips and that might be problematic in the appliance of a three-Level model. Also, it should be noted that there are 25 drivers performed 43 trips.

Table 5.16: Number of observations for each level of the analysis for TeleFOT data Mean Std. Dev. Min Max

Trips per driver 1.72 0.73 1 3

Events per driver 33.44 26.7 4 90

Events per trip 19.44 10.72 3 42

5.2.2.1 Deceleration

The best-fitted model of the linear regression has an adjusted R2 _{of 0.10. The adjusted}

R2 _{is low, indicating that the model does not explain well the dependent variable. The}

most significant explanatory factors are the initial speed, “if the car has to stop” variable and the reason for braking. The next step is to search for group effects that might describe better the dataset.

5.2.2.1.1 2-Level null model

To investigate if the 2-Level model describes better the data than the single-level one, the LR test is performed resulting that there is a group effect for both drivers and trips.The predicted driver and trip effect are displayed in Figure 5.9. Observing the Boxplots for the driver effect, only one driver from the 25 differs significantly from the

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average driver, performing harder braking. Also, from the same graph for the trip level, it can be noted that in all the trips the deceleration values are within the values of the average trip.

Figure 5.9: Plots representing the driver and trip effects in the deceleration values for the 2-Level null models for TeleFOT dataset

5.2.2.1.2 3-Level null model

Moving to the 3-level null model, the LR-test showed that it is not significantly better from neither the single-level model nor any of the 2-Level ones. This was further supported by the low values of the ICC for the driver level in the 3-level model.

5.2.2.1.3 2-Level random intercept

Having concluded that both driver and trip effect play a role, the 2-Level random intercept models for trip level and driver level were calculated. The results show almost the same effects of the explanatory variables to the deceleration value for both models.

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Although, the trip-level model shows better fit since the ICC (0.046) is bigger than the ICC of the driver-level model (0.039).

5.2.2.1.4 2-Level random intercept and random slope

Then, it was tested if by adding a random slope to any of the independent variables, a better-fitted model would have been created. The resulted models were compared to the simpler random intercept model to prove which is the best model to describe the deceleration value. The results of the LR-Test and the comparison of the AIC and BIC concluded that the best model to describe the maximum deceleration value for the TeleFOT dataset is the trip-Level random intercept and random slope for traffic light model, which is displayed in Table 5.17.

Table 5.17: Results of the trip-Level random intercept and random slope for traffic light model for deceleration (TeleFOT dataset)

Deceleration Coef. z P>z Initial speed -0.027 -7.5 0.000 Traffic light -0.083 -1.97 0.049 Roundabout 0.176 3.51 0.000 Junction 0.151 3.29 0.001 Other 0.099 2.2 0.028 Pedestrian crossing -0.022 -0.22 0.830 Car stops -0.227 -6.84 0.000 Rural 0.057 1.98 0.048 Driver reaction 1 0.147 3.83 0.000 Intercept -2.253 -40.11 0.000 Random-effects Parameters Estimate TripID: Independent var(traffi~t) 0.0643 var(Intercept) 0.0066 var(Residual) 0.1378 ICC 0.046 Obs 837 ll(model) -387.15 df 13

The initial speed and if the car stops affect the deceleration value the most. Specifically, 1m/s increase in the initial speed results in 0.027m/s2 _{decrease in the}

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decrease in the deceleration value by 0.227m/s2_{. On the other hand, if the driver is}

looking ahead and the road type is rural, the deceleration value is increasing, resulting in softer braking. Another statistically significant variable is the reason for braking. The effect is positive if the deceleration did not happen due to a dynamic objective or a pedestrian crossing.

As far as the traffic light is concerned, the initial effect for trip j is estimated as -0.083+ u1j and the between trip variance in these slopes is estimated as 0.0643 (σ=0,2536).

Therefore, z=0.083/0.2536=0.327 and from the normal distribution table, it is concluded that 62.9% of the slopes of the traffic light variable give a negative effect on the deceleration value whereas the rest 37.1% a positive one.

5.2.2.2 Duration

The statistical analysis of the duration starts with the calculation of the best linear regression model, which is the ln-ln linear regression model with a satisfactory adjusted R2 _{(0.56). So, 56% of the duration values can be explained well by this model.} 5.2.2.2.1 Multi-level null model

To examine if there is any driver or trip effect, the LR-test was conducted to the null trip-level and drivel-level against the single-level model and there was overwhelming evidence in favour of both 2-Level models. Also, using the LR-test the 3-Level model against the 2-Level and the single level models were examined and it resulted that the 3-Level model is better than the single-level and the driver-level but not than the trip- Level one. So, the best model is the 2-trip level model.

5.2.2.2.2 2-level random intercept

The procedure continues by adding the explanatory variables to the trip-level null model and by keeping the variables that are statistically significant. Also, when the explanatory variables were added to the drivel level model, the model resulted to be inappropriate (ICC value almost equal to 0). This happened because the driver variables (age, driver experience and gender) that were added explained the differences due to the driver. Next, random slopes for the dependent variables were

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added to the trip-level random intercept model. The resulted models were compared with the random intercept trip-level model through the LR-test and it was proven that the best-fitted model is the random intercept trip-Level model (see Table 5.18).

Table 5.18: Trip-Level random intercept model for the Duration (TeleFOT dataset) Trip level Ln_duration Coef. z P>z Ln_initial speed 0.7480 28.92 0.00 Ln_trip distance 0.1800 2.72 0.01 Age_old 0.0840 2.29 0.02 Driven_miles 2 -0.2380 -2.96 0.00 Driven_miles 3 -0.1800 -2.18 0.03 Driven_miles 4 -0.1230 -1.10 0.27 Stop_at_car_block 0.0780 2.25 0.02 Rural 0.0600 2.62 0.01 Car_stops 0.4130 15.36 0.00 Driver_reaction1 -0.0850 -3.85 0.00 Intercept -0.6720 -3.30 0.00 Random-effects Parameters Estimate TripID: Identity var(Intercept) 0.004 var(Residual) 0.095 Level ICC 0.04 TripID Obs 845 ll(model) -217.86 df 13 AIC 461.7207 BIC 523.3321

From the results in Table 5.18, it can be noted that the initial speed and the need to stop affect the most the duration of the deceleration events. They both have a positive effect, meaning that the increase of the initial speed or if the car needs to stop leads to an increase in the deceleration duration. Specifically, if the initial speed increases by 1 m/s, the duration increases by 0.33sec and if the car needs to stop it increases by 1.76 sec. Moreover, some driver characteristics play a significant role, i.e. the age, specifically an old driver brakes longer by 0.36 sec than a middle-age one and the driving experience showing that drivers with more driven miles brake in shorter duration, indicating more experience driving style. Shorter braking is resulting when

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the driver looks in front just at the moment the driver started the braking and not inside the car.

The reason for braking does not affect the duration even if it was inserting in the model. Driving in a rural road instead of an urban or a motorway leads to an increase to the duration by 0.26sec. Also, stopping at a car block has a positive effect on the duration. Last but not least, the trip duration has a positive effect on the duration, meaning that 1 min increase in the trip duration results in 0.05sec increase in the deceleration duration. Finally, the ICC equals to 0.04, which means that 4% of the variation in duration values lies between the trips whereas the rest variation lies between the events on the same trip.