5.2.3.1 Deceleration
In order to explore further factors affecting the deceleration value, the two datasets i.e. OEM and TeleFOT were combined. Therefore, the factors will not be connected only to one dataset and the results would be more generic. First, Table 5.19 displays the observations for each level to establish that it is possible to perform the multi-level analysis. Also, it should be noted that there were 37 drivers and 174 trips.
Table 5.19: Number of observations for each level of the analysis for combination dataset Mean Std. Dev. Min Max
Trips per driver 4.70 4.55 1 12
Events per driver 73.4 67.6 3 217
Events per trip 15.6 9.9 2 42
The LR-test was performed to examine if there are any group effects in the data. Specifically, the 2-Level models showed a better fit than the single-level one. In addition, there was significant evidence that the 3-Level model (driver-trip-event level) is the most parsimonious model with ICC for driver effect equal to 0.061 and for trip effect equal to 0.124. Those values signify that 12.4% of the variation in the deceleration values can be explained by the group effect of the trip and the driver and the 6.1% only from the driver effect. From the boxplots displayed in Figure 5.10, the group effects are visualised. As far as the drivers’ effect is concerned, many drivers
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decelerate in harder than the average driver. Also, the intervals are smaller for those drivers meaning that their braking does not vary a lot. On the other hand, considering the trips, there are some trips where the decelerations that took place were harder or softer than the ones on the average trip.
Figure 5.10: Boxplots of the group effect of the drivers and the trips for the deceleration (Combination dataset)
Continuing to the statistical analysis, after calculating the most parsimonious linear regression model (adjusted R2=0.115) the 2-Level random intercept models were
estimated both for trip and driver level, resulting in two good models with ICC=0.065 for the trip level and ICC=0.036 for the driver level. Then, random slope was added to the explanatory variables and the LR-test indicated that the best model is the driver- level random intercept and random slope for the variable Vehicle C.
Next, the best 3-Level random intercept model was estimated and was compared with the best 2-Level random intercept model, concluding that there is strong evidence in favour of the 3-Level model (LR test). By adding random slope to the variables of the 3-Level model in both driver and trip-level, the best model describing the combination data was revealed from the LR-test and by having the best values of AIC and BIC and it was the 3-Level random intercept and random slope for the variable “Car_stops” in the trip level (displayed in Table 5.20).
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Table 5.20: Results of the 3-Level models for the deceleration value (Combination dataset)
3-LEVEL RANDOM INTERCEPT MODEL
3-LEVEL RANDOM INTERCEPT AND RANDOM SLOPE
Deceleration Coef. z P>z Coef. z P>z
Initial speed -0.0004 -4.68 0.00 -0.0004 -4.60 0.00 Trip distance -0.0116 -3.75 0.00 -0.0114 -3.71 0.00 Traffic light -0.0524 -2.53 0.01 -0.0550 -2.66 0.01 Roundabout 0.1145 4.07 0.00 0.1127 4.02 0.00 Junction 0.0989 4.35 0.00 0.0974 4.30 0.00 Pedestrian crossing -0.1822 -2.94 0.00 -0.1880 -3.04 0.00 Other 0.1175 4.33 0.00 0.1222 4.52 0.00 Car_stops -0.1666 -8.44 0.00 -0.1703 -7.60 0.00 Vehicle A 0.1397 4.17 0.00 0.1397 4.20 0.00 Telefot 0.2248 5.11 0.00 0.2284 5.17 0.00 Vehicle C 0.1721 5.45 0.00 0.1614 5.08 0.00 Intercept -2.5374 -65.21 0.00 -2.5392 -65.36 0.00 Random-effects
Parameters Estimate Estimate
DriverID: Identity var(Intercept) 0.0066 0.0069 TripID: Identity var(Car_stops) 0.0162 var(Intercept) 0.0068 0.0055 var(Residual) 0.1954 0.1916
Level ICC ICC
DriverID 0.0318 0.034
TripIDDriverID 0.0642 0.0608
Obs 2715 2715
ll(model) -1685.99 -1681.18
df 15 16
The results indicate similar effects for most of the explanatory variables as the ones of the best models from OEM and TeleFOT dataset. The main difference lies in the fact the best model is a 3-Level model, where 3.4% of the variation of the deceleration value lies between the drivers, 2,68% of the variation lies between the trips and the rest 93.92% of the variation lies between the events in the same trip of the same driver. Also, the effect of the variable “Car_stops” is different, i.e. it has a random effect and specifically to 91% of the data it has a negative effect and to 9% a positive one effect that varies.
Regarding the other variables, the car model is one of the most statistically significant variables, indicating that driving any other car but Vehicle B results in softer braking
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by 0.16-0.23 m/s2. Decelerating because of approaching a roundabout or a junction,
increases the value of the deceleration by 0.112 m/s2 and 0.097 m/s2 respectively
comparing to braking due to a dynamic obstacle. On the other hand, braking due to a pedestrian crossing and not due to a dynamic obstacle results in harder braking by 0.1880 m/s2. Also, increasing the initial speed and the existence of traffic light have a
negative effect on the deceleration value. Finally, no driver characteristic influences the deceleration value, but the reason might be that these characteristics were taken into consideration in the driver level.
5.2.3.2 Clustering
A different approach to analyse the data and explore the factors that affect the deceleration value is to group the data based on human factors, i.e. sociodemographic factors, to reflect the differences among the drivers, and on the braking pattern. To accomplish that, a cluster analysis was employed and specifically, the 2-step cluster analysis in SPSS was used since this method can handle categorical variables (such as gender, age categories and braking profiles) as well as big datasets. Five clusters were created as an outcome and their features can be seen in Figure 5.11. It can be noted that the size of the clusters does not have big differences (size of smaller cluster=396 and size of bigger cluster=637). Also, all the variables that were included in the cluster analysis are statistically significant. The distribution of the variables inside each cluster is displayed in the upper right part of Figure 5.11. It can be concluded that old people (cluster 1 and 3) slightly prefer the braking pattern (2) whereas young people also use the third braking pattern (3). Moreover, the different clusters present different deceleration characteristics. This can be supported by the results of the Analysis of Variance (ANOVA) test (p=0.045<0.05), conducted to test the differences between the means of the maximum deceleration for each cluster. Additionally, it was concluded from the Tukey’s HSD test that old females brake the hardest whereas old males brake the softest.
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Figure 5.11: Features of the five clusters (Combination dataset)
Having the deceleration events clustered and with the aim of examining all the influencing factors of the braking behaviour, the multilevel mixed-effect model was applied to each cluster using the StataMP 13 software. The factors that were considered are (1) event-level factors, such as situational factors (reason of braking, traffic density), kinematic factors at the beginning of braking, etc. and (2) trip level factors, such as trip duration, trip distance, the model of the car. Therefore, the maximum deceleration value was analysed using statistical analysis for each cluster. Since the driver effect has been included in the clustering, the model that was used was the 2-level linear regression model based on the trip level. The explanatory variables, which include distance, initial speed, if the car should stop, traffic density and the reason for braking, were kept the same among the clusters. The results of the
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analysis are presented in Table 5.21. There was no evidence in favour of any random slope model in any of the clusters. The overall intra-class correlation (ICC) varies from 0.037 (cluster 1) to 0.16 (cluster 4) indicating that 3.7% and 16% of the variation in the deceleration value is explained by the trip-level hierarchical data structure. Therefore, all models show a reasonable goodness-of-fit.
Table 5.21: Results from Multilevel linear regression models in the 5 clusters (Combination dataset)
Cluster1 Cluster2 Cluster3 Cluster4 Cluster5 Deceleration Coef. z Coef. z Coef. z Coef. z Coef. z Distance -0.018 -2.44 -0.020 -4.29 -0.012 -1.86 Initial speed -0.012 -1.89 -0.024 -6.39 -0.012 -1.69 -0.033 -6.33 Traffic light 0.126 2.45 Roundabout 0.164 2.65 0.106 2.16 0.164 2.35 T_junction 0.112 2.13 0.071 1.62 0.161 2.55 Cross_junction n 0.145 1.97 0.133 2.28 0.178 1.96 Pedestrian crossing -0.255 -1.63 -0.553 -3.42 Other 0.109 1.9 0.117 2.58 0.097 1.87 0.117 1.69 Car_stops -0.198 -4.32 -- -0.100 -2.22 -0.217 -5.73 -0.174 -4.2 -0.263 -4.81 Intercept -2.237 -33.7 -2.482 -61.1 -2.150 -38.8 -2.345 -31.3 -2.158 -26.9 Number of observations 396 471 601 596 637 ICC 0.037 0.055 0.07 0.16 0.11 AIC 424.6 840.9 657.4 756.3 764.8 806.9 BIC 448.3 880.7 697.0 795.8 806.9 LogLik -206.3 -411.5 -319.7 -369.2 -372.4 df 6 9 9 9 10
The most statistically significant variables affecting the deceleration value for almost all the models are the initial speed and if the car should stop. Increasing the initial speed by 1m/s leads to harder braking (the decrease varies from 0.012 to 0.033m/s2)
and if the car needs to stop, the deceleration value decreases from -0.1 to 0.263m/s2.
Another important factor is the cause of braking. Specifically, approaching a roundabout or a junction results in softer braking compared to a dynamic obstacle, whereas approaching a pedestrian crossing leads to harder braking. Furthermore, for cluster 4 the existence of a traffic light made the braking softer. The traffic density was revealed to be insignificant for all the clusters.
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