Accident Analysis and Prevention 76 (2015) 118–132

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Accident Analysis and Prevention journal homepage: www.elsevier.com/locate/aap

Driver behaviour profiles for road safety analysis Adrian B. Ellison * , Stephen P. Greaves 1, Michiel C.J. Bliemer 2 Institute of Transport and Logistics Studies, The University of Sydney, NSW 2006 Australia

A R T I C L E I N F O

A B S T R A C T

Article history: Received 5 August 2014 Received in revised form 14 January 2015 Accepted 15 January 2015 Available online xxx

Driver behaviour is a contributing factor in over 90 percent of road crashes. As a consequence, there is significant benefit in identifying drivers who engage in unsafe driving practices. Driver behaviour profiles (DBPs) are introduced here as an approach for evaluating driver behaviour as a function of the risk of a casualty crash. They employ data collected using global positioning system (GPS) devices, supplemented with spatiotemporal information. These profiles are comprised of common risk scores that can be used to compare drivers between each other and across time and space. The paper details the development of these DBPs and demonstrates their use as an input into modelling the factors that influence driver behaviour. The results show that even having controlled for the influence of the road environment, these factors remain the strongest predictors of driver behaviour suggesting different spatiotemporal environments elicit a variety of psychological responses in drivers. The approach and outcomes will be of interest to insurance companies in enhancing the risk-profiling of drivers with on-road driving and government through assessing the impacts of behaviour-change interventions. ã 2015 Elsevier Ltd. All rights reserved.

Keywords: Risk Driver behaviour profiles Naturalistic driving

1. Introduction Road crashes result in 1.24 million avoidable fatalities and between 20 and 50 million injuries annually (World Health Organisation, 2013). Prior research suggests that driver behaviour is a contributory factor in over 90 percent of crashes (Petridou and Moustaki, 2001). As a consequence, there is significant benefit in identifying drivers who engage in unsafe driving practices, placing themselves and other road users at greater risk of involvement in a crash. A number of methods have been used to do this including creating demographic profiles (Wundersitz and Hutchinson, 2008), self-reported behaviour and risk preferences (Goldenbeld and Van Schagen, 2007) and personality and risk perceptions (Machin and Plint, 2010; Musselwhite, 2006). These methods generally rely on a small number of observations and assume homogeneity of behaviour within groups, under or over-predicting road safety outcomes as a result. From a policy perspective, when these methods are applied to insurance premiums they reduce the incentive for drivers to improve their behaviour since the insurance premiums reflect the behaviour of drivers with similar demographics and (rare) crash events. This means there is no

* Corresponding author. Tel.: +61 2 9114 1885. E-mail addresses: [email protected] (A.B. Ellison), [email protected] (S.P. Greaves), [email protected] (M.C.J. Bliemer). 1 Tel.: +61 2 9114 1835. 2 Tel.: +61 2 9114 1840. http://dx.doi.org/10.1016/j.aap.2015.01.009 0001-4575/ ã 2015 Elsevier Ltd. All rights reserved.

immediate tangible benefit to an individual of improving their driving behaviour. With self-reported surveys, enforcement records and speeding studies employing radar guns, a simple measure is typically computed from each observation. This is possible because these measurement methods only capture driver behaviour at distinct points in time and space. Naturalistic driving datasets – data collected from drivers during their day-to-day driving – collected using GPS and other technologies, measure driver behaviour across time and space, generating (potentially) millions of observations for each driver. To make sense of the data and perform statistical analyses it is necessary to aggregate the data to some degree. Aggregation, however, results in a large loss of detail reducing the benefits of naturalistic driving datasets collected at great expense. In many cases, aggregation masks the considerable variation in driver behaviour and, therefore, potentially removes many of the predictors of crash risk. Performing analyses at a disaggregate level and then aggregating the results would mitigate this issue while maintaining the benefits of aggregation in terms of manageability of large datasets. To accommodate the need for a single measure of driver behaviour with respect to safety while simultaneously accounting for the variability and multitude of aspects embedded within the driving task, the current paper details the development of what we term, driver behaviour profiles (DBPs). A DBP is a composite normalised measure/score of driver behaviour that serves as a proxy for assessing crash risk in that it combines a number of measures of risk on a common scale within and across drivers.

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The measure utilises empirical data on driver behaviour such as speeding, aggressive acceleration and aggressive braking, accounting for the frequencies and magnitudes with which they occur. This allows drivers to be compared to each other and for the same driver to be compared across time and space facilitating empirical testing of the effects of behaviour-change interventions. DBPs can be applied by industry and government for several purposes. For instance, since DBPs are derived from the risk of a fatal crash, and by extension the risk of less severe crashes, monetary (dollar) amounts can be tied to each score permitting insurance companies to use the DBPs (and the resulting scores) to determine an appropriate premium (or discount) on the basis of observed behaviour over a period of time. The ability to change driver behaviour (to lower risk behaviours) could be enhanced through this mechanism by providing drivers with their scores, potentially providing a direct financial benefit to both insurance companies and their customers. This could be applied in conjunction with a pay-as-you-Drive (PAYD) insurance scheme such as the scheme offered by Co-operative Insurance in the United Kingdom (The Co-Operative Insurance, 2012). For government, the scores could be used as the basis for measuring a change in behaviour that occurs as a result of an education or enforcement campaign as well as legislative or infrastructure changes. This would be a useful complement to the number of fatalities and serious injuries as, while sample sizes would likely still be low, they would generally be larger than the very small sample sizes that are common in crash analyses in terms of breadth and detail. Furthermore, this could be done at any level of aggregation from a single location to a national level comparison. Once a sufficient quantity of driver scores has been collected from before-and-after studies of this nature, it would be possible to simulate the effect on risk and societal benefits of proposed infrastructure or policy changes at a micro or macro level. With this in mind, this paper reviews the existing literature on naturalistic driving data and driver behaviour profiling. The DBP framework and methodology are then introduced. An example of an application of how DBPs have been used to identify the driver characteristics associated with risky driving behaviour is then discussed. The paper concludes with a discussion on the implications of the results, how DBPs can be applied to other research and how DBPs can be applied in practice by industry and government. 2. Background and literature review As part of efforts to improve our understanding of driver behaviour, an increasing number of studies have employed improvements in technology to collect more detailed and richer data. These have led to substantially larger and more complex datasets of driver behaviour necessitating new methodologies to analyse them, including driver behaviour profiles. Global positioning system (GPS) devices and other in-vehicle sensors for the study of driving behaviour (employed in, for example Biding and Lind, 2002; Dingus et al., 2006) have – at a cost of smaller sample sizes – reduced a number of issues associated with other forms of data collection. This includes a tendency towards under or over reporting of driver behaviour (speeding in particular) (Corbett, 2001; Hatfield et al., 2008) and limited time series data found in self-reported surveys, enforcement records and hospital records. Studies have employed GPS, accelerometers, video cameras, distance sensors and on-board diagnostics (OBD). Although this technology has its own limitations it has the potential to provide a more complete record of day-to-day driving. Although the number of naturalistic driving studies (as research employing this technology are known) are more limited due to the

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cost and resources involved they are nonetheless becoming more common. 2.1. Naturalistic driving studies Naturalistic driving data has been used to study a number of issues. Among the most pertinent for this paper include research on commercial vehicle fleets (Toledo et al., 2008), young driver behaviour (Prato et al., 2010) and driving patterns (Bagdadi and Várhelyi, 2011). Of the studies using GPS, two of the largest and most well known studies are the U.S. 100-Car Naturalistic Driving Study (Dingus et al., 2006)1 and the Swedish Intelligent Speed Adaptation (ISA) trial (Biding and Lind, 2002). The 100-Car Naturalistic Driving Study incorporated a number of in-vehicle devices to monitor the driver, vehicle and other vehicles (Dingus et al., 2006) and served as a pilot for the national US naturalistic driving study, which included almost 2000 vehicles (Antin et al., 2011). The final dataset contained data recorded from 100 vehicles and 241 drivers over a period of 12–13 months. In total there were 43,000 h of data and 2 million vehicle miles travelled (VMT). The Swedish ISA trial conducted between 1999 and 2002 involved almost 5000 vehicles making it the largest ISA trial to date (Biding and Lind, 2002). Unlike the aforementioned study, 4000 of the vehicles in this study used street-level reference transmitters to determine the position, providing data less prone to the issues commonly found with GPS data such as cold start problems and urban canyons.2 2.2. Benefits and drawbacks of naturalistic driving data GPS data provides a more complete picture of drivers’ behaviour than can be achieved from traditional methods but has a number of disadvantages. For example, the data collection process is more expensive and resource intensive and once collected requires extensive processing (Boonsiripant et al., 2010; Greaves et al., 2010). The large amount of data requires researchers to either aggregate data at some level or to isolate small segments of the data to make it manageable. Some researchers have suggested using pattern matching algorithms to identify patterns that are of interest and to focus analysis on these portions of the data (Musicant et al., 2010). Others have developed software applications to identify particular events and use video footage to determine if they are valid and to determine who is driving the car since this cannot be determined from GPS (Dingus et al., 2006). GPS data, in its raw form, can also be difficult to model as observations are highly correlated with each other. The other main drawback of naturalistic driving studies is that they are susceptible to ‘noise’ from exogenous factors which may not be measured by any of the sensors in the vehicle. These include factors in the road environment such as congestion, construction, traffic light timings and other vehicles. The use of video cameras goes some way towards reducing (but not eliminating) this problem but requires a degree of manual processing that is very labour intensive. Accelerometers, which have been employed in several studies (for example, Barr et al., 2011; Lee et al., 2011), provide detailed information on lateral and longitudinal acceleration, which provides additional data on cornering, lane changes and other more precise movements which are not easily detectable

1 A larger study (SHRP-2) based on the methodology of the 100-Car study has recently completed data collection (Strategic Highway Research Program, 2013). 2 The cost of installing the necessary infrastructure means it is only financially feasible in dense environments. Differential GPS has similar advantages (and disadvantages) but can fall back on standard GPS when it is unavailable.

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with GPS and cameras. The data is, however, more difficult to analyse given the high sampling rate which can be over 30 observations per second compared to every second with GPS. On the other hand, GPS and other sensor-collected data sources are, with some caveats, more reliable than other sources of data and provide a richer picture of driver behaviour through space and time. The location attributes make it significantly simpler to supplement the behavioural data with other sources, in particular with geographic information system (GIS) data. Naturalistic driving studies also benefit from describing observed behaviour in (most cases) day-to-day driving providing an arguably more realistic view of how drivers behave in their vehicles than is found in surveys (Vassallo et al., 2007), pre-defined routes or simulator studies (Elliott et al., 2007) where the role of the researcher is more visible to the participant. 2.3. Creation of driver profiles from naturalistic driving data A number of researchers have used naturalistic driving data to create behavioural profiles of drivers. The most pertinent include the work by Toledo et al. (2008) in which a risk index was created for drivers in a fleet of commercial vehicles using data collected with in-vehicle data recorders (IVDR). The risk index incorporated a number of events such as lane changes, speeding and sudden braking behaviour that were identified using pattern matching techniques run on the raw data. Each recorded event was then weighted by the severity of the event and this was used to calculate a risk index using a linear function normalised using driving time. Subsequently, the values were transformed to fit on a zero to one scale where one represents a higher risk. The main purpose of the risk index was to provide a measure that would be understandable to drivers. The researchers also calculated an additional speed index due to the importance of speeding as a predictor of crash involvement. The risk indices were then tested against the participating drivers' crash records using a Poisson regression. The authors found a statistically significant relationship between the risk index and crash history. The approach was also used to look at young drivers and the effect of supervised driving sessions (Prato et al., 2010) with comparisons made by examining changes in the risk index for each driver. The main drawback of this approach is that it does not take into account the influence of the road environment and, therefore, in a before-and-after study potentially identifies in changes in when and where driving took place than any factors inherent in the driver. Toledo et al. (2008) also used time to normalise the risk indices between drivers but this tends to under-report events that occur at higher speeds since these occupy a shorter period of time than another event taking place at a lower speed. Jun (2006) examined patterns of speeding, acceleration and braking to predict crash involvement using data collected with an in-vehicle device incorporating GPS and onboard diagnostics (OBD). The objective here was to identify behaviours and their relationship to crash risk. These (individual) behavioural measures correctly predicted 68 percent of crash-involved drivers (26 drivers) and 87 percent of non-crash-involved drivers (141 drivers). These patterns were represented by a number of variables in the modelling that was conducted. A key finding was that the same behaviours were not observed with drivers with the same demographic characteristics but, in general, speeding patterns, hard acceleration and hard braking were associated with crash involvement. A similar process was used by Bagdadi and Várhelyi (2011) for acceleration and braking to determine that changes in acceleration (jerks) were the strongest predictors of crash involvement. A more recent paper by the same authors (Bagdadi and Várhelyi, 2013) further developed this technique, named the critical jerk method, to differentiate between critical and

potentially critical situations based on acceleration and braking patterns collected using accelerometer data. Due to small samples, however, further validation is necessary. Other researchers have recognised the importance of temporal differences in driver behaviour and have used GPS data to construct speed-time profiles as feedback for fleet vehicles (Şimşek et al., 2013). This does not, however, attempt to control for exogenous factors. Taken together, these studies suggest that profiles of driver behaviour can be created from GPS data and can, in turn, be related to crash involvement specifically and road safety more generally. The work by Toledo et al. (2008) in particular provides a useful and comprehensive methodology for monitoring drivers across time. However, what these and other similar profiling methods fail to take into account is the way in which driver behaviour is strongly related to the road environment and the way in which all aspects of the road environment are interdependent. This potentially creates situations in which the risk indices measure the road environment instead of the driver-influenced risk of interest, such as when driver behaviour is constrained by the road environment. The same issue complicates comparisons between drivers and limits the use of profiling to measure improvements in behaviour that occur after an external policy or environmental change since changes in when and where driving occurs would be captured in addition to the change (if any) due to the intervention. While in some cases it may be sufficient to use a number of measures in unison to deal with these issues, there are a number of situations in which this is not ideal. For example, in a PAYD insurance scheme drivers need to be provided with information on their behaviour in a way that allows them to see how they are improving (or not) over time. In this situation providing several measures of information may be confusing as they may move in opposite directions. Some statistical methodologies also require a single dependent variable and in cases where crash risk is the dependent variable, using several measures of risk limits the use of these methodologies. This suggests the need for a methodology which accounts for these factors and the complexity of the driving task and provides a single measure of risk. It is acknowledged that using a single measure can mask the contribution of individual behaviours and, as such, in some cases it is better to use separate measures for each of the behaviours. In the methodology presented in this paper, it is possible to use either the composite measure or individual measures as desired. 3. Framework and methodology To benefit from the advantages of naturalistic driving data while also providing a means to analyse, interpret and communicate the results of what are very large datasets, a driver behaviour profile (DBP) framework is proposed. The framework is designed around a composite measure of speeding, aggressive acceleration and aggressive braking behaviour but could easily be expanded to accommodate any number of behaviours and magnitudes if available, such as high speed cornering, lateral car control and frequent lane changes. In the case of this paper, these measures (or risk scores) are functions of the risk of involvement in a casualty crash. It extends the principles identified by other researchers (Bagdadi and Várhelyi, 2011; including Jun, 2006; Toledo et al., 2008) but conducts the assessment of risk at the disaggregate rather than aggregate level. Crucially it aims to isolate the impacts of the driver, by controlling for the interacting combination of exogenous factors (such as speed limit, time of day and weather) using what we have termed, temporal and spatial identifiers – TSIs (Ellison et al., 2013). It must be noted that the ability to control for confounding factors is reliant on the availability of data on those factors or proxies thereof and this needs to be considered when analysing results.

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Fig. 1. TSI road segments.

The primary purpose of DBPs is to provide a common measure of behaviour that enables comparisons across drivers, within drivers across time, within a driver across spatiotemporal environments and any other combinations of driver, time and space. Since the profiling is normalised, i.e. controls for spatiotemporal factors and vehicle kilometres travelled (VKT), and the algorithm automatically eliminates infrequent situations it is possible to compare scores (and thereby behaviours) when the data in the comparison subsets have different characteristics. The most suitable application for this is when testing road safety interventions in a before and after study. 3.1. Temporal and spatial identifiers (TSI) TSIs capture temporal and spatial factors in a set of metrics, which can be used to describe particular travel situations. For example, an observation made within a school zone, away from an intersection, with a 40 km/h speed limit, in the morning and on a weekday made by a driver with no passengers on a dry day can be uniquely identified using TSIs (Fig. 1). Unlike prior research which treats each spatiotemporal variable as independent (see Wang et al., 2009) TSIs recognise the interactions and interdependencies inherent in the conditions experienced by the driver including from the road environment, rainfall, time of day and the number of passengers. This is done by grouping these factors into a TSI, which using the example from Fig. 1 above, takes the form ST{S-40,TM-D-P0} where spatial factors are separated from temporal factors by a comma, factors are delimited by hyphens and each spatiotemporal factor is assigned one or more unique codes.3 The absence of a factor in the TSI, such as rainfall above, represents the absence of that factor in the spatiotemporal environment. In grouping these factors together in a TSI, this approach acknowledges that an environment where any one aspect changes has a direct or indirect effect on all the other factors. By first comparing behavioural observations collected from the same TSI, it is possible to control for spatiotemporal factors

3 The number of codes is determined by the number of categorical variables minus one.

since within a TSI these are common to all observations such that the observations are considered to be spatially and temporally similar. Spatiotemporal factors were selected for inclusion in the TSI on the basis of their contribution to the variability of speeding behaviour. This was determined from the results of multilevel (hierarchical) null models created using naturalistic driving data (see Familar et al., 2011). These null models contain no variables but use hierarchical associations between observations to identify the variability of speeding behaviour contained within four levels. Contribution to variability in speeding varied primarily by speed limit. Variability in speeding behaviour associated with segment, trip and day levels (combined) comprised 86 percent in 50 km/h zones reducing incrementally to 58 percent in 100 and 110 km/h zones. Driver-level variability contributed the remaining proportion of speeding variance. The variables included in the TSIs applied here are shown in Table 1. Most variables can also be used as proxies for other variables for which data may be more limited. In this paper, congestion is not explicitly included in the TSI but is managed by only including driver behaviour where the vehicle speed is at least 75 percent of the speed limit as a proxy for opportunity to speed (Lin and Niemeier, 2003). 3.2. DBP framework The framework (illustrated in Fig. 2) consists of characteristics associated with the road environment and the trip4 and relative risk factors associated with each behaviour and magnitude of relevance. The relative risk factors are themselves comprised of three components: frequency, magnitude and weights. Weights are relative risks5 associated with the magnitude (i.e. severity) of each behaviour, such as the risk of speeding by 10 km/h. Frequency refers to how often a single behaviour at a particular magnitude is observed as a proportion of distance.

4 Fig. 2 contains the road environment and trip characteristics included in the dataset used for this paper. The framework can accommodate any number of variables where the data is available. 5 See Section 3.4 on how these weights are determined.

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Table 1 Factors included in TSIs.

a

Variable Spatial

Description

Proxy for:

Speed limit School zonea Rain Signalised intersection Non-signalised intersection Roundabout

Speed limit of road Active school zone Presence of rainfall Signalised intersection within 25 m Non-signalised intersection within 25 m Roundabout within 25 m

Road type, lane width, land use Presence of children Weather, visibility, road surface conditions Pedestrian activity, high number of other vehicles Pedestrian activity, presence of other vehicles Presence of other vehicles

Temporal Time of day Weekend Number of passengers

Morning, day, afternoon or night Saturday or sunday

Light conditions, traffic conditions Traffic conditions In-vehicle distractions

Only applies on weekdays 08:00–09:30 and 14:30–16:00 during school terms.

Fig. 2. Driver behaviour profile framework.

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These inputs are combined into a DBP consisting of individual behavioural risk scores and a composite (or total) risk score on a zero to 100 point driver risk index. Drivers with higher risk scores are at greater risk of involvement in a casualty crash while, conversely, drivers with lower risk scores are at lower risk. The framework also includes a risk margin representing the upper and lower bounds of an individual driver’s typical behaviour.6 In addition, the standard deviation is provided as a measure of variability within a particular measure and overall. The DBP methodology permits the use of individual behavioural measures or the composite measure as desired. While the individual behavioural measures are not comparable to each other directly as they represent different relative risks, applying a weighted average permits them to be used together. This means that, for example in a PAYD scheme, drivers can be shown their composite score alone or as a stacked bar on a 0 to 100 scale indicating the contribution of each of the behaviours to the total score. In this way it is possible to gain the advantages of using a single measure where that is of benefit and the advantages of using distinct measures where that is the better option. The characteristics of the road environment and trip characteristics are (using TSIs) used to group together observations which have the same TSI and are, therefore, temporally and spatially similar to each other. Risk scores are then calculated for each TSI individually and in so doing this controls for the influence of these factors on driver behaviour – as they are held constant within a TSI – allowing for the isolation of the influence of the driver on driver behaviour. The methodology discussed in this paper applies DBPs to study speeding, acceleration and braking behaviour as a function of the risk of involvement in a casualty crash. If the outcome of interest is the risk of a collision at an intersection then the behaviours and the weights that are used should reflect the behaviours that are associated with higher risks of collisions at that intersection. It may also be appropriate to identify driving behaviour at and approaching intersections using TSIs (Ellison et al., 2013). 3.3. Driver behaviour profile algorithm The driver behaviour profile algorithm is an implementation of the DBP framework. The algorithm calculates the score, margins and standard deviation for each of the behaviours in each TSI and a composite score for each TSI and overall. The algorithm works through each driver, TSI and road segment7 in sequence and outputs the results to a database for review, export and analysis. The algorithm has been designed to accommodate various datasets and behaviours of interest. As such, observations can be excluded dynamically based on particular road characteristics (if desired) and minimum thresholds for distance, time or frequency of segments and TSIs can be used to remove unusual situations or, alternatively, to isolate particular situations. Fig. 3 graphically illustrates the algorithm. The basic element of the risk score calculations is the frequency and magnitude of the behaviours of interest. In this research these are speeding, acceleration and braking events derived from second-by-second GPS observations. In this case, measurements are recorded by the GPS device at one second intervals. Computationally, the algorithm starts by defining the data to be used and a number of indicators to represent attributes associated with each data point. As such, for each driver d,d = 1, . . . , D, we

6

The upper and lower bounds represent the standard deviation, maximum or minimum whichever is lower (for the upper bound) or higher (for the lower bound). 7 A new road segment is created every time the TSI changes. For more background see Ellison et al. (2013).

Fig. 3. Driver behaviour profile algorithm.

have Id + 1 GPS observations denoted by (xi, ti) for i = 0, . . . , Id, spanning the entire observation period, comprising multiple trips over multiple days, where xi is the location (coordinates) of observation i observed at time instant ti. We let the total time travelled by driver d be defined by Td and let the total distance travelled be Ld. We also define each time interval by Dti
ðti1 ; ti Þ; i = 1, . . . , Id. For notational convenience, index d is omitted for the moment. For each GPS observation we have an observed speed, denoted by v(xi, ti), which we assume is fixed over interval Dti. The distance travelled during time interval Dti
ðti1 ; ti Þ – which is typically one second – is given by li ¼ Dxi
k xi  xi1 k ; where k  k denotes the Euclidean distance between locations xi1 and xi. The change in speed during time interval Dti (i.e. acceleration or deceleration) can be computed as

Dvðxi ; ti Þ ¼

vðxi ; ti Þ  vðxi1 ; ti1 Þ : Dt i

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This may yield a positive value (acceleration), negative value (braking), or zero meaning the speed is the same as for the previous observation. Each observation of (xi, ti) can be mapped to a road segment comprised of sequential GPS observations with the same spatiotemporal characteristics. We let each segment be denoted by index g, g = 1, . . . , G. Then we define a segment mapping indicator dg(xi, ti), which equals one if (xi, ti) is of segment g, and zero otherwise. Similarly, each observation of (xi, ti) can be mapped to a unique TSI used to control for the influence of the road environment. We let each TSI be denoted by index m, m = 1, . . . , M. Then we define a TSI mapping indicator dg(xi, ti), which equals one if (xi, ti) is of TSI m, and zero otherwise. We can in turn map segment g to TSI m. We let dgm equal 1 if segment g is of TSI m, and zero otherwise. This is used later to determine the risk margin and standard deviations for each TSI. We further define a number of indicators to represent the magnitudes of behaviour of speeding, acceleration and braking. Let

dspeed ðxi ; ti Þ be an indicator that equals one if the speed v(xi, ti) falls mc in speeding category c2Cs, where this set of categories is defined as ranges of speeds in excess of the speed limit of TSI m, namely 1– 4 km/h, 5–9 km/h, 10–14 km/h, 15–19 km/h, and 20 km/h or more. acc In a similar manner, we let dc ðxi ; ti Þ be an indicator that equals one if the change of speed Dv(xi, ti) falls in acceleration category c2Ca, where the categories are defined as ranges of (positive) acceleration of 1 m/s2 each, namely 0–1 m/s2, 1–2 m/s2 to 9 m/s2 or more. brake

Finally, we define dc ðxi ; ti Þ as the indicator that equals one if the change in speed Dv(xi, ti) falls in braking category c2Cb, where the categories are defined as ranges of (negative) acceleration of 1 m/s2 from 0 to 1 m/s2, 1 to 2 m/s2 until 9 m/s2 or greater. From the previously defined indicators, we can then calculate speeding, acceleration and braking scores for each segment in each TSI for each driver (adding driver index d again at this point) using a per-km rate such that: Total speeding score for segment g, TSI m and for driver d is defined as: sgmd ¼

1 XX dg ðxi ; ti Þdm ðxi ; ti Þdspeed ðxi ; ti Þli wspeed c c Lgmd i c2C s

Total acceleration score for segment g, TSI m and for driver d is defined as: agmd ¼

1 XX acc dg ðxi ; ti Þdm ðxi ; ti Þdacc c ðxi ; t i Þli wc Lgmd i c2C

Total speeding score for TSI m for driver d: 1 XX dm ðxi ; ti Þdspeed ðxi ; ti Þli wspeed c c Lmd i c2C

smd ¼

s

Total acceleration score for TSI m for driver d: amd ¼

1 XX acc dm ðxi ; ti Þdacc c ðxi ; t i Þli wc Lmd i c2C a

Total braking score for TSI m for driver d: bmd ¼

1 XX dm ðxi ; ti Þdbrake ðxi ; ti Þli wbrake c c Lmd i c2C b

brake where wspeed ; wacc are the same exogenous weights c c ; and wc used to calculate the segment-level scores. We now normalise the scores to the ninetieth percentile8 of each of the behaviours at the segment level which we define as smax the speeding scores smd are normalised as m . Subsequently,   smd ; 8m; d. Similarly, the acceleration follows: smd ¼ 100=smax m   amd ; and the braking scores are normalised as amd ¼ 100=amax m  max  scores as bmd ¼ 100=bm bmd . This normalisation ensures that all scores have a range from 0 to 100 and are on the same scale regardless of if it is a segment-level, TSI-level or driver-level score. Using these normalised scores we can then compute the average score for each driver and for each TSI:

md ¼

1X s ; 8d M m md

mm ¼

1X s ; 8m D d md

Furthermore, the standard deviations can be calculated. The purpose of providing a measure of variability using the standard deviation statistic is to describe the variability within and between drivers and to adjust drivers’ risk margins to account for this. The standard deviations within drivers can be computed as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 X sd ¼ ðs  md Þ2 ; 8d M  1 m md

a

Total braking score for segment g, TSI m and for driver d is defined as: bgmd ¼

1 XX dg ðxi ; ti Þdm ðxi ; ti Þdbrake ðxi ; ti Þli wbrake c c Lgmd i c2C

The standard deviation within a TSI is derived from the segment-level scores sgmd, agmd and bgmd for segments g (1 to G) of TSI m which were defined earlier and can be shown as: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1 XX sm ¼ s  mm ; 8m D  1 d g gmd

b

brake where wspeed ; wacc are exogenous weights which relate c c ; and wc to the contribution to casualty crash risk of a particular behaviour at a particular magnitude. The derivation of these weights is discussed in Section 3.4. In the same way we can calculate speeding, acceleration, and breaking indicators for each driver in each of the TSIs as follows:

In order to calculate the speeding, acceleration, and braking scores for each individual driver, we compute the weighted average of the normalised scores over all TSIs such that the contribution of each TSI to the driver score is equivalent to the

8 The ninetieth percentile is used to constrain the scale because the highest scores are very unusual and setting the scale to account for these reduces the magnitude of the differences of the majority of the scores.

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proportion of total distance covered by that TSI such that, for example, speeding can be described as sd ¼

1X Lmd s : M m md Ld

.

The speeding risk margin for driver d is comprised of an upper   bound which can be defined as sud ¼ min sd þ s d ; maxfsmd g and a md   l lower bound that can be defined as sd ¼ max sd  s d ; minfsmd g . md

The risk margins for acceleration and braking are calculated in the same manner. The final score for a driver d then becomes ld ¼ vs sd þ vd ad þ vb bd ; where vs 2 ½0; 1 is the weight attached to speeding, va 2 ½0; 1 is the weight attached to acceleration, and vb 2 ½0; 1 is the weight attached to braking, respectively, where vs + va + vb = 1. Each weight represents the contribution of each behaviour (in aggregate) to the overall risk of involvement in a casualty crash. brake ; wacc where these represent a This contrasts with wspeed c c ; and wc set of weights of different magnitudes in a specific event.

3.4. Interpretation and derivation of weights Interpreting the scores requires an understanding of how the extreme scores (zero and 100) are computed. All the scores included in the output are on a common zero to 100 point scale where zero represents the lowest risk of involvement in a casualty crash and 100 represents the highest risk of involvement in a casualty crash.9 Crucially, a score of zero does not imply that there is no risk but instead represents the risk associated with driving according to recommended and legislative practices. Similarly, a score of 100 represents the risk associated with behaviours that are above the 90th percentile of (for example) speeding behaviour observed within the dataset.10 Since the objective here was to identify the driver characteristics that are associated with behaviour consistent with greater risk of involvement in a casualty crash, the weights were based on prior research into the relative risks associated with speeding, acceleration and braking, and crashes. The speeding magnitude ) were based on the weights (represented in the algorithm by wspeed c risk curve identified by Kloeden et al. (1997), shown in Table 2, which represents the risk of a casualty crash associated with exceeding the speed limit in a 60 km/h zone in Australia. A sensitivity analysis was conducted on the impact of different weights derived from Kloeden et al. (1997), Elvik (2012a) and a uniform weight for all speeding magnitudes. This was done by calculating the risk scores using three Kloeden-derived weights (relative risk, lower bound and upper bound), four Elvik-derived weights (shown in Table 3 from Elvik (2012b)) and one using a value of one as the weight for all magnitudes. In all cases, everything was held equal except for the weights. With the exception of the uniform weights, the relative positions of the drivers along the index remained largely unchanged among the seven other risk curves tested. Since the relative positions of drivers was largely consistent – as would be expected since all were derived from relative crash risk curves – the lower bound

9 Involvement in this case does not necessarily indicate fault although drivers with higher risk scores are also less likely to be able to avoid crashes caused by other drivers. 10 This maximum point on the scale can be adjusted depending on the factors of interest.

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Table 2 Relative risk of involvement in a casualty crash relative to travelling at 60 km/h in a 60 km/h speed zone (Kloeden et al., 1997). Speed range (km/h)

Relative risk

Lower bound

Upper bound

58–62 63–67 68–72 73–77 78–82 83–87 88+

1.00 2.00 4.16 10.60 31.81 56.55 Infinite

1.00 1.17 2.12 3.52 6.55 6.82 N/A

1.00 3.43 8.17 31.98 154.56 468.77 N/A

relative risks determined by Kloeden et al. (1997). This was selected because although speeding by the higher magnitudes is of significantly higher risk, this behaviour is uncommon in many road environments and therefore the large separation at the lower magnitudes relative to the higher magnitudes creates greater differences in speeding scores between drivers. brake The weights for acceleration (wacc ) c ) and braking (wc magnitudes were derived from thresholds identified in the literature (Bagdadi and Várhelyi, 2011; including Dingus et al., 2006; Jun et al., 2007) to be associated with crashes or near crashes. Specifically, drivers with higher frequencies of acceleration and braking events greater than approximately 3 m/s2 are involved in statistically significantly higher rates of crash involvement (Jun et al., 2007). Bagdadi and Várhelyi (2011) have identified that most crashes involve braking magnitudes of between 4 and 8 m/s2. Using naturalistic driving data Dingus et al. (2006) found 5 m/s2 accelerations to be a good threshold for identifying nearcrashes and crashes. As with the speeding weights, a sensitivity analysis was performed where equal, linear, exponential and threshold weights were changed while all else was held equal. Low magnitude acceleration and braking behaviour was given a zero weight in all cases since all driving requires a minimum magnitude of acceleration and braking. The final weights are shown in Table 4 and reflect the consensus of prior research. It should be noted that the acceleration and braking weights (as with speeding) should not be compared with each other since these reflect relative risks for acceleration and braking independently of each other. The individual behavioural scores were in turn weighted by the contribution of each of the behaviours to crash risk (vs, va, vb) to compute a total composite score. Kaplan and Prato (2012) examined the relationship between crash avoidance manoeuvres – including acceleration, braking and speeding – and crash severity. Using the crash database of the National Highway Traffic Safety Administration (NHTSA), Kaplan and Prato (2012) developed ordered logit models for different types of crashes. The model for crashes involving non-motorists, determined the probability of different behaviours forming part of crash avoidance manoeuvres. The relative probabilities of speeding, acceleration and braking factors from this model were used to weigh the individual behaviour scores to calculate the composite score. These weights were 0.42 for speeding (vs), 0.36 for braking (vb) and 0.22 for acceleration (va). This process accounts for the different contribution of each behaviour to crash risk. To provide some points of reference, in the dataset used in this paper, a synthetic driver created by treating the entire sample as a single driver has a total score of 34 with an upper margin of 57 and a lower margin of 11. The driver with the highest (riskiest) score has a total score of 55 and upper and lower margins of 76 and 34, respectively. In contrast, the driver with the lowest (least risky) score has a total score of 18, an upper margin of 34 and a lower margin of 1 which is only marginally above the lowest possible score of zero. Changes in behaviour between any two subsets of observed driving data can be interpreted in the same way. Keeping in mind

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Table 3 Crash ratios derived from Elvik (2012b). Initial speed (km/h)

Final speed (km/h)

Exponent

Initial crashes

Final crashes

Crash ratio

55 km/h Base speed 55 55 55 55 55 55 55

85 80 75 70 65 60 55

4.12 4.12 2.35 2.35 1.46 1.46 –

6 6 6 6 6 6 6

37 29 13 11 8 7 6

6.01 4.68 2.07 1.76 1.28 1.14 1.00

65 km/h Base speed 65 65 65 65 65 65 65

95 90 85 80 75 70 65

5.41 5.41 5.77 5.77 3.39 3.39 –

8 8 8 8 8 8 8

62 46 37 26 13 10 8

7.78 5.81 4.71 3.32 1.62 1.29 1.00

75 km/h Base speed 75 75 75 75 75 75 75

105 100 95 90 85 80 75

5.58 5.58 6.63 6.63 8.50 8.50 –

13 13 13 13 13 13 13

85 64 62 43 37 22 13

6.54 4.98 4.79 3.35 2.90 1.73 1.00

Average Speed limit Speed limit Speed limit Speed limit Speed limit

20 15–19 10–14 5–9 1–4

– – – – –

– – – – –

– – – – –

5.16 3.86 2.81 1.93 1.38

that the scores at the extreme ends of the scale are constrained as described previously, it can be said that the driver with the highest score (55) has a relative risk of involvement in a casualty crash three times higher than the driver with the lowest score (18) during the study period or subset thereof. This is because all the risk scores are determined based on relative risk curves and therefore the resulting scores are also relative risks. The interpretation would differ depending on the derivation of the weights that are used. 4. Data sources and application Using surveys and GPS data collected from 106 drivers during a 10 week pay-as-you-drive (PAYD) study in Sydney, Australia (Greaves et al., 2010), the DBP framework and algorithm were applied to assess the relationship between driver characteristics and behaviour. The study comprised a number of different phases, illustrated in Fig. 4, of which the recruitment surveys and GPS data from weeks 1 to 5 are used in this paper.

At the recruitment stage, drivers completed a demographic, vehicle and psychological survey (Greaves and Ellison, 2011). During the five-week GPS phase used here, second-by-second GPS data were collected using a Mobile Devices Ingenierie C4 GPS device installed in each participant’s car. These devices collected GPS data including speed, position (latitude and longitude), time and date, which were transmitted to a processing server using General Packet Radio Service (GPRS) every 20 s. These data were then used to identify the speed limit and other spatiotemporal characteristics associated with each observation using the TSI methodology (Ellison et al., 2013). Trip characteristics such as the driver of the vehicle, trip purpose and the number of passengers were collected from participants using an online prompted-recall website which participants were asked to visit every day (Greaves et al., 2010). GPS data were then processed and run through the DBP algorithm described earlier. The final distributions of driver scores for the individual behaviours and the composite (total) scores, by driver, are shown in Fig. 5, sorted in all cases by the composite score by driver.

Table 4 Acceleration and braking magnitude weights. Acceleration categories (m/s2)

Acceleration weight

Braking categories (m/s2)

Braking weight

1 2 3 4 5 6 7 8 9 >9

0 0 0 3 5 7 9 9 9 9

1 2 3 4 5 6 7 8 9 >9

0 0 3 6 12 24 48 48 48 48

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Fig. 4. Study phases.

It should be noted that although the highest total score is 58 (on average over all TSIs), the same drivers exhibit scores from 0 to 100 in particular TSIs demonstrating the variation in behaviour by the same drivers in different situations (see Fig. 6). The final dataset run through the algorithm includes driving over a distance of 107,701 km across 344,264 road segments in 385 unique TSIs. In addition, as previously discussed, the algorithm (with the default options set) excludes road segments with fewer than five observations (i.e. 5 s) and excludes TSIs that were observed less than three times. In addition, for braking and acceleration scores, segments with fewer than five observations with non-zero acceleration and braking were also excluded. 5. Applications DBP scores can be applied in a number of ways. We first briefly illustrate their use in measuring changes in driver behaviour over time. Secondly, the scores are used as input into a regression model to determine the driver and vehicle factors associated with higher (i.e. more dangerous) scores. 5.1. DBP scores across time Fig. 7 shows the change in speeding scores before and after the introduction of the PAYD scheme (Greaves et al., 2013). Here, it can be observed that the majority of drivers exhibited reduced speeding scores (shown in the green shaded area) indicating that

the financial intervention resulted in lower risks of involvement in a casualty crash. Similarly, DBPs can be used to examine differences within or between drivers across time and space. For example, Fig. 8 is an illustration of the distribution of TSI speeding scores for high risk, medium risk and low risk drivers on weekends and weekdays. It can be observed that the pattern, particularly for the high risk driver, is quite different on weekends than on weekdays alluding to the (more frequent) constraints imposed by congestion during weekdays. It is also quite apparent that high, median and low risk drivers are quite different between them as well as within their own driving. While these plots alone are of limited use, they do suggest that there may be some factors worth investigating. The modelling results (presented in Section 5.2) confirm this. 5.2. Examining influencing factors in crash risk using DBP scores To illustrate the use of DBPs in modelling, analyses were run to identify the driver demographics, vehicle and road environment factors associated with higher risks of involvement in a casualty crash as measured by drivers’ speeding, acceleration, braking and total scores. The intention here was to determine the factors that are associated with higher DBP scores which represent a greater risk of involvement in a casualty crash. Individual models were developed for each of the behaviours (speeding, acceleration and braking) and for the total score. To account for the interactions between the spatiotemporal environment (as represented by the

Fig. 5. Behaviour and composite scores (before phase) by driver.

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Fig. 6. Total score ranges (before phase) by driver.

Fig. 7. Changes in speeding scores between before and after periods by driver. Website logins were used as a proxy for exposure and awareness of the intervention.

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Fig. 8. Density of speeding score for three example drivers by weekday/weekend.

TSIs) and driver behaviour, multilevel regression modelling was applied. Multilevel models are a method of applying regression that recognises that observations are not completely independent of each other but instead are associated with each other by sharing common elements such as the participant, road environment or time. In a multilevel model, independent variables (shown in Table 5) are assigned to levels in a hierarchical structure – as shown in Fig. 9 – such that within a particular level all the observations share the same value for the level above. In this case, it was also possible to define the driver as level 1 and the TSI as level 2, Table 5 Multilevel regression model independent dummy variables.a Variable Spatial

Level

Description

Speed limit School zone Rain

TSI TSI TSI

40, 50, 60, 70, 80, 90, 100, 110 (km/h) 0: No, 1: yes 0: No, 1: yes

Temporal Time of day Weekend Number of passengers

TSI TSI TSI

1: Morning, 2: day 3: afternoon, 4: night 0: No, 1: yes 0: None, 1: 1, 2: 2, 3: 3+

Driver Driver Driver

1: 1: 1: 3:

Driver Driver

1:Male, 2: female 1:18–30, 2: 31–45, 3: 46–65 (years)

Vehicle Vehicle Vehicle Vehicle

characteristics transmission body model year

Driver demographics Gender Age

Automatic, 2: manual Sedan, 2: hatchback, 3: other 1999, 2: 2000–2004, 2005 or newer (year)

Note: Bolded values refer to the regression reference categories and units are shown in brackets. a Since many variables are categorical, both parametric and non-parametric models were run with little difference between them. The non-parametric models are shown here because they are simpler to interpret.

however the best results were observed for the structure shown here. To ensure the dataset does not violate the assumptions of regression, three main adjustments were made to the scores after they were calculated. First, TSIs with a total VKT of less than 1 km were excluded from the model. Second, scores at the extreme ends of the scale (exactly zero or 100) were tested in separate models (not shown). Lastly, rank transformation was employed to fit the data to a Poisson distribution. This is permissible because the behavioural scores are on a common relative scale and, therefore, an observation with a score of 25 represents safer driving (half the risk) of a score of 50. As a consequence, performing a rank transformation does not change the underlying differences between them. To maintain consistency the same process was applied to all models. The variables are listed in Table 5 and are divided into four categories. Spatial variables represent the road environment and vary by location, temporal variables represent the factors that vary by time while vehicle characteristics and driver demographics remain unchanged for the duration of the study. The results – shown in Table 6 – show that across all the models, the strongest predictors of behaviour are the spatiotemporal characteristics captured at the TSI level. This means that although some driver and vehicle characteristics (specifically younger drivers and those driving a vehicle with an automatic transmission) have a statistically significant impact on a higher risk11 of a casualty crash, the effects of these are overshadowed by the road environment. In terms of spatiotemporal characteristics, the results suggest that higher speed limits are associated with lower (relative) DBP scores, and consequently, lower risk. While this appears

11 In this paper, unless otherwise stated, risk refers to the risk of involvement in a casualty crash.

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weather respectively. This is particularly pronounced for speeding behaviour. Temporally, each additional passenger is associated with lower risk driving relative to driving with no passengers. There may be some interaction here with other demographics (Fleiter et al., 2006) but when this was tested there were no significant findings. Additionally, weekend driving is associated with higher speeding scores but lower braking scores demonstrating that in some circumstances the same situation can result in mixed effects on behaviour, and by extension, risk. Vehicle characteristics are also related to lower risk scores albeit to a lesser extent than spatial characteristics. Newer vehicles are associated with higher (more risky) speeding scores while compared to automatic vehicles, vehicles with a manual transmission are associated with lower DBP scores. 6. Discussion and conclusions

Fig. 9. Multilevel model structure.

counter-intuitive, given speeding is more common in higher speed zones (Familar et al., 2011), it reflects the greater contribution of the individual on driver behaviour in higher speed zones. On roads with lower speed limits, there are (typically) more constraints on the possibility to engage in higher risk driving (and speeding in particular). This includes the roadway design and temporal effects such as congestion which are largely controlled for with the TSI and DBP approaches used here. As a consequence, the modelling results are for the driver effects that emerge in different situations. Driving in school zones and rain are also strongly associated with lower DBP scores relative to non-school zones and dry

This paper introduces the concept of driver behaviour profiles (DBPs) and presents the results of an investigation into the factors associated with a higher probability of involvement in a casualty crash. This was done using DBPs to account for the complexity of the driving task and applying multilevel models and temporal and spatial identifiers (TSIs) to control for the spatiotemporal environment. While changing the road environment to constrain driver behaviour would likely have a significant benefit on safety – albeit at a very high financial cost – this research shows that different road environments elicit different behavioural responses in drivers over and above any constraining effects. These psychological responses in drivers then translate into more (or less) risky driving behaviour. If these responses can be identified, driver behaviour could potentially be improved by focusing education or enforcement campaigns on shifting these responses in higher risk environments to be more similar to the lower risk environments. Put another way, education campaigns are

Table 6 Parameter estimates for multilevel models. Speeding

Acceleration

Braking

Total

Intercept

B 4.105

Std. Error 0.069

Sig. 0.000

B 3.760

Std. Error 0.065

Sig. 0.000

B 3.453

Std. Error 0.401

Sig. 0.000

B 4.030

Std. Error 0.349

Sig. 0.000

Spatial elements Speed limit (50) Speed limit (60) Speed limit (70) Speed limit (80) Speed limit (90) Speed limit (100) Speed limit (110) School zone Rain

0.229 0.428 0.513 0.481 0.590 0.463 0.640 0.276 0.136

0.057 0.057 0.059 0.060 0.064 0.070 0.080 0.078 0.046

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.000 0.003

0.020 0.108 0.324 0.477 1.112 1.544 2.109 0.007 0.057

0.050 0.050 0.052 0.054 0.069 0.109 0.153 0.092 0.056

0.689 0.031 0.000 0.000 0.000 0.000 0.000 0.942 0.305

0.444 0.436 0.250 0.072 -0.290 0.880 0.871 0.033 0.142

0.398 0.398 0.398 0.398 0.399 0.404 0.405 0.079 0.046

0.264 0.273 0.531 0.857 0.467 0.029 0.031 0.681 0.002

0.001 0.109 0.333 0.455 0.854 0.920 1.059 0.157 0.221

0.347 0.347 0.347 0.347 0.348 0.349 0.350 0.050 0.033

0.998 0.753 0.337 0.190 0.014 0.008 0.003 0.002 0.000

Temporal elements Time (day) Time (afternoon) Time (night) Weekend Num. passengers

0.014 0.064 0.038 0.077 0.019

0.025 0.025 0.029 0.017 0.008

0.586 0.010 0.187 0.000 0.023

0.039 0.036 0.015 0.018 0.012

0.027 0.027 0.033 0.018 0.009

0.150 0.182 0.644 0.332 0.162

0.010 0.016 0.153 0.079 0.009

0.028 0.028 0.032 0.019 0.009

0.729 0.549 0.000 0.000 0.313

0.024 0.015 0.141 0.006 0.018

0.019 0.018 0.022 0.013 0.006

0.202 0.414 0.000 0.647 0.004

Vehicle characteristics Type (hatchback) Type (other) Model year Transmission (manual)

0.023 0.000 0.035 0.077

0.020 0.021 0.011 0.020

0.246 0.982 0.001 0.000

0.006 0.033 0.006 0.021

0.021 0.022 0.012 0.020

0.782 0.137 0.592 0.295

0.004 0.004 0.002 0.005

0.020 0.022 0.011 0.019

0.862 0.857 0.822 0.805

0.039 0.021 0.008 0.058

0.015 0.016 0.008 0.015

0.009 0.190 0.301 0.000

Driver demographics Male: age Female: age

0.063 0.061

0.011 0.013

0.000 0.000

0.005 0.010

0.012 0.013

0.651 0.472

0.032 0.027

0.011 0.013

0.005 0.038

0.060 0.059

0.008 0.009

0.000 0.000

Note (1): Cells in bold are significant at the p = .01 level. Note (2): Cells in italics are significant at the p = .05 level.

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frequently targeted at particular driver demographic groups. Targeting of behaviour in particular road environments, as is occasionally done for school zones, could be used as an additional targeting or framing strategy. The DBP framework and methodology itself can be applied, as demonstrated in this paper, towards studying driver behaviour to improve road safety. These profiles provide measures of behaviour tied to the outcome of interest – in this case the risk of involvement in a casualty crash – and account for the non-linear and nonuniform impact of each behaviour and magnitude. Without an approach such as this, different models of behaviour would need to be created for each magnitude since the consequences vary. Due to its modular structure, the methodology can be extended to incorporate any number of additional measures of behaviour as long as they can be reliably measured. This includes cornering, lateral acceleration, lane changing and following distance. Therefore, there is the potential to use this methodology for assessing a large number of potential behaviours in addition to those presented in this paper. More broadly, DBPs can be applied by industry or government for several purposes. The most widely applicable use of DBPs is likely the ability to empirically test the effectiveness of changes to infrastructure, education campaigns or legislation on road safety outcomes (Ellison et al., 2015). This includes cost-benefit analyses by placing a value on the risk score. The combination of a common measure of risk and a disaggregate approach allows for this to be carried out for a large spatial area (such as a city, state, province or country) down to, given sufficient data, specific road segments or intersections. Similarly, it is possible to use the disaggregate results to examine differences for the same driver across time or in different situations enabling investigations into the effects of, for instance, insurance schemes, fines, signage or education campaigns. While this paper presents an improvement on current methods of assessing driver behaviour, some limitations remain. The TSI and DBP methodologies employed here are only as good as the data that are used. In particular, the spatiotemporal factors incorporated into the TSI should be expanded if data are available to account for external factors that have not been explicitly accounted for here. Congestion, road surface conditions, lighting conditions and more detailed weather information would all be beneficial. It should also be noted that the analyses presented here exclude behaviour observed at intersections. This is because behaviour at intersections is strongly associated with traffic light status for which data were not available in this study. However, the framework and TSI methodology have been designed to accommodate these additional elements in the future. DBPs also rely heavily on naturalistic driving data that are not always available, although in small scales these could be imputed from other sources such as simulators or video footage. The major limitation is the lack of crash data with which to validate the DBP scores. Larger and longer duration naturalistic driving studies such as the Strategic Highway Research Program 2 (SHRP2) (Antin et al., 2011) could be used as input into the DBP algorithm for validation as it contains incidents of recorded casualty crashes while the dataset available to the authors did not. Disaggregate crash data would also allow for refinement of the magnitude weights such as using different sets of weights in each TSI. In conclusion, driver behaviour profiles are a means of describing and assessing driver behaviour within a single normalised measure that accounts for the complexity of the driving task in a manner that aggregate measures do not. These have been applied to identify the driver characteristics that are associated with speeding, acceleration and braking as a function of the risk of a casualty crash. The flexibility in its design further allows the approach to be extended to apply to a large number of

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