Road traffic congestion and crash severity: econometric analysis using ordered response models

Transcription

1 Loughborough Unversty Insttutonal Repostory Road traffc congeston and crash severty: econometrc analyss usng ordered response models Ths tem was submtted to Loughborough Unversty's Insttutonal Repostory by the/an author. Ctaton: QUDDUS, M.A., WANG, C. and ISON, S.G., Road traffc congeston and crash severty: econometrc analyss usng ordered response models. Journal of Transportaton Engneerng, 136 (5), pp Metadata Record: Verson: Accepted for publcaton Publsher: c Amercan Socety of Cvl Engneers Please cte the publshed verson.

2 Ths tem was submtted to Loughborough s Insttutonal Repostory ( by the author and s made avalable under the followng Creatve Commons Lcence condtons. For the full text of ths lcence, please go to:

3 Road Traffc Congeston and Crash Severty: An Econometrc Analyss Usng Ordered Response Models Mohammed A Quddus Chao Wang Stephen G Ison Transport Studes Group Department of Cvl and Buldng Engneerng Loughborough Unversty Loughborough, Lecestershre LE11 3TU UNITED KINGDOM

4 Abstract: There s an ongong debate among transport planners and safety polcy makers as to whether there s any assocaton between the level of traffc congeston and road safety. One can expect that the ncreased level of traffc congeston ads road safety and ths s because average traffc speed s relatvely low n a congested condton relatve to an un-congested condton whch may result n less severe crashes. The relatonshp between congeston and safety may not be so straghtforward however as there are a number of other factors such as, traffc flow, drver characterstcs, road geometry and vehcle desgn affectng crash severty. Prevous studes have employed count data models (ether Posson or negatve bnomals and ther extensons) whle developng a relatonshp between the frequency of traffc crashes and traffc flow or densty (as a proxy for traffc congeston). The use of aggregated crash counts at a road segment level or at an area level wth the proxy for congeston may obscure the actual relatonshp. The objectve of ths study s to explore the relatonshp between the severty of road crashes and the level of traffc congeston usng dsaggregated crash records and a measure of traffc congeston whle controllng for other contrbutory factors. Ordered response models such as ordered logt models, heterogeneous choce models and generalsed ordered logt (partally constraned) models sutable for both ordnal dependent varables and dsaggregate crash data are used. Data on crashes, traffc characterstcs (e.g., congeston, flow, speed) and road geometry (e.g., curvature and gradent) were collected from the M25 London orbtal motorway between 2003 and Our results suggest that the level of traffc congeston does not affect the severty of road crashes on the M25 motorway. The mpact of traffc flow on the severty of crashes however shows an nterestng result. All other factors ncluded n the models also provde results consstent wth exstng studes. Keywords: Traffc congeston, traffc flow, crash severty, ordered response models, M25 motorway 2

5 INTRODUCTION Two major factors n promotng economc productvty of a healther economy are enhanced moblty and mproved safety. There s an ongong debate among transport planners and safety polcy makers on the ssue as to whether there s any assocaton between moblty and road safety. Prevous research suggests that the ncreased level of traffc congeston (less moblty) mproves road safety (Shafer and Retveld, 1997). Ths s because average traffc speed s relatvely low n a congested condton n contrast to an un-congested condton whch may lead to less severe traffc crashes. However, ths may ncrease the occurrence of traffc conflcts often resultng more slght njury crashes. The ncreased level of traffc congeston reduces moblty whch results n an economc loss to socety. On the other hand, t s more lkely that the level of crash severty would ncrease f a transport network s not congested. Ths suggests that the total external costs of crashes may be hgh n an un-congested condton relatve to a congested condton and as such t can be thought that traffc congeston ads road safety but decreases economc productvty. Ths poses a potental dlemma for transport polcy makers: on the one hand wantng to reduce congeston but ths may lead to more severe traffc crashes ncreasng the total external cost of congeston. In other words, the beneft of reducng congeston mght be offset by more severe crashes (Noland and Quddus, 2005). It s, therefore, mportant to understand the assocaton between traffc congeston and road safety so that effectve polcy can be mplemented to address both congeston and road safety. The relatonshp between traffc congeston and road safety, especally crash severty may not be so straghtforward as there are other factors affectng the severty of a crash. Ths ncludes other traffc characterstcs (e.g., traffc flow and traffc speed), drver characterstcs (e.g., seat-belt usage, age, experence, gender and alcohol consumpton), vehcle condtons and road geometry (e.g., gradent, curvature, road wdth). To take all of these factors nto account, researchers have employed varous statstcal models to develop a relatonshp between crashes and ther contrbutng factors such as traffc characterstcs, drver behavour, vehcle desgn and road nfrastructure. Some of the studes are dscussed below. In order to estmate the external cost caused by road crashes, Person et al. (1998) proposed that t s necessary to nvestgate the relatonshp between road accdents and traffc flow and found that crash frequency ncreases (ether proportonally or at one and a quarter) f traffc flow ncreases. Research undertaken by Dckerson et al. (2000) nvestgated the relatonshp between the frequency of road crashes and traffc flow wth the am of estmatng the change n the external cost of crashes caused by addtonal traffc flow. Dfferent road types and geographcal areas were consdered and they found that a strong negatve crash externalty was assocated wth hgh traffc flows. Ivan et al. (2000) nvestgated sngle and mult-vehcle hghway crash rates and ther relatonshp wth traffc densty whle controllng for land use, tme of day and lght condtons. Temporal effects were also consdered. For sngle-vehcle crashes, they found a negatve-exponental relatonshp wth the densty (volume/capacty rato), meanng that the crash rate s hghest at a low volume/capacty rato, but ths s not fully consstent wth the study by Lord et al. (2005) who conducted the analyss on the relatonshp among crash, densty (vehcles per km per lane) and v/c rato. They found that wth v/c rato ncreasng, fatal and sngle-vehcle crashes decreases at some pont, and crash rates follows a U-shape relatonshp. Bascally, all these studes suggested a postve relatonshp between flow and frequency of traffc crashes. Some studes looked at ths ssue further by nvestgatng hourly traffc flow and crash rates. For example, Martn (2002) nvestgated the relatonshp between crash ncdence and traffc flow on French motorways, fndng that crash rates are the hghest n lght traffc 3

6 compared to heavy traffc, especally on 3-lane motorways. There s no sgnfcant dfference between daytme and nght-tme crashes. However, f crash severty s consdered, nght-tme and lght-traffc hourly crashes are much worse. Therefore, the author concluded that lght traffc (low traffc flow) s a safety problem both n terms of crash rates and severty. Many thngs however could affect road safety durng nght-tme such as lghtng and as such needs further research. Hselus (2004), on the other hand, showed the mportance of the consderaton of traffc flows,.e., the crash rate would be dfferent dependng on whether the traffc flows s homogeneous or not. It s notceable that most of the prevous studes examned aggregated crash counts (ether at a road segment level or at an area level) n developng a relatonshp among crashes, traffc characterstcs and other contrbutng factors. Moreover, varous proxes were used to represent traffc congeston such as traffc flow and densty. Therefore, the prmary am of ths study s to nvestgate the assocaton between the severty (slght, serous and fatal) of ndvdual crashes and the level of traffc congeston measured by total delay. Other contrbutory factors such as traffc flow, traffc speed, crash characterstcs (e.g., a sngle-vehcle or a multple-vehcle crash, number of casualtes per crash, etc.), weather condtons, lght condtons, road surface condtons and road geometry (e.g., gradent and curvature) are also consdered whle developng the relatonshp. It should be noted that no attempt s made to estmate the actual probablty of a specfc accdent occurrng. Statstcal models sutable for both dsaggregated crash data and ordered dependent varable (such as slght, serous and fatal) are used. The paper s organsed as follows. The next secton provdes a dscusson of the statstcal models used n the study. Ths s followed by a descrpton of the data used n the analyss. The estmaton results along wth a dscusson on the fndngs are then presented. The paper ends wth conclusons, lmtatons and future research drectons. ORDERED RESPONSE MODELS (ORM) The severty of a traffc crash can be expressed by the serousness of the crash classfed as slght, serous and fatal. It s explctly clear that the dependent varable s categorcal and ordered n nature n whch a slght njury crash can be coded as 1, a serous njury accdent can be coded as 2 and a fatal njury accdent can be coded as 3. It should be noted that when a dependent varable s both categorcal and ordnal, the dstances between categores are unknown. When such an ordnal varable appears on the left-hand sde of a statstcal model, t s obvous that ordnary least-squares (OLS) estmaton suffers from many shortcomngs (see Long, 1997 for detals). In order to deal wth an ordered categorcal varable, the use of an ordered logt (an OLOGIT) or ordered probt (an OPROBIT) model s more approprate (Long 1997; Greene 2000; Gujrat 2003). These models are condtonal as t assumed that an accdent has already occurred and the factors affectng the accdents are known. However, a recent study byyamamoto et al. (2008) suggested that tradtonal unordered models may provde unbased estmate of the parameters, especally n the case for mssng data such as under-reportng. Readers are also referred to a number of exstng studes that recommend to explore alternatve models (Mlton et al., 2008; Eluru et al., 2008, Anastasopoulos et al., 2008). Therefore, n order to nvestgate the mpact of traffc congeston on the severty of road crashes, the concept of ordered models s retaned and the selected model s an OLOGIT model and ts varous extensons. Although, the OPROBIT model s also sutable 4

7 for an ordered categorcal varable, the OLOGIT model s selected 1 because both logt and probt formulatons provde very smlar results. Assumng that the severty of a road crash s an ordered dscrete varable wth j categores (slght, serous and fatal), an OLOGIT model (n terms of probablty) can be wrtten as (Long, 1997): Pr( y exp( X β j ) j X ) g( X β ), j 1,..., m 1 (1) 1 exp( X β ) j where X s a (k 1) vector of observed non-random explanatory varables; β s a (k 1) vector of unknown parameters to be estmated; m s the number of categores of the ordnal dependent varable. The parameters of the model ( β ) and the cut-ponts ( 1 and 2 ) are estmated by the method of maxmum lkelhood (Long, 1997). In equaton (1), t s assumed that the effects of explanatory varables on the level of severty are assumed to be fxed across observatons. However, ths may not be true as the effect of a explanatory varable may vary across observatons. To overcome ths problem, a number of recent studes have suggested to employ random parameters models (e.g., Anastasopoulos and Mannerng, 2009; McFadden and Tran, 2009; Ben-Akva et al., 2002). One of the prmary assumptons of an OLOGIT (and an OPROBIT) models s that the error varances are homoskedastc. In the context of ordnary least squares (OLS), a volaton of ths assumpton (.e., heteroskedastcty) does not bas the estmates, rather t ether nflates or underestmates the standard errors. Heteroskedastcty, however, s more problematc n the case for models dealng wth categorcal dependent varables such as logt or probt and ther ordered varants. If varances of the error term are non-constant, not only the standard errors are ncorrect, but also the parameters are based and nconsstent (Keele and Park, 2006 ). In order to deal wth unequal error varances, Wllams (2006a) suggests the use of a heterogeneous choce model (HCM) whch can be wrtten as: Pr( y X β exp( j ) X β j X ) g( ), j 1,..., m 1 (2) X β 1 exp( j ) n whch ln Z where Z s the vector of explanatory varables (ether dummy or contnuous varables) that effect the error varance ( ). Z could ether be a subset of X or a set of new varables not ncluded n X. Another mportant assumpton assocated wth an OLOGIT (and an OPROBIT) regresson s that the relatonshp between each par of outcome groups s the same. In the lterature, ths s known as the proportonal odds assumpton or the parallel regresson assumpton (see Long, 1997 for detals).. If the proportonal odds assumpton s not vald, one needs dfferent models to descrbe the relatonshp between each par of outcome groups. 1 The logt model s preferred to the probt. The logt model assumes that the dsturbances are Webull dstrbuted (Gumbel extreme value type I), whereas the probt model assumes that the dsturbances are multvarate normally dstrbuted 5

8 Therefore, t s essental to test the proportonal odds assumpton after estmatng an OLOGIT model. The Brant test (Brant, 1990) could be employ to test the above assumpton. A sgnfcant test statstc provdes evdence that the proportonal odds assumpton s volated. If ths s the case, then the use of the OLOGIT model may lead to ncorrect, ncomplete or msleadng results (Fu, 1998). A soluton s then to employ a generalsed ordered logt (GOLOGIT) model whch does not mpose the constrants of parallel regressons (Fu, 1998). The unconstraned GOLOGIT model can be rewrtten as: Pr( y exp( X β j j ) j X ) g( X β j ), j 1,..., m 1 (3) 1 exp( X β ) j j An ssue wth ths GOLOGIT model s that t estmates far more parameters than s really necessary (Wllams, 2006b). For nstance, f a dependent varable has 4 categores and there are 10 ndependent varables, the GOLOGIT model estmates a total of 30 coeffcents. Ths sometmes makes t dffcult to nterpret the results. Wllams (2006b) then proposes a partally constraned GOLOGOT model known as a partal proportonal odds model n whch only a subset of coeffcents are constraned across values of j and therefore, s less restrctve than a GOLOGIT. In a recent study, Wang and Abdel-Aty (2008) employed ths model to nvestgate the left-turn crash njury severty at ntersectons. Ths model can be rewrtten as: exp( X1 β 1j X 2 β2 j ) Pr( y j X ), j 1,..., m 1 (4) 1 exp( X β X β ) 1 1j 2 2 j n whch the coeffcents assocated wth a subset of ndependent varables X 2 are the same across values of j and the coeffcents related to other ndependent varables ( X 1 ) dffer across values of j. Eluru et al. (2008) consdered a mxed GOLOGIT model for examnng pedestran and bcyclst njury severty level n traffc crashes but could not fnd any statstcally sgnfcant unobserved heterogenety effects on the latent njury rsk propensty and the cut-ponts and therefore, used a GOLOGIT model. Ths research examnes whether there s any assocaton between the severty of road crashes and the level of traffc congeston employng three ordered response models: (1) an OLOGIT (2) a HCM and (3) a PC GOLOGIT. DATA In order to examne the assocaton between the level of traffc congeston and the crash severty, the UK M25 motorway has been chosen as a case study. The M25 motorway s a 188 km (each drecton) London orbtal motorway whch almost completely encrcles London. There are two prmary reasons for selectng the M25: (1) ths motorway s consdered as one of the busest (about 200,000 vehcles a day n 2003) motorways n Europe and, therefore, there s suffcent spato-temporal varaton n congeston condtons whch 6

9 allow us to develop statstcal models that relate traffc congeston and crash severty. (2) data on traffc characterstcs (e.g., traffc congeston, traffc speed, traffc flow) and road geometry (e.g., radus of road curvature, gradent, number of lanes) are avalable to us for the M25 motorway from 2003 to However, one of the dsadvantages (from a purely research perspectve) of usng the M25 as a case study s that the number of fatal and serous crashes on the M25 s qute low - there were 23 people klled and 116 serously njured on the M25 n In order to tackle ths problem, statstcal models that can look nto ndvdual crash records are used and crash data for multple years (2003 to 2006) are consdered. STATS19 UK road crash data from 2003 and 2006 were obtaned from the UK data archve (UKDA 2 ). STATS19 data have three data fles: (1) crash data (2) vehcle data and (3) casualty data. A unque crash reference number allows one to ntegrate these three data fles. The vehcle data fle contans nformaton regardng drver age and gender. Although drver age and gender affects the severty of a crash, such data cannot be used whle analysng multple-vehcle crashes 3 as there s no nformaton as to whether whch drver s at-fault (or not-at-fault) for the crash. Traffc characterstcs data such as traffc congeston, traffc speed (km/h) and traffc flow (vehcles/h) were obtaned from the UK Hghways Agency (UKHA 4 ). These data were avalable from 2003 to 2006 for a total of 72 segments of the M25 (both drectons) at 15- mnute ntervals. Traffc congeston at each of these segments s measured by the total delay (mnutes) encountered by all vehcles travellng on that segment. In order to take nto account the lengths of the segments, the total delay s averaged over a 10-km stretch of the motorway. Snce each segment starts and also termnates at a juncton, t s reasonable to assume that delays, traffc speed and traffc flow are the same on dfferent locatons of the segment. Road geometry data such as the radus of road curvature (m) and gradent or vertcal grade (%) were also obtaned from the UKHA. Snce a seres of curvatures and gradents were avalable for a segment, the mnmum radus of curvature and the maxmum gradent were consdered. Data on the number of lanes were also obtaned from the UKHA. Snce STATS19 data have the eastng and northng coordnates of a crash locaton, t s possble to dentfy the motorway segment (out of the 72 segments) on whch the crash occurred. Snce both crash locaton data and dgtal motorway segment data contaned errors and the two drectons (clockwse and ant-clockwse) of the M25 motorway are treated separately, a matchng technque consderng the drecton(s) of the vehcle(s) just before the crash relatve to the drecton of the motorway segment (ether clockwse or ant-clockwse) and the dstance from the crash locaton to the segment was used to match the crash locaton onto the correct motorway segment (see Wang et al., 2009 for detals). In order to ntegrate STATS19 data wth the traffc data, a common varable between these datasets was used. There was only one common varable between them whch was the tme epoch as the tme of the crash (for the STATS19 data) and the tme at whch the traffc data were measured (for the UKHA data) were known. Therefore, t was possble to determne the level of congeston, the average traffc speed and traffc flow for each crash record. In order to avod the mpact of the crash tself on the traffc varables, a 30-mnute tme lag was consdered. For nstance, f a crash happened at 15:00 then traffc data measured at 14:30 were used when these two datasets were combned. A total of 3,998 crashes occurred on the M25 motorway between 2003 and Of whch 1.28% were fatal crashes, 8.83% were serous njury crashes and 89.89% were slght njury crashes. Table 1 shows summary statstcs of the varables that wll be consdered n the models About 85% of the M25 motorway crashes are multple-vehcle crashes 4 7

10 Table 1 s about here The combned dataset shows that the average total delay (over all 72 motorway segments) at whch fatal crashes occurred s 4 mnutes. Ths ncreases to 8 mnutes for the case of serous njury crashes and 9.6 mnutes for the case of slght njury crashes. Ths suggests that there may be a relatonshp between total delay and the severty of crashes. Ths s also true for traffc flow as the mean traffc flow at whch fatal crashes happened on the M25 s 2131 veh/h. Ths ncreases to 3345 veh/h for the case of serous njury crashes and 3911 veh/h for the case of slght njury crashes suggestng that there s an assocaton between traffc flow and the severty of crashes. The average traffc speed at whch fatal crashes occurred s 93km/h. Ths decreases to 86km/h for the case of serous njures and 84.5km/h for the case of slght njury crashes. The M25 motorway has a varable number of lanes wth a mnmum two-lane and a maxmum sx-lane (n each drecton). Accordng to data from the UKHA, the motorway has three-lane for most of ts length (66.8%) and four-lane for 24.9% of ts length. There are a few short stretches whch are two-lane (2.4%), fve-lane (4.2%) and sx-lane (1.7%). It mght be nterestng to see whether road wdth (number of lanes) has any mpact on the level of crash severty. The detals of other explanatory varables can be found n Table 1. VARIABLES SELECTION AND RESULTS Before estmatng any models usng the data, a multcollnearty test among the explanatory varables was carred out suggestng that fne and ranng weather condtons were hghly correlated (correlaton coeffcent: 0.7) wth dry and wet road surface condtons and as expected, traffc congeston was found to be hghly and negatvely correlated (correlaton coeffcent: -0.8) wth average traffc speed. Snce our nterest s to examne the assocaton between traffc congeston and the severty of road crashes, average traffc speed was taken out from the set of explanatory varables along wth weather condtons. Surprsngly, posted speed lmt was found to be un-correlated wth average traffc speed. Ths may be due to the fact that average speed vares wth the level of traffc congeston. When a road s congested, the average speed s much lower than the posted speed lmt; whereas motorsts would drve faster than the speed lmt f a road s not congested. Ths may also be the results of motorst's percepton and psychology, hghway hypnoss (see Werthem, 1978; Cerezuela et al., 2004) and rsk compensaton (Assum et al., 1999; Dulsse, 1997; Wnston et al., 2006). Another nterestng observaton was that tme of the day (.e., peak and off-peak perods) was not correlated wth traffc congeston as one would expect that traffc congeston s normally hgh durng the peak hours. The set of un-correlated explanatory varables was used to estmate dfferent ordered response models such as OLOGIT, HCM, GOLOGIT and PC-GOLOGIT. The results are presented n Table 2. The varable speed lmt was found to be statstcally nsgnfcant n all models and n addton, a log-lkelhood rato (LR) test also confrmed that the ncluson of ths varable dd not mprove the model goodness-of-ft. Therefore, ths varable was dropped from all models. Table 2 shows that the lkelhood rato (LR) Ch-square s hgher n the HCM compared wth the OLOGIT model. The dfference n the LR Ch-squares between these two models was found to be statstcally sgnfcant (p-value<0.01) suggestng that the results of the HCM are much better than those of the OLOGIT model. As notced, the explanatory varables of the HCM were dvded nto two classes: (1) the varables affectng the ordnal categorcal choce (.e., fatal, serous and slght njury crashes) and (2) the varables affectng 8

11 varances of the error term known as the determnants of varablty n the error term across observatons. It was expected that all explanatory varables had an mpact on the level of crash severty. The set of varables for the error varance equaton was dentfed by a stepwse selecton method employng a LR test 5. The test suggested that crash category by vehcle type (ether a sngle-vehcle crash or a mult-vehcle crash) and casualtes per crash are the statstcally sgnfcant varables for the ncluson n the varance equaton. Ths was also confrmed by the HCM estmaton results n whch both varables were found to be statstcally sgnfcant n the error varance equaton. Therefore, t s reasonable to beleve that crash category and casualtes per crash could be a potental source of heteroskedastcty whle analysng the severty of crashes. In addton to the fxed-parameter ordered logt model, the random- parameter ordered logt model was also estmated. It was found that the random effects were statstcally nsgnfcant. The mxed multnomal logt model n whch certan parameters were assumed to be random was also estmated. Once agan, the standard devatons of random parameters were found to be statstcally nsgnfcant. The Brant test (Brant, 1990) was carred out to see whether the proportonal odds assumpton was volated for the data used n the analyss. A sgnfcant test statstc provded evdence that the assumpton has been volated. A user-wrtten STATA routne ologt2 (developed by Wllam (2006)) was used to dentfy the varables whch dd not meet the proportonal odds assumpton. It was found that two explanatory varables (log of traffc flow and number of vehcles nvolved n the crash) dd not meet the assumpton and therefore, ther coeffcents dffered across dfferent thresholds suggestng that the OLOGIT model s a msspecfed model and GOLOGIT or PC-GOLOGOT models should be used. Table 2 s about here Table 2 shows that the coeffcents of all explanatory varables are dfferent across thresholds for the GOLOGIT model whereas only the coeffcents of log of traffc flow and number of vehcles nvolved n the crash were dfferent across thresholds for the PC- GOLOGIT model. Although the value of the lkelhood rato (LR) Ch square s hgher n the GOLOGIT model relatve to the PC-GOLOGIT model, the dfference s not statstcally sgnfcant as the value n the GOLOGIT model s only 10.5 unts more for 13 degrees of freedom (p-value=0.65). Ths suggests that the model goodness-of-ft s better n the PC- GOLOGIT model compared to the GOLOGIT model. In terms of both log-lkelhood at convergence and LR Ch square, there s no dfference between HCM and PC-GOLOGIT models (see Tables 2 and 3). However, HCM handles the effect of heteroskedastcty and PC- GOLOGIT addresses the volaton of proportonal odds assumpton. Snce the results from these two models are qute smlar n terms of sgns and the set of statstcally sgnfcant varables, the PC-GOLOGIT model wll be used to nterpret the effects of the explanatory varables on the crash severty. Table 3 s about here Usng these estmated coeffcents and cut ponts, the probabltes of three dfferent outcomes (slght, serous and fatal) for the gven values of explanatory varables were obtaned. From these estmated probabltes, factors that are more lkely to reduce the probablty of a partcular level of severty were dentfed. Table 3 shows the margnal effects 5 By usng a user-wrtten STATA routne known as oglm by Wllams (2006a) 9

12 for the probabltes of dfferent outcomes wth respect to the statstcally sgnfcant ndependent varables. The nterpretaton of each of the explanatory varables s gven below. Traffc congeston: As dscussed prevously, traffc congeston at the tme of a crash s measured as the total delay encountered by all vehcles travellng on a segment (averaged over a 10km-stretch) where the crash occurred. It was hypotheszed that the level of traffc congeston has an mpact on the severty of the crash outcome. More specfcally, when a crash happens on a road segment wth a hgh level of traffc congeston, one would expect that the severty of the crash would be relatvely low resultng n a slght njury crash and vce-versa. However, our data from the M25 motorway do not support ths hypothess and ths s the case for all ordered response models estmated n ths study. Fgure 1 s about here Other measurements of traffc congeston such as a congeston ndex based on actual and free flow travel tme proposed by Taylor et al. (1999) was used but also found to be statstcally nsgnfcant n all models. One would expect that total delay representng the level of traffc congeston may be correlated wth the tme of the day varable (an ndcator varable for peak perod) and therefore, ths fndng may be ncorrect. Ths was not the case however as we found that there s no correlaton (correlaton coeffcent: 0.2) between these two varables for the data we analysed. Fgure 1 shows the observed hourly delay (averaged over the four years) just before the crashes happened. It s notceable that the pattern of delay s dfferent for weekends and weekdays. Durng the weekdays, the total delay s hgh at peak perods but ths s not the case for the total delay durng the weekends. However, all ordered response models were also estmated when the dummy varable for the peak perod was beng dropped. Nevertheless, the level of traffc congeston was stll found to be statstcally nsgnfcant. Another possble reason would be the ncluson of traffc flow n the models as one would expect that hgher traffc flow (per lane per hour) would be correlated wth total delay. Although ths was not the case, all models were estmated wth the excluson of total flow varable. The sgn of the coeffcent was found to be the expected negatve sgn but agan statstcally nsgnfcant n all models. In addton, the LR test dd not support the excluson of total flow varable from the set of explanatory varables. Models were also estmated by other dfferent combnatons of explanatory varables but total delay was consstently found to be statstcally nsgnfcant. Traffc flow: Ths varable was found to be one of the mportant varables n explanng the severty of a road crash snce the excluson of ths varable sgnfcantly ncreased (about 25 unts) the log-lkelhood at convergence. Not surprsngly, ths varable was found to be statstcally sgnfcant at the 95% confdence level n all models. As dscussed, the Brant test suggested that traffc flow nfluences the cut-off ponts (thresholds) and, therefore, the mpact of ths varable on the level of crash severty dffered across dfferent thresholds. In general, t was found that f traffc flow ncreases then the level of crash severty decreases meanng that a road segment wth hgh traffc flow would result n less severe crashes, f all else reman constant. It s notceable that the value of the coeffcent s sgnfcantly dfferent (about 70%) between the thresholds. It was found to be more negatve n the threshold that dvdes serous njury and fatal crashes suggestng that t s more lkely that hgher values on traffc flow ncrease the lkelhood of beng a slght njury crash. The mpact of traffc flow on the severty of crashes s not unform across dfferent crash categores and ths type of effect could not be found from an OLOGIT model. 10

13 Fgure 2 s about here It s also of nterest to estmate the probablty of a specfc crash occurrng (.e., slght, serous and fatal) for a gven value of traffc flow. Fgure 2 shows how the predcted probabltes of dfferent categores of crashes change wth the change n the traffc flow. These probabltes were obtaned from the results of the PC-GOLOGIT model. For an average traffc flow (3843 veh/h) on a three-lane stretch of the M25 durng weekends, daylght, off-peak perods and at dry weather condtons, the estmated probabltes of dfferent categores of a crash nvolvng a sngle-vehcle n 2003 are as follows: Pr( Slght ) 0.8, Pr( Serous) and Pr( Fatal ) Table 3 shows the margnal effects of the probabltes of a specfc crash occurrng for changes n the explanatory varables. For nstance, the margnal effect for the probablty of a slght njury crash occurrng wth respect to traffc flow (veh/h) s postve and the value s ,.e.: Pr( y Slght) ( TraffcFlow) The margnal effect for the probablty of a serous njury crash occurrng wth respect to traffc flow (veh/h) s negatve and the value s ,.e.: Pr( y Serous) ( TraffcFlow) The margnal effect for the probablty of a fatal crash occurrng wth respect to traffc flow (veh/h) s negatve and the value s ,.e.: Pr( y Fatal) ( TraffcFlow) Number of vehcles nvolved n the crash: Road traffc crash data ( ) from the M25 suggest that sngle-vehcle crashes were more severe than mult-vehcle crashes. For nstance, 3.4% sngle-vehcle crashes were fatal crashes compared to only 0.9% n the case for mult-vehcle crashes. Ths s also true for the case of serous njury crashes n whch 14% of sngle-vehcle crashes were serous njury crashes and on the other hand, 8% of mult-vehcle crashes were serous njury crashes. Therefore, t was expected that the models used n ths study should be able to pck up such effects. The dummy varable used to represent a sngle-vehcle crash was found to be postvely assocated wth the severty of crashes meanng that a sngle-vehcle crash s lkely to result n a more severe crash compared wth a mult-vehcle crash, f all else are held constant. As dscussed, ths varable dd not meet the proportonal odds assumpton and therefore, the coeffcent value dffers across thresholds. For the frst threshold, the value s 0.66 and for the second threshold, ths ncreases to 1.19 suggestng that the effect of a crash nvolvng a sngle-vehcle on the severty was not unform. A crash nvolvng a sngle-vehcle on the M25 s more lkely to result n a more severe crash relatve to a crash nvolvng multple-vehcle. 11

14 The margnal effects of probabltes of a specfc crash occurrng for a change from a mult-vehcle crash to a sngle-vehcle crash are shown n Table 3. When the dummy varable (representng whether a crash s a sngle-vehcle crash) changes from 0 (a mult-vehcle crash) to 1 (a sngle-vehcle crash), the predcted probablty of outcome: slght njury changes by , serous njury changes by 0.05 and fatalty changes by 0.014, holdng all other varables at ther means. Ths fndng also confrms that a sngle-vehcle crash s more lkely to result n a hgher level of severty on M25. Fgure 3 shows observed and predcted probabltes of serous and slght njury categores for both sngle-vehcle and mult-vehcle crashes. Both actual and predcted probabltes are qute smlar ndcatng that a good measure of ft for the model. Fgure 3 s about here Road surface condtons: Two types of road surface condtons (at the nstant of a crash) are consdered: (1) dry and (2) wet. An ndcator varable was used to characterse them n the models where 0 means dry road surface condtons and 1 means wet road surface condtons. Ths ndcator varable was hghly and postvely correlated (correlaton coeffcent = 0.7) wth weather condtons (specfcally wth ranng ) suggestng that wet surface condtons are mostly due to the result of ranng weather condtons. Our results suggest that wet road surface condtons reduce the level of M25 crash severty compared wth dry surface condtons. Ths fndng s consstent wth other studes (e.g., Quddus et al., 2002; Duncan et al., 1998; Shankar and Mannerng, 1996). Quddus et al. (2002) argued that ths s lkely to be an effect of reduced speed levels. All models were also estmated wth weather condtons categorsed as fne, ranng, snowng and others (whle the ndcator varable for road surface condtons was beng dropped). The results (not shown here for brevty) also suggest that ranng weather condtons reduce the level of M25 crash severty compared wth fne weather condtons whlst snowng and others weather condtons were not statstcally sgnfcant. Number of lanes: As dscussed, the number of lanes wthn the M25 vares from twoto sx-lane n each drecton. STATS19 UK road crash data (2003 to 2006) suggest that 71% of all serous njury crashes and 67% of all fatal crashes happened on the three-lane stretches of the motorway. In order to see whether the varablty n lanes has an mpact on the level of crash severty, a categorcal varable wth three categores was used n the models. The categores were: (1) three-lane (or less) (2) four-lane (3) fve- lane (or hgher) and the second category was taken as a reference case. The results suggest that the level of crash severty on the stretches wth three-lane (or less) was statstcally and sgnfcantly dfferent than that of on the stretches wth four-lane. There was no dfference n the crash severty between stretches wth four-lane and stretches wth fve-lane (or hgher) gven that all other varables ncluded n the models were held constant. Crashes on the stretches of M25 wth three-lane appear to ncrease crash severty levels. Ths s also reflected n the sgns of the margnal effects of ths categorcal varable (three-lane, fve-lane where four-lane s taken as a reference) on the probabltes of dfferent njury crashes (see Table 3). The sgn s negatve for the margnal effect of the probablty of a slght njury crash and postve for margnal effects of the probabltes of a serous njury crash or a fatal crash. Tme trend: Both a tme trend varable representng the month n whch the crash occurred and a categorcal varable representng the crashes that occurred n dfferent years 12

15 were tested and the results were found to be very smlar. Therefore, models only wth a categorcal varable are shown for brevty. Ths categorcal varable has four categores such as year 2003, year 2004, year 2005 and year The frst category was used as a reference case. It can be seen that the coeffcents for 2004, 2005 and 2006 are negatve suggestng that there s a downward trend n njury severty 6. Some factors (not ncluded n the models) that vary over tme are leadng to ths trend. The sgns of the margnal effects of probabltes for ether a serous or a fatal crash occurrng are also negatve for 2004, 2005 and 2006 (see Table 3). Ths fndng s consstent wth other studes that used STATS19 data (e.g., Noland and Quddus, 2004). Number of casualtes per crash: About 65% of the crashes occurred on the M25 between 2003 and 2006 had a sngle casualty, 22% of the crashes had two casualtes, 7% of the crashes had three casualtes and 3% of the crashes had four casualtes. The average number of casualtes per crash s A slght njury crash wth a sngle casualty and a slght njury crash wth multple casualtes were taken as an dentcal dependent varable n our models. Ths mght be a problem gven that a slght njury crash wth multple casualtes s consdered to be more severe than a slght njury crash wth a sngle casualty. In order to control for such effects, a contnuous varable representng the number of casualtes per crash was used n the models. The results suggest that the level of severty ncreases wth the ncrease n the number of casualtes per crash. Fgure 4 shows how the predcted probabltes of dfferent categores of crashes change wth the change n the number of casualtes per crash. Fgure 4 s about here Other factors: Other factors that had an effect on the severty of road crashes were found to be the radus of road curvature, day of the week and lght condtons. However, all of these varables were statstcally sgnfcant only at the 90% confdence level. If the radus of road curvature of a road segment ncreases then the severty of a crash that occurred n that segment also ncreases suggestng that crashes on a straghter road segment (relatvely hgh radus of curvature) were more severe than a curved road segment (relatvely low radus of curvature). Although one would thnk that ths s a surprsng result, exstng studes (Haynes et al., 2007 and Wang et al., 2008) whle examnng the frequency of klled and serously njured (KSI) crashes at the area-wde level also found that curved roads are safer than straghter roads. Mlton and Mannerng (1998) also found that sharp horzontal curves tend to decrease accdent frequency. Whle comparng wth a dsaggregated crash data, ths result s nconsstent wth the fndng of Quddus et al (2002) that reported that bends n the road appear to result n more severe njures whle nvestgatng the severty of road crashes n an urban area. Snce the characterstcs of road confguraton between an urban area and a motorway (M25 n our case) s qute dfferent, a dssmlar result can be expected. Lookng at day of the week effects (weekdays = 1 and weekend = 0), more severe crashes are predcted durng weekdays. However, ths fndng s not consstent wth the fndng of Gray et al. (2008) who found that crashes n Great Brtan are more severe on Frdays, Saturdays and Sundays (relatve to Mondays). In order to nvestgate ths, a categorcal varable of seven categores representng seven days of the week was also examned (the results are not shown for brevty). However, less severe crashes are predcted on Sundays, Tuesdays, Frdays and Saturdays (relatve to Mondays). Ths agan suggests that 6 The coeffcent for 2006 s statstcally sgnfcant at only 80% confdence level 13

16 day of the week effects on the crash severty between motorways and other types of roadways may be dfferent. The varable lght condtons (darkness=1, daylght=0) allows us to nvestgate the effect of the level of lght on the njury severty. Less severe njury crashes are predcted durng darkness. Ths fndng s also not consstent wth that of Gray et al. (2008) whle analysng the crash severty n London. CONCLUSIONS Dsaggregated crash data from the M25 motorway have been used to nvestgate the assocaton between the severty of road crash and the level of traffc congeston. Ths has been done whle controllng for other contrbutory factors such as traffc characterstcs (e.g., traffc flow), road geometry (e.g., curvature and gradent) and crash characterstcs (e.g., sngle-vehcle or mult-vehcle). Statstcal models such as ordered logt models, heterogeneous choce models and partally constraned generalsed ordered logt (PC- GOLOGIT) models sutable for an ordered response varable have been employed. Our results suggest that ordered logt models are not approprate for the data we analysed. Both heterogeneous choce models and partally constraned generalsed ordered logt models have ftted the data equally. The results are also consstent between these two models. Our results suggest that that the level of traffc congeston (measured by total delay or congeston ndex) does not affect the severty of road crashes on the M25 motorway. However, the mpact of traffc flow on the severty of crashes shows an nterestng result. Whle prevous studes show a postve assocaton between the frequency of traffc crashes and traffc flow, our dsaggregated analyss suggests that ncreased traffc flow reduces the severty of crashes. The PC - GOLOGIT model has also been used to estmate the change n the relatve probablty of three dfferent levels of severty of a crash for gven values of explanatory varables. The factors that result n less severe crashes have been found to be traffc flow, radus of road curvature, darkness lght condtons, wet road surface condtons and tme trend. The factors resultng n hgh severe crashes have been found to be three-lane stretches of the motorway, sngle-vehcle crash and weekdays. The gradent of road segment and tme of the day have found to be nsgnfcant. One of the lmtatons of ths study s that traffc flow and speed values were assgned to crashes based on segment measurements. However, segments would not necessarly have unform condtons over 10km length f queues are present. There are a number of ways to extend the analyss used n ths study. It would be nterestng to analyse sngle-vehcle crashes separately as there s clear evdence that crashes nvolvng a sngle-vehcle are more severe than those nvolvng multple-vehcle. In such an analyss, the effects of drver age and gender on the severty of a crash can also be estmated. Another possble extenson would be to consder crashes that occurred on dfferent types of roads such as motorways, A roads, B roads and mnor roads. ACKNOWLEDGEMENTS The authors would lke to thank the UK Hghways Agency for provdng traffc characterstcs data for the M25 motorway. The content of the paper however does not express the vews of the Hghways Agency and the authors take full responsblty for the content of the paper and any errors or omssons. 14

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20 Table 1: Summary statstcs of varables ncluded n the models Varables Mean Std. Dev. Mn Max The level of crash severty* Level of traffc congeston (mnutes) Traffc flow n vehcles/h Average traffc speed (km/h) Radus of road curvature n m Gradent (%) Number of casualtes per crash Speed lmt (km/h) (20mph) (70mph) Categorcal or dummy varables Number of lanes Descrpton Three-lane (or less) 1=Three-lane or less (count= 2420), 0=otherwse (count=1578) Four-lane 1=Four-lane (count=1218), 0=otherwse (count=2780) Fve-lane (or more) 1=Fve-lane or more (count=360), 0=otherwse (count=3638) Tme of the day Day of the week Lght condtons 1=peak (count=1574), 0=off-peak (count=2424) 1=weekdays (count=3137), 0=weekends (count=861) 1=darkness (count=1328), 0=daylght (count=2670) Weather condtons Fne 1=Fne (count=3313), 0=otherwse (count=685) Ranng 1=Ranng (count=547), 0=otherwse (count=3451) Snowng 1=Snowng (count=13), 0=otherwse (count=3985) Others (Fog/mst) 1=others (count=125), 0=otherwse (count=3873) Road surface condtons Number of vehcles nvolved 1=wet road surface (count=1072, dry road surface=2926) 1=sngle-vehcle (count=528), 0=mult-vehcle(3470) Year of the crash Year =Year 2003 (count=956), 0=otherwse (count=3042) Year =Year 2004 (count=1067), 0=otherwse (count=2931) Year =Year 2005 (count=1039), 0=otherwse (count=2959) Year =Year 2004 (count=936), 0=otherwse (count=3062) *1=Slght (count=3594), 2=Serous (count=353), 3=Fatal (count=51) 18