Crash Frequency and Severity Modeling Using Clustered Data from Washington State

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1 Proceedngs of the IEEE ITSC IEEE Intellgent Transportaton Systems Conference Toronto, Canada, September 17-20, 2006 WB7.1 Crash Frequency and Severty Modelng Usng Clustered Data from Washngton State Janmng Ma and Kara Kockelman Abstract Ths study nvestgates the relatonshp between crash frequences, roadway desgn and use features by utlzng the benefts of clustered panel data. Homogeneous hgh-speed roadway segments across the State of Washngton were grouped usng cluster analyss technque, resultng n grouped observatons wth reasonably contnuous crash count values. Ths permtted applcaton of both fxed- and random-effects lnear regresson models for the total number of crashes 100 per mllon vehcle mles traveled (VMT). A crash severty model also was estmated, usng an ordered probt regresson, allowng transformaton of total crash counts nto counts by severty. Speed lmt nformaton s found to be very valuable n predctng crash occurrence. For roadways wth average desgn and use attrbutes, a 10 m/h ncrease speed lmt from 55 m/h results n 3.29% more crashes expected for the average roadway secton at a speed lmt of 55 m/h. However, speed lmts may have based coeffcents, most lkely attrbutable to unobserved safety-related effects. In addton, the authors also conducted a cost/beneft analyss of rasng speed lmt. An ncrease n speed lmt from 55 m/h to 65 m/h would save 106,879 hours per 100 mllon VMT, whch s equvalent to $1,607,455. The addtonal crash counts due to the ncrease n speed lmt only cause $437,964 loss. The results suggest that rasng speed lmts can offer some consderable tme savngs benefts. T I. INTRODUCTION RAFFIC crashes reman a major publc health problem. In ,815 persons ded on U.S. roads, and almost 3 mllon were njured n over 6 mllon polce-reported motor vehcle traffc crashes [1]. NHTSA[1] estmates the total cost at $230 bllon, or over $800 per person annually. Through a better understandng of what mpacts crash frequency and crash severty, effectve lfe- and cost-savng measures can be pursued. Roadway segments vary dramatcally n ther desgn and use levels, even durng the course of a mle along a sngle routng. In modelng crash counts as a functon of desgn detals, lke vertcal grade and horzontal curvature, modelers often must analyze data from very short segments n order to obtan unformty n desgn and use characterstcs. Over the course of a year, crashes on short segments are typcally few, Manuscrpt receved February 25, Ths work was supported n part by NCHRP project Janmng Ma s wth the Center for Transportaton Research of the Unversty of Texas at Austn, Austn, TX USA (e-mal: mjmng@mal.utexas.edu). Kara Kockelman s wth the Department of Cvl, Archtectural and Envronmental Engneerng, the Unversty of Texas at Austn, Austn, TX USA. (Correspondng author, ; fax: ; e-mal: kkockelm@mal.utexas.edu). partcularly fatal crashes. Under these condtons, classcal lnear regresson models are not workable. Dscrete models of counts are used. For example, Maou and Lum [2] employed Posson regresson models to nvestgate the relatonshp between crash occurrence and hghway geometrc desgn features n Utah. Shankar et al. [3] used negatve bnomal models to nvestgate the effects of roadway geometrcs and envronmental factors on rural freeway crash occurrence. Poch and Mannerng [4] and Mlton and Mannerng [5] also used negatve bnomal regresson models. And Shankar et al. [6] have used zero-nflated Posson (ZIP) models. McCarthy [7] employed fxed-effects negatve bnomal models to examne fatal crash counts usng 9 years of panel data for 418 ctes and 57 areas n the U.S. Noland [8] used fxed- and random-effects negatve bnomal models to nvestgate the effects of roadway mprovements on traffc safety usng 14 years of data for all 50 U.S. states. Kweon and Kockelman [9] also used such models (along wth zero-nflated and smpler, pooled models) to study the effects of speed lmts, desgn, and use on crash occurrence n Washngton State. There are certan drawbacks to usng count models, such as possbly nconsstent estmaton and nference due to potentally napproprate dstrbutonal assumptons, together wth dffculty n quanttatve nterpretaton of parameters (due to exponental or other transformatons of the rate equaton n order to ensure postve predctons). In order to account for these ssues, another approach s taken here, whch frst classfes roadway segment observatons nto relatvely homogeneous clusters, and then models crash frequences usng a lnear specfcatons. Others n transportaton safety analyss have used cluster analyss, but for dfferent applcatons. Almost three decades ago Moellerng [10] studed the patterns of traffc crashes usng geographcal cluster analyss. Golob and Recker [11] utlzed cluster analyss to classfy traffc flow regmes for dfferent freeway crash types. Le Blanc and Rucks [12] clustered crashes occurrng on the lower Msssspp Rver by crash type, traffc level, and locaton. Wong et al. [13] grouped safety projects for Hong Kong roadways and examned the relatonshp wth crash rates usng lnear regresson models wth statstcally sgnfcant tme trends. Wells-Parker and Cosby [14] clustered DUI (drvng whle under the nfluence of alcohol or drugs) offenders nto fve subgroups based on number of traffc volatons and other characterstcs and examned relatonshps between varables lke alcohol consumpton and accdent rsk. Gregersen and Berg [15] /06/$ IEEE 1621

2 clustered young persons by lfestyle and examned crash rsk. Ulleberg [16] also clustered young drvers and nvestgated ther responses to a traffc safety campagn. Fnally, Sohn [17] nvestgated the relatonshps between crash counts, roadway desgn, and other factors usng Posson regresson models for clustered Korean crash data. Among all these, only Wong et al. [13] and Sohn [17] used regresson analyss based on ther clustered data, resultng n applcatons most smlar to those pursued here. The remanng sectons of ths paper descrbe the data sets and methods used here, as well as emprcal fndngs. Conclusons, ncludng suggestons for further study, are then summarzed. II. DATA SET AND CLUSTER ANALYSIS The crash data sets used here were collected from Washngton State through the Hghway Safety Informaton System (HSIS). A total of more than 760,000 occupants were nvolved n about 263,970 reported crashes, resultng n more than 2,400 fataltes from 1993 to 1996 and from 1999 to 2002 on Washngton State hghways. These data contan nformaton on occupants demographcs, roadway desgn features, vehcle characterstcs, envronmental condtons (at the tme of crash), and basc crash nformaton (such as crash severty, tme, locatons and type). Speed lmts are a key varable for ths work, so the data emphasze the years 1993 through 1996, and 1999 through 2002, whch bracket the repeal of the Natonal Maxmum Speed Lmt (NMSL). Ths work also emphaszes hgh-speed roadways, so straght roadway segments havng speed lmts less than 50 m/h were removed from the data set. (Some hgh-speed roadways have relatvely tght horzontal curves along them, wth lowered speed lmts. These curved sectons were kept n the data set, snce ther assocated corrdor s hgh-speed n nature.) Usually the average crash count and rate per roadway segment n the orgnal data set are very low, featurng prmarly zeros, even over the course of a year or more. Aggregaton of smlar segments, va cluster analyss, rases these response values, ultmately permttng the use of contnuous regresson models. Contnuous model results are easer to apprecate than those of dscrete, count-based models, where a latent term and non-lnear transformatons complcate the data analyss and the evaluaton of regresson model results. Cluster analyss groups observatons nto relatvely homogenous collectons (.e., clusters) by essentally mnmzng the varance or spread across defnng varables of nterest wthn the clusters, and maxmzng that between clusters. The results of ths technque are descrbed here. The 100,457 short segments were clustered on the bass of ther desgn attrbutes. In order to mantan a consstent panel after clusterng, roadway segments experencng changes n desgn features durng 1993 through 2002 (ncludng number of lanes, roadway classfcaton, terran, presence of medan, degree of curvature, vertcal grade, and rght shoulder wdth) were removed from the further analyss. The remanng 41,348 segments account for 59% of total mles, 65% of VMT and 63% of total crashes. The groups of each varable for clusterng are shown n Table I. The clusterng of data was performed as follows: Assgn a specfed membershp to the segments whose attrbutes are n the same group n terms of tems lsted n Table I, and repeat ths process untl all segments have been assgned a membershp. Each unque membershp refers to a cluster. After gettng membershp for each segment, aggregaton wthn each membershp was appled to get the correspondng values for the nterested varables. Ther assocated dependent varable nformaton (.e., crash counts and VMT) were summed to create overall crash rates for each cluster n each year of the data set. For ther assocated ndependent varables, values were VMT-weghted averages. The membershp obtaned from clusterng the 1993 data set of segments was employed to cluster the remanng observatons, from 1994 through 1996, and from 1999 through Clearly, the data have been made much more contnuous n nature, permttng applcaton of more standard and easer to nterpret lnear models. III. MODEL ESTIMATION AND ANALYSIS A. Crash Frequency Model Panel datasets, such as the one descrbed above, can have a number of advantages compared to less structured data. Panel data permt dentfcaton of varatons across ndvdual roadway segments and varatons over tme. Accommodaton of observaton-specfc effects also mtgates omtted-varables bas, by mplctly recognzng segment-specfc attrbutes that may be correlated wth control varables. Models that are appled to analyze such datasets must take account of ther panel nature. Two of the standard model types that are approprate for panel data are fxed and random effects models. In the fxed-effects (FE) lnear model, the specfcaton s as follows [18]: y x for 1, 2,, N and t 1, 2,, T (1) t t t where s the roadway segment s specfc effect, a constant term that does not vary over tme. In random-effects (RE) lnear panel models, the specfcaton s as follows [18]: t t t y x u (2) where u s the random effect specfc to roadway segment, and t s as above. There s one random effect for each segment and t remans constant over tme; however, each segment s ndvdual u s assumed to be a realzaton from 1622

3 an underlyng dstrbuton of effects that s common to all segments. Usually, RE estmates are more effcent than FE estmates snce they are obtaned by makng use of both wthn-group and between-group varatons (rather than only wthn-group varatons). However, when there s correlaton between omtted unobserved varables and ncluded explanatory varables, the RE estmates are based whle the FE estmates are unbased [19]. The queston arses as to whch model should be used n practce. If FE models are used, there wll be a loss of N 1degrees of freedom n estmatng the segment specfc effects. If RE models are used, t must be assumed that the segment-specfc effects are uncorrelated wth other, ncluded varables. The Hausman test for such correlaton can be performed usng the followng ch-squared statstc [18]: 2 ˆ W K 1 b ˆ 1 ˆ FE RE bfe RE where ˆ Var b ˆ FE RE Var bfe Var RE where b FE s the LSDV estmator for the FE panel model, and ˆRE s the GLS estmator for the RE panel model. Greene [18]) notes that Hausman s mplct assumpton for calculatng s that the covarance of a random effect estmator wth ts dfference from a fxed effect estmator s zero. Interested readers are encouraged to read Greene s book [18] for further proof. Hsao [19] argues that an FE model s more approprate when the nvestgator only ams to nfer results for ndvduals n the sample, whle the RE model s preferred for nferences relatng to the larger populaton. However, whch specfcaton gets used depends more on whether there exst correlatons between omtted varables and the ncluded control varables. Both the FE and RE model forms are estmated here, and Hausman s test s appled to evaluate the possblty of error-term correlaton wth control varables. In order to avod havng the varable of VMT (where VMT s the multple of segment length and Washngton DOT s AADT estmates for each segment) on both sdes of the equaton (n the denomnator of the crash rate varable and n the numerator of traffc ntensty/densty varable), whch can create spurous correlatons, we have moved VMT to the rght-hand sde, nteractng t wth all former varables. Ths leaves crash count (rather than rate) as the dependent varable. t t t t Count VMT X (5) where Count refers to crash count (number of crashes per year per segment), and the X ' s are varables lke speed lmt, degree of curvature, lane-use densty (AADT per lane), (3) (4) rght shoulder wdth, presence of medan, vertcal grade, and ndcators of roadway classfcaton and rural locaton, as well as a constant term. B. Crash Severty Model To estmate the ordered response of crash severty, an ordered probt regresson was used. The crash severty model s concerned wth predctng the dstrbuton of crashes or njures by severty, gven that a crash has already occurred: the model does not predct crash probablty tself. The ordered probt s approprate when the outcome beng modeled can be naturally represented by an ordered sequence of dscrete values. For example, a crash may result n no njures or n any of a progresson of njury severty levels up to fatalty. The ordered probt model accounts for ths property of njury severty data. The ordered probt model s formally specfed as follows (Greene, 2002): Y X (6) where 1, 2, n desgnates an observaton (clustered group), Y s a latent contnuous measure of crash severty for clustered group, X s a vector of group characterstcs relevant n explanng the crash severty, s a vector of parameters to be estmated, and ~ N 0,1 s an unobservable error term, assumed to be dentcally and ndependently dstrbuted as a standard normal dstrbuton. The observed, dscrete severty level varable Y can be computed usng the followng equaton: 1 f Y 1 0 PDO crash Y 2 f 1 Y 2 njury crash (7) 3 f Y 2 fatal crash where 1 s a threshold value fxed at 0, and 2 s a threshold parameter to be estmated. The probabltes correspondng to each dscrete crash severty can be obtaned va the followng equaton: PY ( j) P( j 1 Y j) P X P X (8) where j j1 j X j 1 X represents the standard normal dstrbuton functon, and j 1, 2, 3. The log-lkelhood functon can be constructed as follows. n 3 j LogL k ln j X j 1 X (9) 1 j1 1623

4 j where k s the number of crash type j for clustered group. The log-lkelhood n Equaton (9) s maxmzed wth respect to and the scalar threshold parameter 2 by an teratve procedure, to obtan maxmum lkelhood estmates (MLE) of the parameters. IV. MODEL RESULTS A. Crash Frequency Estmaton and Analyss Both FE and RE lnear models were estmated for total crashes. Hausman test results suggest that there s no sgnfcant correlaton between the RE model random error terms and ncluded varables, so the RE estmates are preferred for reasons of statstcal effcency. Moreover, as dscussed above, most desgn features are tme nvarant, and thus ther assocated parameters cannot be estmated usng FE models. The fnal estmaton results for the RE model are shown n Table II. The adjusted R-square goodness of ft statstc suggests that 96% of the varaton n crash count occurrence s explaned by the model s control varables. In nterpretng ths table, t s mportant to note that, although VMT was nteracted wth all of the varables shown n the model specfcaton, the coeffcent estmates shown n the table have not been multpled by VMT. Consequently, the reported values are estmates of the crash rate coeffcents. In order to nterpret the results n terms of ther crash count mplcatons, the coeffcents must be multpled by VMT. Based on the standardzed coeffcents calculated usng the results n Table II, speed lmt s an mportant factor that postvely mpacts crash frequency. However, the presence of the squared speed lmt wth a negatve coeffcent moderates the smple lnear effect to some extent. The combnaton of these two terms mples that 3.29% more crashes would be expected f speed lmts were to ncrease 10 mph (from 55 m/h to 65 m/h), holdng all other control varables at ther average values. Holdng all factors fxed (ncludng roadway desgn and traffc ntensty), the relatonshp between total crash rate and speed lmt s concave, wth a maxmum around 73 mph. Because of the quadratc specfcaton, the curve eventually falls, but extrapolaton beyond 70 mph goes outsde the range of observed data and s not credble. The results of Table II also suggest that roadway desgn plays an mportant role n predctng crash occurrence. For example, more crashes are expected on sharper horzontal curves as well as on steeper vertcal curves. Crash rates are also predcted to rse wth ncreasng traffc ntensty (measured as AADT per lane). Ths s probably due to the greater nteracton among vehcles that occurs under more congested condtons. The presence of a medan also sgnfcantly reduces crash frequency. A summary of results for speed lmt and all other control varables s presented followng the dscusson of crash severty models, n Table III. Ths table allows one to apprecate the effects of varous desgn and use varables on crash severty as well as crash frequency. B. Crash Severty Estmaton and Analyss An ordered probt regresson model was estmated usng the clustered data aforementoned after flterng the zero crash observatons. The estmaton results are shown n Table III. The table only ncludes a fnal model, n whch explanatory varables not exhbtng statstcal sgnfcance at the 0.1 level have been removed va a process of step-wse deleton [18]. Varables of every type were found to be nformatve n the fnal model. Crashes on steeper vertcal curves were found to be less severe. Other thngs equal, crashes on freeways tend to be less severe. Speed lmts appear to have no sgnfcant effect on the dstrbuton of crashes by severty, gven that a crash has occurred. (However, to the extent that speed lmts may affect crash occurrence, they wll have an effect on the total number of crashes by severty.) To compare these results wth the crash occurrence models presented prevously, consder a segment of hghway havng the same average characterstcs as dscussed n crash frequency secton. For a speed lmt ncrease from 55 m/h to 65 m/h, the basc crash count model presented n that secton predcts a 3.29% ncrease n the crash rate. If the dstrbuton of crashes by severty were unaffected by speed lmt changes, ths would mean an average of 4.03, 2.73 and more PDO, njury and fatal crashes per 100 mllon VMT, respectvely. Predcted changes n crash rates due to changes n other varables of nterest are shown n Table IV, based on crash occurrence models developed before. C. Analyss of Crash Costs vs. Tme Savng Based on a summary of prevous studes [see, e.g. (20)], observed traffc speeds are expected to rse roughly 3.4 mph f speed lmts are rased 10 mph. Thus, the tme savngs per 100 mllon VMT due to a 10 mph ncrease n speed lmts s estmated to be 106,879 hours. Ths tme savngs s equvalent to $1,607,455, when usng the USDOT s assumed value of travel tme of $15.04 per hour per vehcle [21, 22]. Based on crash count and crash severty model results, ths same 10 mph ncrease n speed lmts s predcted to result n 4.03, 2.73 and more PDO, njury and fatal crashes per 100 mllon VMT, respectvely. The equvalent average cost estmate for ths ncrease n crashes s just $437,964 (n 2000 dollars). Therefore, the estmated cost-beneft rato s 1:3.67. The results suggest that rasng speed lmts can offer some consderable tme savngs benefts. V. CONCLUSIONS Traffc crashes reman a major health problem for the U.S., as well as for other countres. Roadway desgn and speed lmt polces are mportant determnants of crash outcomes. The models estmated here frst employ cluster analyss, to create 337 groups of what were orgnally 41,348 homogeneous hgh-speed roadway segments throughout the 1624

5 State of Washngton. These clustered data ponts then provde relatvely contnuous crash count and, therefore, crash rate data, permttng use of lnear models and straghtforward estmates of speed, use and desgn effects. The eght-year panel data sets were analyzed usng two model specfcatons. The RE models were preferred FE models, based on Hausman tests (for correlaton between random effects and control varables). Addtonally, a crash severty model was estmated usng an ordered probt regresson. The models reveal that speed lmt nformaton s hghly valuable n predctng crash frequences, but has lttle effect on crash severty. As expected, many desgn, use, and speed lmts varables are hghly statstcally and practcally sgnfcant. For roadways wth average desgn and use attrbutes, a 10 m/h ncrease speed lmt from 55 m/h results n 3.29% more crashes for the average roadway secton. An ordered probt regresson model was estmated to examne the effects of speed lmts as well as varous geometrc desgn features on crash severty. The speed lmt appears to have no sgnfcant effect on crash severty. However, speed lmts do have a postve effect on the crash occurrence. It therefore can correspondngly ncrease the fatal crashes. Gven these attrbutes f speed lmt ncreases from 55 m/h to 65 m/h, 4.03, 2.73 and more PDO, njury and fatal crashes per 100 mllon VMT would be expected to occur on the segment. Crash count model results also suggest that roadway desgn plays an mportant role n predctng crash occurrence. For example, more crashes are expected on sharper horzontal curves as well as on steeper vertcal curves. Crash rates also are predcted to rse wth ncreasng traffc ntensty (measured as AADT per lane). The presence of a medan also sgnfcantly reduces crash frequency. The R-square s qute hgh, thanks n large part to the ncluson of a sze term (VMT) on the rght-hand sde of the equaton. If crash counts were normalzed wth respect to ths sze term, the dependent varable would become a crash rate, and regresson of the segments crash rates on all other control varables would result n an R-square of In addton, the authors also conducted a cost/beneft analyss of rasng speed lmt. An ncrease n speed lmt from 55 m/h to 10 m/h would save 106,879 hours per 100 mllon VMT, whch s equvalent to $1,607,455. The addtonal crash counts due to the ncrease n speed lmt only cause $437,964 loss. Therefore, the results suggest that rasng speed lmts can offer some consderable tme savngs benefts. In sum, ths work appears to be the frst of ts knd: clusterng roadway segments n order to permt lnear model calbraton and estmatng crash rates and severty when rasng speed lmts. Such estmates should prove useful n the desgn of new roadways and speed lmt polces on new and exstng roadways. ACKNOWLEDGMENT The authors thank Mr. Bob Howden and Mr. Chrstan Cheney of the Washngton State DOT for generously sharng the updated speed lmt nformaton and loop detector data, and the Natonal Cooperatve Hghway Research Program for fundng ths research under contract number Whle the Natonal Cooperatve Hghway Research Program (NCHRP) sponsored ths research project, the opnons expressed here do not necessarly reflect the polcy of NCHRP. The authors also are grateful to the FHWA s Yusuf Mohamedshah for provson of the crash data sets, to Young-Jun Kweon and Xaokun Wang for offerng useful dscussons related to the data sets and analytcal methods, and to Ms. Annette Perrone for edtoral assstance. APPENDIX TABLE I VARIABLE THRESHOLDS FOR CLUSTER DEFINITIONS IN THE CRASH COUNT MODEL Varable Group descrpton #groups # lanes 2 & 3; 4 & 5; 6,7 & 8 lanes 3 Presence of medan yes/no 2 Rural yes/no 2 Interstate yes/no 2 Terran Level; rollng; mountanous 3 Non-nterstate freeway yes/no 2 Degree of curvature DC=0; 0<DC10; DC>10 3 Rght shoulder wdth RSW=0; 0<RSW20; RSW>20 ft 3 Vertcal grade VG=0; 0<VG5; VG>5% 3 Total possble clusters =3888 TABLE II LINEAR RANDOM EFFECTS MODELS OF CRASH COUNTS Models Fnal Model Varables Coef. P-value Constant Degree of curvature ( /100ft) 6.18E Vertcal grade (%) 8.81E Total rght shoulder wdth -9.33E Posted speed lmt (mph) 3.84E Posted speed lmt squared (m 2 /hr 2 ) -2.63E AADT per lane (veh/year/lane) 1.01E Indcator for nterstate hghway -2.15E Indcator for non-nterstate freeway -9.63E Indcator for presence of medan -1.87E Indcator for rollng terran 2.24E Indcator for mountanous terran 4.04E Indcator for rural locaton -4.81E Indcator for 2- or 3-lane hghway -7.18E Indcator for 4- or 5-lane hghway 1.31E Indcator for year E Indcator for year E Indcator for year E Indcator for year E Indcator for year E R-sqrd Number of Observatons. 2,

6 TABLE III ORDERED PROBIT REGRESSION MODEL OF CRASH SEVERITY Varable Coef. Std. Err. P-value Mu Constant Degree of curvature ( /100ft) Vertcal grade (%) AADT per lane 4.669E E Indcator for nterstate hghway Indcator for non-nterstate freeway Indcator for mountan terran Indcator for 2- or 3- lane hghway Indcator for 4- or 5- lane hghway Indcator for year Indcator for year Indcator for year Indcator for year Indcator for year LogLk value at constant LogLk value (full model) Number of Observatons 1,379 TABLE IV CRASH RATE SENSITIVITY TO VARIABLES OF MODELS Explanatory Varables Change n Expected Percentage Changes Varable Fatal Injury PDO Total Roadway Desgn Varables Degree of curvature % 0.28% 0.93% 0.30% Vertcal grade (%) % 0.45% -0.68% 0.42% Total rght shoulder wdth % -4.49% -4.49% -4.49% Posted speed lmt (m/h) % 3.29% 3.29% 3.29% Roadway Classfcaton & Locaton Varables Indcator for nterstate Yes -9.74% % % % Indcator for non-ntst Yes -4.45% -4.88% -5.30% -4.63% Indcator for medan Yes -8.99% -8.99% -8.99% -8.99% Indcator for rollng Yes 1.08% 1.08% 1.08% 1.08% Indcator for mountanous Yes 1.88% 2.02% 2.17% 1.94% Indcator for rural area Yes -2.31% -2.31% -2.31% -2.31% Indcator for 2 or 3 lane Yes -3.70% -3.11% -2.58% -3.45% Indcator for 4 or 5 lane Yes 0.68% 0.57% 0.47% 0.63% Traffc Volume & Yearly Indcator Varables AADT per lane % 0.49% 0.48% 0.49% [6] Shankar,V., Mlton, J. and Mannerng F. (1997) Modelng Accdent Frequences as Zero-altered Probablty Processes: An Emprcal Inqury. Accdent Analyss and Preventon, 29(6), [7] McCarthy, P. S. (1999) Publc Polcy and Hghway Safety: A Cty-wde Perspectve. Regonal Scence and Urban Economcs, 29, [8] Noland, R. B. (2003) Traffc fataltes and njures: the effect of changes n nfrastructure and other trends. Accdent Analyss and Preventon, 35(4), [9] Kweon, Y.J. and Kockelman, K. (2004) Spatally Dsaggregate Panel Models of Crash and Injury Counts: The Effect of Speed Lmt and Desgn. Proceedngs of the 83rd TRB Annual Meetng. Washngton D.C. [10] Moellerng, H. (1976) The Potental Uses of A Computer Anmated Flm n the Analyss of Geographcal Patterns of Traffc Crashes. Accdent Analyss and Preventon, 8(4), [11] Golob, T.F. and Recker, W.W. (2004) A Method for Relatng Type of Crash to Traffc Flow Characterstcs on Urban Freeways. Transportaton Research Part A, 38(1), [12] Le Blanc, L.A. and Rucks, C.T. (1996) A Multple Dscrmnant Analyss of Vessel Accdents. Accdent Analyss and Preventon, 28(4), [13] Wong, S.C., Leung, B.S.Y., Loo, B.P.Y., Hung, W.T., and Lo, H.K. (2004) A Qualtatve Assessment Methodology for Road Safety Polcy Strateges. Accdent Analyss and Preventon, 36(2), [14] Wells-Parker, E. Cosby, P.J. and Landrum, J.W. (1986) A Typology for Drnkng Drvng Offenders: Methods for Classfcaton and Polcy Implcatons. Accdent Analyss and Preventon, 18(6), [15] Gregersen, N.P. and Berg, H.Y. (1994) Lfestyle and Accdents Among Young Drvers. Accdent Analyss and Preventon. 26(3), [16] Ulleberg, P. (2001) Personalty Subtypes of Young Drvers: Relatonshp to Rsk-takng Preferences, Accdent Involvement, and Response to a Traffc Safety Campagn. Transportaton Research Part F, 4(4), [17] Sohn, S.Y. (1999) Qualty Functon Deployment Appled to Local Traffc Accdent Reducton. Accdent Analyss and Preventon, 31(6), [18] Greene, W.H. (2002) Econometrc Analyss, Ffth Edton. Prentce Hall, New Jersey. [19] Hsao, C. (2003) Analyss of Panel Data. Cambrdge Unversty Press, Cambrdge. [20] Kockelman, K., and Bottom, J. (2006) Safety Impacts and Other Implcatons of Rased Speed Lmts on Hgh-Speed Roads. Natonal Cooperatve Hghway Research Program Project #17-23, Report Draft, Transportaton Research Board, Washngton, D.C. [21] U.S. Department of Transportaton. (1997) Departmental Gudance for the Valuaton of Travel Tme n Economc Analyss. Offce of the Secretary of Transportaton, U.S. Department of Transportaton, Avalable at: [22] U.S. Department of Transportaton. (2003) Revsed Departmental Gudance: Valuaton of Travel Tme n Economc Analyss. Offce of the Secretary of Transportaton, U.S. Department of Transportaton. Avalable at: REFERENCES [1] NHTSA (2003) Traffc Safety Facts Retreved June 16, 2004, from Natonal Center for Statstcs and Analyss (NHTSA/USDOT) Web ste: /nrd-30/ncsa/avalinf.html [2] Maou, S.P. and Lum, H., (1993) Modelng Vehcle Accdents and Hghway Geometrc Desgn Relatonshps. Accdent Analyss and Preventon, 25(6), [3] Shankar, V., Mannerng, F., and Barfeld, W. (1995) Effect of Roadway Geometrcs and Envronmental Factors on Rural Freeway Accdent Frequences. Accdent Analyss and Preventon, 27(3), [4] Poch, M. and Mannerng, F. (1996) Negatve Bnomal Analyss of Intersecton Accdent Frequences. Journal of Transportaton Engneerng, 122(2), [5] Mlton, J. and Mannerng, F. (1998) The Relatonshp Among Hghway Geometrcs, Traffc-Related Elements and Motor-Vehcle Accdent Frequences. Transportaton, 25(4),