Open Journal of Cvl Engneerng, 2014, 4, 240-254 Publshed Onlne September 2014 n ScRes. http://www.scrp.org/journal/ojce http://dx.do.org/10.4236/ojce.2014.43021 Pedestran Crash Predcton Models and Valdaton of Effectve Factors on Ther Safety (Case Study: Tehran Sgnalzed Intersectons) Pegah Jafar Haghghatpour 1*, Reza Moayedfar 2 1 Master of Scence, Department of Engneerng, Islamc Azad Unversty South Tehran Branch, Tehran, Iran 2 Department of Engneerng, Arak Unversty, Iran Emal: * st_p_jafar@azad.ac.r, r-moayedfar@araku.ac.r Receved 7 July 2014; revsed 27 July 2014; accepted 29 August 2014 Copyrght 2014 by authors and Scentfc Research Publshng Inc. Ths work s lcensed under the Creatve Commons Attrbuton Internatonal Lcense (CC BY). http://creatvecommons.org/lcenses/by/4.0/ Abstract The quantty and severty of traffc accdents have ncreased wth the development of machnery lfe and traffc growth n ctes and roads n the past 50 years. Among the road users, pedestrans are the most vulnerable groups to be exposed to hgh rsks. Vehcle crashes wth pedestran are almost nevtable and cause njury or death to pedestran. Crash nvestgaton and statstcal studes ndcate that percentage of pedestran deaths caused by vehcle accdents are much more than all deaths. A consderable amount of accdents occur at sgnalzed and urban ntersectons whch are the ntensve crash places. Therefore n ths paper approprate models that could specfy safety ndcators have been ndcated wth exstng nformaton by characterzed parametrc and nonparametrc varables for twenty sgnalzed ntersectons. Categores and correlatons of varables also have been nvestgated. Three models ncludng Regresson, Posson, and Negatve bnomal wth defned varables have been determned. T and ch square tests, calbraton and comparson of varables have been done by curve fttng. The role of each parameter was specfed n pedestran crashes. Valdatng models had the followng outcomes: Pedestran crash predcton models were based on none lnear relatons at ntersectons. Predctable varables, developng extended lnear models and also pedestran crash predcton are on the bass of Negatve bnomal dstrbuton whch s used due to more data dsperson. As observed, the Negatve bnomal regresson because of ts more R 2 correlaton factor has more valdty among other regresson models such as lnear regresson and Posson. Calbrated models are put nto senstvty analyss to study the effect of each prevously mentoned parameter n overall performance. Hence much better percepton of future transportaton plans can be acheved by development of safety models at plannng levels. * Correspondng author. How to cte ths paper: Haghghatpour, P.J. and Moayedfar, R. (2014) Pedestran Crash Predcton Models and Valdaton of Effectve Factors on Ther Safety (Case Study: Tehran Sgnalzed Intersectons). Open Journal of Cvl Engneerng, 4, 240-254. http://dx.do.org/10.4236/ojce.2014.43021
Keywords Crash Predcton Models, Pedestran, Senstvty Analyss, Sgnalzed Intersecton, Valdaton 1. Introducton Dependng on accdents, they may have dfferent causes. Elmnatng the rsk of each cause requres separate solutons. Intersectons safety has always been the man purpose of plannng and transportaton due to specal mportance and role of ntersectons n street network. Important prorty of decson s to reduce the number of pedestran accdents at ntersectons. Pedestran crashes and actvtes depend on demographc, land use, road network, geometrc and transt characterstcs. An ncrease n demographc and soco-economc characterstcs such as populaton, household unts, and total employment wthn walkng dstance of an ntersecton may ncrease pedestran volume and the number of pedestran crashes at ntersecton. Whle an ncrease n mean ncome level wthn the same area may result n a decrease (or sometmes ncrease) n pedestran volume and the number of pedestran crashes at the ntersecton. Pedestran volume and pedestran crashes could also depend on land use characterstcs wthn the walkng dstance of an ntersecton. People lvng n apartments may walk more than those lvng n resdental neghborhoods, or vce versa. Lkewse, an ncrease n street wdth (or the number of lanes); speed lmt, traffc volume, and the number of transt stops wthn the vcnty of an ntersecton may ncrease pedestran exposure to rsk and crashes at the ntersecton. Therefore, data pertanng to these characterstcs are requred for developng and assessng pedestran crash estmaton models [1]. Research on the feasblty of modelng crash counts at ntersectons as a functon of traffc volume and other varables has been ongong for over a decade. Example efforts n the 1990s nclude modelng ntersecton crash counts by [2]. Some examples of recent efforts nclude forecastng crashes at the plannng level and crash predcton modelng n New Zealand and Australa. Research has also been undertaken to understand pedestran safety problems and estmate rsk to pedestrans. Brude and Larsson studed the effect of pedestran and traffc volumes on pedestran crashes at ntersectons (121 sgnalzed, 155 unsgnalzed, and 9 roundabouts) n Sweden. They found that pedestran volume had a sgnfcant and postve relatonshp to pedestran crashes n a sngle predctve model that covered all ntersecton types [3]. Huang et al. proposed a Full Bayes (FB) modelng approach to account for heterogenetes of crash occurrence due to spato-temporal effects on traffc safety; an emprcal evaluaton was conducted to compare the proposed FB method to the state-of-art approaches. Results showed that Bayesan herarchcal models wth accommodaton for ste specfc effect and seral correlaton have better goodness of ft than non-herarchcal models [4]. Lyon and Persaud used data from Toronto, Canada n the development of pedestran crash predcton models usng pedestran and vehcular volumes and vehcular volumes only for three and Four-legged urban ntersectons, wth and wthout sgnal control. It was observed that the use of pedestran volume nformaton results n a much rcher model, emphaszng the mportance of collectng ths nformaton n routne traffc countng programs [5]. Wer et al. dscussed multvarate regresson models usng data for 176 census tracks n San Francsco, Calforna and 5 years worth of crash data. The study found that traffc volume, arteral streets wthout publc transt, proporton of land area zoned for neghborhood commercal use and resdental-neghborhood commercal use, employment, resdent populaton, and populaton below poverty level have a postve correlaton whle the proporton of people aged 65 and over have a negatve correlaton wth pedestran crashes [6]. Torbc et al. developed a methodology to quantfy pedestran safety effects related to exstng ste characterstcs or proposed mprovements on urban and suburban arterals. The methodology ncluded base models for three- and four-legged Sgnalzed ntersectons and several accdent modfcaton factors (AMFs). The study found that daly pedestran crossng volume has a statstcally sgnfcant relatonshp to vehcle-pedestran crashes at sgnalzed ntersectons [7]. Lee based on models developed usng data for two hundred sgnalzed ntersectons n Washngton DC, reported that pedestran volume and vehcular volume are two strong predctor varables that can be used to estmate pedestran Crashes [8]. Elvk found that the total number of pedestran crashes could go down f a substantal share of trps by motorzed travel were transferred to walkng or cyclng. The effect depends strongly on the degree of non-lnearty of rsk [9]. Harwood et al. suggested that the relatonshp between the number of pedestran crashes and the vehcular volume and pedestran traffc are not altered when other varables such as the Proxmty to a school, the presence of a 241
bus stop or the presence of an alcohol sales establshment s ncluded n a model. The role of demographc characterstcs, soco-economc characterstcs, land use characterstcs, road network characterstcs and the presence of transt stops on pedestran crashes was not examned and used n pedestran crash estmaton models for sgnalzed ntersectons [10]. Those that examned dd not consder ste specfc data or the effect of spatal proxmty (or buffer wdth) to extract demographc characterstcs, soco-economc characterstcs, and land use characterstcs n estmatng pedestran crashes. So consderng these varables and examnng the effects would help to make better transportaton plannng and land use decsons. Feld of study has been consdered as Tehran n ths artcle. Tehran s one of the major and Sxteenth cumulated ctes wth a densty of about eleven thousand square klometers n the world. Large populaton and the hgh volume of vehcle traffc have ncreased the number of traffc accdents n Tehran. Perod studed accordng to the exstng nformaton n polce statstcs collecton system and traffc Studes has been consdered from 2012 to 2013 n ths paper. Durng these years accordng to traffc polce statstcs, about 17.3 percent of the total 648,615 traffc accdent has occurred at the ntersecton of Tehran. Assumng that the occurred accdent at Tehran Intersecton s ndependent and the number of accdents s dscrete, non-negatve and nteger varable and also consderng that the nformaton n the traffc polce crashes database and traffc studes Company are correct and free of errors, 20 ntersectons have been nvestgated by usng lnear regresson, Posson and negatve bnomal methods for the perod of two years.16 ntersectons data s used n Statstcal models. These ntersectons nclude Behesht-Sohrevard, Jannat Abad-Iran s Pars (nayesh), Keshavarz-Jamalzadeh, modrat (darya)-saadat Abad, Shaghayegh-Ferdos, Taleghan-Bahar, Aboozar-Aemmeye Athar, Afrca-Haghan (Jahan koodak), Behesht-Ghaem Magham, Behesht- Mrza Shraz, Emam Khomen-Khosh, Farahzad-Darya, Farjam-Nrooye Daryaee, Felestn-Keshavarz, Karm Khan-Hafez, Motahar-Ghaem Magham. However, the artcle ntroduces 3 ntersectons of 20 ntersectons used n the statstcal models ncludng Behesht-Sohrevard, Taleghan-Sharat, Nabard-Aemmeye Athar. The modelng of pedestran crashes have been done at 16 ntersectons then curve fttng and statstcal tests have valdated by usng data s from four ntersectons comprsng Taleghan-Sharat, Motahar-Sohrevard, sardar E Jangal-Golestan, Nabard-Aemmeye Athar. Moreover mpact of each factor on the number of crashes has been nvestgated. It s consderable that SPSS 18 software s used n the data analyss. 2. Type of Pedestran Crashes The pedestran route s cut off when the vehcle s turnng approxmately. 32.2% of all pedestran crashes of ths type and over 50% of these accdents occur at ntersectons. Also 22% of crashes occur when the drver vsblty before ntersecton has been lmted. 16% of accdents due to drver volaton from rght of way. 26.5% of all pedestran crashes are vehcle accdent wth a pedestran crossng the street except through the ntersecton. 32% of accdents are whle the drver has enough vsblty and pedestran quckly ran to the street. 72% of pedestran s crash s occurred n the vehcle-pedestran collsons when the vehcles movng n reverse gear [11]. 3. Methodology The model represents realty to understand how the system behaves n dfferent stuatons, whch mpossble to use n practcal experence. Models are dvded nto three groups ncludng Descrpton, predcton and plannng n transportaton ssues. The descrptve models have scentfc value and ablty to smulate n future and plannng models used results of the predcted models to acheve specfc goals. The am of ths study s to select the best model for predctng pedestran crashes at ntersectons and determnng effectve factors on them. Scatter plots and prelmnary statstcal tests ndcated that the relatonshp between pedestran crashes and predctor varables are non-lnear n nature. Non-lnear relatonshps based on Posson dstrbuton, negatve bnomal dstrbuton, and lognormal dstrbutons as well as zero-nflated model were tested to dentfy the best model that can explan the relatonshp between pedestran crashes and the selected predctor varables. Also the ncremental model has been tested to dentfy the best model that could elaborate the relatonshp between pedestran crashes and selected predctor varables. Pedestran crash estmaton models based on statstcal analyss software (SPSS, 18) was used to develop the models n ths study. As a frst step, effectve factors are evaluated n accdent and predctve Varable wth good correlaton was used to develop a pedestran crash estmaton models for close range ntersectons. The sgnfcance level for each selected predctor varable has been nvestgated. Varables whch ther Sgnfcance level was greater than 0.5 play an mportant role n the estmaton of pedestran crashes n 95% confdence nterval. Independent varables such as demographc, soco-economc, land use 242
characterstcs that crash predcton are related to them can be used to assess the relevance of pedestran crashes and pedestran crash predcton models developed by the spatal proxmty and functon level. However, because the collecton of ths nformaton n the database s very dffcult n Tehran and there s no organzaton to provde such nformaton to us. Or f there s, unfortunately these data are not avalable to students. Therefore, some of the effectve parameters nformaton n crash predcton model that have been obtaned by comprehensve studes company be nvestgated n ths paper. The methodology nvolves the followng steps: 1) Identfy study ntersectons. 2) Identfy data elements. 3) Identfy the number of pedestran crashes as the predcted varable whch dependent to other characterstcs. 4) Extract ncomng vehcles volume on the man and secondary routs. 5) Extract the number of transt stops and schools wthn the vcnty of ntersectons. 6) Extract the number of lanes at man and auxlary road, Area traffc plan, Type of sgnal, one way streets, Intersecton s angle and pedestran volume. 7) Examne correlaton between the predctor varables. 8) Develop pedestran crash estmaton models. 3.1. Identfy Study Intersectons and Data Elements Examnng Behesht-Sohrevard, Taleghan-Sharat, Nabard-Aemmeye Athar ntersectons from nvestgated Tehran 20 ntersectons n statstcal models to develop pedestran crash predcton models have been selected n ths paper. Demographc, soco-economc, land use, road network and transt characterstcs n the vcnty of these sgnalzed ntersectons should represent typcal characterstcs of an urban area. Pedestran crashes and actvty depends on demographc, soco-economc, land use, road network and transt characterstcs. An ncrease n demographc and soco-economc characterstcs such as populaton, household unts, and total employment wthn walkng dstance of an ntersecton may ncrease pedestran volume and the number of pedestran crashes at the ntersecton. It s noteworthy that to calculate and consder these parameters some lmts should be specfed. Ths requres geographcal surveys, census studes and etc but the possblty of such study does not exst n ths paper. Only Several factors n crashes such as ncomng vehcles volume on the man and secondary routs, the number of transt stops and schools wthn the vcnty of ntersectons, the number of lanes at man and auxlary road, area traffc plan, type of sgnal, one way streets, ntersecton s angle and pedestran volume can be addressed. The average number of pedestran crashes as the dependent varable s used to develop pedestran crash estmaton models at ntersectons. Pedestran crashes data to extract pedestran crashes have been covered around the ntersecton for two-year perod. 3.2. Extract Incomng Vehcles Volume on the Man and Secondary Routs Traffc volume s mportant varables n occurrng crashes at ntersectons. Research also ndcates that wth ncreasng ncomng vehcle volume, the number of accdents ncreases at ntersecton. Pckerng knows traffc volume s one of the man parameters n hs research [12]. It s notable that for every 10,000 vehcles per day, the number of crashes between 15 to 20 percent ncrease but n hgh volume the percentage decreases. The number of crashes depend on ncomng traffc volume on the man and secondary routs. Ths parameter s ndependent that the number of pedestran crashes depends on t. 3.3. Extract the Number of Transt Stops and Schools wthn the Vcnty of Intersectons People generally walk or use bcycle to acheve the publc transportaton system (bus) from ts locaton n the vcnty of the ntersecton. To study these affects, the number of publc transportaton statons dentfed from ntersectons and consder n pedestran crash estmaton model. In addton pedestrans that cross ntersectons to go to school are effectve n the number of crashes. Ths parameter s also ndependent of the parameters. 3.4. Extract the Number of Lanes at Man and Auxlary Road, Area Traffc Plan, Type of Sgnal, One Way Streets, Intersecton s Angle and Pedestran Volume All the factors mentoned n the capton are ndependent parameters and affectng on pedestran crashes. For example, the slope of ntersectons s the pont that n collsons between vehcles and pedestrans creates nc- 243
dent pont for road users. So ntersecton entrance ramp should gve the possblty to drver that do necessary movement wth complete vsblty, enough safety and mnmal collson wth others to cross through ntersectons. Streets along at ntersecton should somewhat drect and have less slope. Optmum angle of ntersecton s 90 degree or near t due to ntersectons safety and economc ssues. Intersecton wth nclned angle requres a greater level and especally reduces vsblty for truck drvers. Also vehcles wll requre a lot of space for turnng left or rght. Traffc sgnals are used to control traffc separaton and dfferent traffc flow mprovement at the ntersectons. Drvers ncrease speeds to cross the ntersecton on the fnal green tmes and suddenly stop when traffc sgnal s red. Also pedestran volume has been done n man and secondary routes durng the 15- mnute study. 4. Statstcal Propertes of the Intersectons 4.1. Sohrevard-Behesht Intersecton Behesht Avenue s one-way and has 5 lanes n each drecton and Sohrevard Avenue s blateral and has 3 lanes n each drecton also there s a left turn at Sohrevard. Fgure 1 llustrates ths ntersecton. Intersecton angle s not 90 degrees and has 3-phase ntellgent traffc sgnal. Ths ntersecton has bus stop and specal bus way. Schools are around the ntersecton and there sn t any area traffc plan. In 2012 the average daly volume of vehcles s 24,253,695 n the man rout and 12,861,049 n secondary path and n 2013 the average daly volume of vehcles s 25,369,563 n the man rout and 13,889,933 n the secondary path. In 2012 the volume of pedestrans durng the 15-mnute study s 342,580 n the man rout and 185,253.00 n the secondary path. The number of pedestran crashes s 17 persons. In 2013 the volume of pedestrans durng the 15-mnute study s 369,986 n the man rout and 195,236 n the secondary path. The number of pedestran crashes s 15 persons. 4.2. Sharat-Taleghan Intersecton Taleghan Avenue s one-way from west to east and has 4 lanes n each drecton and Sharat Avenue s oneway from north to south and has 3 lanes n each drecton also there s dscrete turn on two-sdes n ths ntersecton. Fgure 2 llustrates ths ntersecton. Intersecton s angle s not 90 degrees and has 2-phase ntellgent traffc sgnal. Ths ntersecton has bus stop and specal bus way. Schools are around the ntersecton and there s an area traffc plan. In 2012 the average daly volume of vehcles s 2,060,326 n the man rout and 6,160,350 n secondary path and n 2013 the average daly volume of vehcles s 2,282,929 n the man rout and 7,220,330 n the secondary path. In 2012 the volume of pedestrans durng the 15-mnute study s 226,784 n the man rout and 143,457 n the secondary path. The number of pedestran crashes s 12 persons. In 2013 the volume of pedestrans durng the 15-mnute study s 285,365 n the man rout and 162,209 n the secondary path. The number of pedestran crashes s 11 persons. Fgure 1. Sohrevard-Behesht ntersecton. 244
Fgure 2. Sharat-Taleghan ntersecton. 4.3. Aemmeye Athar-Nabard Intersecton Aemmeye Athar Avenue from west to east has 2 lanes n each drecton and Nabard Avenue from north to south has 2 lanes n each drecton also there sn t any dscrete turn and area traffc plan. Fgure 3 llustrates ths ntersecton. Intersecton s angle s 90 degrees and has 2-phase ntellgent traffc sgnal. Ths ntersecton has bus stop and specal bus way. Schools are around the ntersecton. In 2012 the average daly volume of vehcles s 14,340,120 n the man rout and 6,298,805 n secondary path and n 2013 the average daly volume of vehcles s 14,108,345 n the man rout and 6,163,025 n the secondary path. In 2012 the volume of pedestrans durng the 15-mnute study s 248,325 n the man rout and 100,236 n the secondary path. The number of pedestran crashes s 9 persons. In 2013 the volume of pedestrans durng the 15-mnute study s 259,664 n the man rout and 112,349 n the secondary path. The number of pedestran crashes s 12 persons. 5. Development of Pedestran Crash Predcton Models The focus of ths stage s usng extracted ste-specfc nformaton, ntegraton, evaluaton and selecton for developng pedestran crash estmaton models at earler stages. As prevously mentoned only ndependent varables that are well correlated wth each other are used to develop models. Generalzed lnear models that based on Posson dstrbuton and negatve bnomal dstrbuton or ncremental models usually are used to develop pedestran crash estmaton models. The average number of pedestran crashes s used as the dependent varable at ntersectons durng 2-year perod. Incomng vehcles volume on the man and secondary rout n the early months of the year, publc transt stops (bus) and schools wthn the vcnty of ntersectons, total ncomng vehcles volume, the number of lanes at man and auxlary road, area traffc plan, type of sgnal, one-way streets, ntersecton s angle and pedestran volume have been collected and consdered as the predcted and ndependent varable. Scatter plots and prelmnary statstcal tests ndcated that the relatonshp between pedestran crashes and predctor varables are non-lnear n nature. Non-lnear relatonshps are based on Posson dstrbuton, negatve bnomal dstrbuton, and lognormal dstrbutons. Also ncremental models to dentfy the best model that can explan the relatonshp between pedestran crashes and the selected predctor varables have been tested. As the frst step after enterng data s nto spss software, dependent and ndependent varables that have well correlated wth greater than 0.5 s kept. Correlaton between the ndependent varables should be less than 0.5, other varables that do not qualfy wll not be partcpatng n crashes predcton models. Correlaton between the varables s nvestgated to select the fnal set of predcted varables to develop pedestran crash estmaton models. Accordng to the correlaton matrx obtaned from the SPSS software NL1, NL2, TT, LS, OW, S, BR varables among other varables are removed for modelng n ths paper. After examnng the correlaton, three types of models ncludng: regresson, Posson and Bnomal have been done to predct crashes. By valdatng (Curve Fttng) each of tests and nvestgatng a varety of tests ncludng ch-square and T-test n connecton wth each of models, the most approprate model that has R 2 close to 1 wll be selected for predctng pedestran crashes n future. Effectve varables n crashes are shown n Table 1. 245
Table 1. Effectve varables n crashes. Fgure 3. Aemmeye Athar-Nabard ntersecton. Varable Abbrevated Name Encoded 0 1 2 3 The average number of crashes per year NOA No code Pedestrans volume from Man road to ntersecton VP1 No code Pedestrans volume from secondary road to ntersecton VP2 No code Incomng vehcles volume from man road V1 No code Incomng vehcles volume from secondary road V2 No code Number of lanes on Man road NL1 No code Number of lanes on auxlary road NL2 No code Area traffc plan TT Not have have Dscrete turn GM Not have One-way Two-way Type of sgnal LS Flashng 2-phase 3-phase 4-phase One-way street OW Not have One-way Two-way Angle of ntersecton AN 90 degrees Not 90 degrees - Schools S Not have have - Bus stop BS Not have have - Specal bus way BR Not have have - 6. Pedestran Crash Predcton Models The pedestran crash estmaton models have been developed by consderng nformaton for ntersectons.the purpose of statstcal model s to dentfy the relatonshp between the expected number of crashes at ntersectons E (Y ) and dependent parameters to ntersecton X j, (j = 1, 2,..., n). So a set of seres ncludng q parameter that descrbe road characterstcs, traffc volume, and other related propertes wll be devoted to t. Accordng to research, lnear regresson, Posson and negatve bnomal models were more approprate for pedestran crashes 246
modelng and are very useful n the crashes analyss [12]. Modelng of quanttatve factors s used as numercal. Qualtatve factors are used 0, 1 and 2 as coded. NOA Varable (number of crashes per year) has been consdered as the dependent varable and the other varables have been consdered as ndependent varables. Independent varables should not well correlate wth each other. Therefore Pearson correlaton coeffcent was used to calculate data correlaton ndex. Data shows that the number of pedestran crashes ncreased by populaton growth near schools, publc transportaton statons, and the number of sdeway approaches at ntersectons, pedestran volume ncreases, and the number of dscrete turn. However, we can observe fewer pedestran crashes f commercal and resdental centers are close to the ntersecton. Because drvers reduce ther speed when faced wth such centers. 6.1. Lnear Regresson The general form of the model s as follows: Y = β + β X + β X + + β X (1) 0 1 1 2 2 n n where: Y s dependent varable, X s are ndependent varables and β s are the regresson coeffcents. The generalzed form for predctng crashes at ntersectons s as follows: Y = β + β X (2) j j where: Y : Number of crashes at ntersecton I; X j : ndependent varables; β j : unknown varable coeffcents. The method of mnmum squares and maxmum lkelhood are used to estmate β. Dstrbuton of β s not consdered n mnmum squares method, but normal dstrbuton wth zero mean and constant varance σ 2 > σ are consdered n the maxmum lkelhood method. T-test s used to test whether the varables are normally dstrbuted and sample mean s equal to populaton mean. NOA s the number of crashes and dependent varable n ths model. The results of the lnear regresson wth studed ntersectons data have been ndcated n Table 2. The results show that the varables are sgnfcantly hgher than 0.05 and adjusted R 2 of the model s 0.538, whch ndcates a relatvely poor fttng of the model and also varables have weak relatonshp wth dependent varable (number of crashes per year). Lnear regresson model wth Computatonal coeffcent s as follows: NOA = 6.559 + 0.000008774VP1 0.000003077VP2 + 0.0000003741V 1 + 0.0000002920V 2 1.719GM 1.630AN 3.042BS 6.2. Posson Regresson Posson regresson models are dscrete models and used when consequence are rare. Consderng that crashes statstcs are dscrete, non-negatve, nteger varable and the average number of crashes at ntersectons s low, ths method can well modelng crashes at ntersecton. The general form of the model s as follows: ( ) PY Y e µ µ = (3) Y! The relatonshp between the number of crashes at ntersecton ( = 1, 2, and 3, n) and the q parameter (X l, X 2, X q ) s as follows: q X j j ln ( ) 0 j= 1 µ = β + β (4) x ( ) e β µ = E Y = (5) where: Y : the ndependent varable wth Posson dstrbuton and μ mean, X : ndependent varables at ntersecton. The results of the Posson model wth studed ntersectons data can observe n Table 3. It can observe that 247
Table 2. Results of lnear regresson model [13]. Varable B Standard Devaton t Sg Constant 6.559 4.021 1.631 0.116 VP1 8.774E 6 0.000 1.086 0.288 VP2 3.077E 6 0.000 0.276 0.785 V1 3.741E 7 0.000 2.794 0.101 V2 2.920E 7 0.000 2.466 0.212 GM 1.719 0.622 2.766 0.107 AN 1.630 1.450 1.124 0.272 BS 3.042 1.179 2.579 0.165 F test 1.828 R 0.793 R Square 0.697 Adjusted R Square 0.538 Sg 0.002 Table 3. Results of Posson regresson model [13]. Parameter B Standard Devaton 95% Profle Lkelhood Confdence Interval Hypothess Test Lower Upper Wald Ch-Square df Sg. (Intercept) 1.316.4413.451 2.181 8.898 1 0.003 VP1 7.260E 7 1.0325E 6 1.298E 6 2.750E 6 0.494 1 0.482 VP2 3.176E 7 1.2879E 6 2.207E 6 2.842E 6 0.061 1 0.805 V1 2.822E 8 1.9797E 8 1.058E 8 6.703E 8 2.032 1 0.154 V2 1.900E 8 1.5097E 8 1.059E 8 4.859E 8 1.584 1 0.208 [GM = 0.00] 0 0.1773 0.011 0.684 3.601 1 0.058 [GM = 1.00] 0.182 0.3160 0.437 0.802 0.333 1 0.564 [GM = 2.00] 0 a...... [AN = 0.00] 0.041 0.1946 0.340 0.423 0.045 1 0.832 [AN = 1.00] 0 a...... [BS = 0.00] 0.145 0.1375 0.125 0.414 1.111 1 0.292 [BS = 1.00] 0 a...... Value df Value/df Devance 8.040 23 0.350 Scaled evance 8.040 23 Pearson Ch-Square 8.090 23 0.352 Scaled Pearson Ch-Square 8.090 23 Log Lkelhood 74.649 Akake s Informaton 167.298 Fnte Sample Corrected AIC 175.480 Bayesan Informaton 180.489 Consstent AIC (CAIC) 189.489 Lkelhood rato ch-square 34.387 sg 0.0000 248
varables standard devaton s less than 1. So the actual dstrbuton of data s lower than model and model fttng would not be approprate. Posson regresson model wth varable computatonal coeffcents are calculated as follows: ( NOA = EXP VP + VP + V + 0.00000001900V 2 + 0.182GM + 0.041AN + 0.1452BS 6.3. Negatve Bnomal 1.316 e 0.0000007260 1 0.0000003176 2 0.00000002822 1 Negatve bnomal dstrbuton s dscrete dstrbuton and used for hgh dsperson of crashes data. Also unlke the Posson dstrbuton, t has two parameters. If Y s the number of crashes wth negatve bnomal dstrbuton by α and k parameters at ntersecton and predctor varables s X q, The number of crashes relatonshp s calculated as follows: 1 γ y + y k k PY y µ k 1 1+ kµ y! γ k k ( = ) = ( 1 + µ ) ( = 1,2,3,,n) where: γ : Gamma functon. Mean and varance of crash data s negatve bnomal dstrbuton are as follows relatonshps: ( ) Mean = E Y = µ 2 ( ) µ kµ Varance = Var Y = + If dsperson parameter (k) s zero, negatve bnomal dstrbuton wll tend to Posson dstrbuton. And f k s negatve (varance s smaller than mean), negatve bnomal model s not approprate. Therefore Posson model should be used. The results of the negatve bnomal model wth studed ntersecton data are shown n Table 4. The p-value s greater than 0.5 ndcates that the model s sutable for varable. Negatve bnomal regresson model wth varable computatonal coeffcents are calculated as follows: ( 1.359 e EXP 0.0000009094 1 0.00000022046 2 0.000000022576 1 NOA = VP + VP + V + 0.00000001707V 2 + 0.183GM + 0.071AN + 0.147BS 7. Comparson the Output of Lnear Regresson, Posson and Negatve Bnomal Models Due to the fact that crashes are accdental, scattered and ndependent, Posson model s more approprate than the lnear regresson model to nvestgate crashes. Some researches were used Posson regresson models to establsh any relatonshp between traffc accdents and effectve factors n creatng them. The lmtaton of the Posson model s equalty of mean and varance and does not establshed n crashes. If ths assumpton s not true, the statstcs derved from the model wll be ncorrect and the standard devaton that usually estmated by maxmum lkelhood method wll be devated. Some researchers n recent years have concluded that crashes data are sgnfcantly too scattered. It means that the varance s much greater than the mean of data. So ths wll lead to ncorrect estmates of crashes probablty. Negatve bnomal model s more approprate because the Pearson ch-square value s less than the Posson model. Indcated summary results show non-lnear relatonshp between predctor varables and pedestran crashes. Therefore, the best pedestran crash estmaton models s created when classfed are based on the level of pedestran s actvty. 8. Valdatng Models Model was calbrated by ch square and t tests wth crashes statstc at ntersectons and the dsperson between observed and predcted values wth Curve-Fttng graphs can be observed n Fgure 4 and Fgure 5 n ths sec- ) ) (6) 249
Fgure 4. Scatter plot between observed and predcted Posson model at ntersectons. Table 4. Results of Negatve bnomal regresson model [13]. Parameter B Standard Devaton 95% Profle Lkelhood Confdence Interval Hypothess Test Lower Upper Wald Ch-Square df Sg. (Intercept) 1.359 0.2319 0.904 1.813 34.311 1 0.000 VP1 9.094E 7 0.0912 0.144 0.501 12.524 1 0.000 VP2 2.204E 7 0.1808 0.171 0.538 1.027 1 0.031 V1 2.576E 8...... V2 1.707E 8 0.1155 0.156 0.297 0.374 1 0.054 [GM=0.00] 0...... [GM=1.00] 0.183 0.0878 0.025 0.319 2.793 1 0.095 [GM=2.00] 0 a...... [AN=0.00] 0.071 6.1856E 7 3.029E 7 2.122E 6 2.162 1 0.014 [AN=1.00] 0 a 8.0441E 7 1.356E 6 1.797E 6 0.075 1 0.078 [BS=0.00] 0.147 1.1115E 8 3.978E 9 4.755E 8 5.373 1 0.020 [BS=1.00] 0 a 8.9102E 9 3.921E 10 3.454E 8 3.671 1 0.055 Value df Value/df Devance 0.553 23 0.024 Scaled evance 22.978 23 Pearson Ch-Square 0.553 23 0.024 Scaled Pearson Ch-Square 23.000 23 Log Lkelhood 115.548 Akake s Informaton 249.097 Fnte Sample Corrected AIC 257.279 Bayesan Informaton 262.289 Consstent AIC (CAIC) 271.289 Lkelhood rato ch-square 98.04 sg 0.002 250
Fgure 5. Scatter plot between observed and predcted negatve bnomal model at ntersectons. ton. Accordng to results, t can be observed that the negatve bnomal regresson model due to R 2 = 0.8 has better performance than the Posson model. Also remanng four ntersectons that were not ncluded n the model can be used for specfyng the error rate n observaton and model and model valdatng. That only the frst ntersecton wll be menton n ths paper. Scatter plots and prelmnary statstcal tests ndcated that the relatonshp between pedestran crashes and predctor varables are non-lnear n nature. Non-lnear relatonshps based on Posson, negatve bnomal, and lognormal dstrbutons. Also the ncremental model has been tested to dentfy the best model that could elaborate the relatonshp between pedestran crashes and selected predctor varables. By valdatng (Curve Fttng) each of tests and nvestgatng a varety of tests ncludng ch-square and T-test n connecton wth each of models, the most approprate model that has R 2 close to 1 wll be selected to predct pedestran crashes n future. Informaton about the ntersecton of Taleghan-sharat s explaned n Secton 5. Negatve bnomal model: AN = 1, GM = 2, BS = 1, NOA = 11, VP1 = 285365, VP2 = 162209, V1 = 2282929, V 2 = 7220330 1.359 NOA = e EXP( 0.0000009094VP1 + 0.00000022046VP 2 + 0.000000022576V 1 + 0.00000001707V 2 + 0.183GM + 0.071AN + 0.147BS ) 1.359 ( ( ) ( ) 0.00000002257( 2282929) 0.00000001707( 7220330) 0.183( 2) 0.071( 1) 0.147( 1)) EXP ( 0.25939 + 0.03568 + 0.05022 + 0.12325 + 0.366 + 0.071 + 0.147) = 0.9881 NOA = e EXP 0.0000009094 285365 + 0.00000022046 162209 + + + + + 1.359 0.9881 e e = 3.892 2.869 = 11.17 ( ) ( ) NOA( ) ( ) ( ) NOA( ) NOA new NOA before NOA 11.17 NOA 11 Calbratng = 100 = 100 before 11 = 1.545%Error ok 9. Senstvty Analyss and Provde Solutons for the Pedestrans Safety at Intersectons Study the effects of output varables from nput varables of statstcal model s called senstvty analyss 1. In other words, senstvty analyss s a method for changng the statstcal model nputs to an organzed (systemat- 1 Senstvty Analyss (SA). 251
c), that can be predcted the effects of changes n model s output. Calbrated models wll be under the senstvty analyss to study the effect of each mentoned factor n overall performance. At frst, three ntersectons profle as sample be selected for ths method then the number of pedestran crashes change rate due to change of any parameters wll be examned by Excel software. Only one ntersecton s senstvty analyss s nvestgated n ths paper. The results of the senstvty analyss are shown n Table 5 and Table 6. As the rate of change, the parameters that expressed n to percentage are used to calculate the effect of changes rate n performance value. The results of senstvty analyss for Taleghan-Behesht ntersecton show that the maxmum senstvty of pedestran crashes s related to bus stop whch nears to ntersecton and ncreases 17.13% of pedestran crashes. Ths happens because more pedestrans are crossng statons. Dscrete turn reduces 16.72% of pedestran crashes at ntersectons. Pedestran crashes due to drver vsblty reducton wll be ncreased when streets angle leadng to ntersecton s other than 90 degrees than when t s 90 degrees. 10% ncreases n pedestran volume n man route causes 2.63% ncrease n crashes rate and 10% decreases n pedestran volume n man route causes 2.56% decrease n crashes rate. Other results can be observed n Table 5. These factors are classfed based on the type and nature of each factor after determnng effectve factors on pedestran crashes at ntersectons. Many strateges that outlned below can help to reduce pedestran crashes and mprovng pedestran safety and ther convenence at ntersectons and passage. These methods nclude the followng: Reduce vehcles speeds. Reduce the probablty of ntersectng streets wth pedestran pathways. Create partcular lanes whch separated from vehcles. Increase vsblty between vehcles and pedestrans and ncrease safety warnngs. Improvement of pedestrans and drvers behavor. Construct overpass and underpass brdges for pedestran or cyclsts. Reducng the wdth of streets n ntersectng wth pedestran path. Emphass on not dong other actvtes whle pedestrans and cyclsts move from pathways (speak, watch shops,use cell phone, etc.). Increased n front of vehcles safety to reduce njures to vulnerable groups. Install specal pedestran sgnals at ntersectons. Table 5. 10% ncrease and decrease of effectve parametrc varables results n man and secondary routes of ntersecton [14]. Effectve Parameters on the Number of Crashes The average volume of pedestran n man rout( vp1) The average volume of pedestran n secondary rout( vp2) The average volume of enterng vehcles n man rout( v1) The average volume of enterng vehcles n secondary rout ( v2) The Number of The Number of Crashes Accdents Resultng Caused by10% Increase of from the Model Each Parameters Percentage Changes from Senstvty Analyss The Number of Crashes Caused by10% Decrease of Each Parameters Percentage Changes from Senstvty Analyss 11.17 11.46 2.63 10.88 2.56 11.17 11.21 0.36 11.13 0.36 11.17 11.23 0.52 11.11 0.51 11.17 11.31 1.24 11.03 1.22 Table 6. Presence or absence of effectve nonparametrc varables results n the man and secondary routes [14]. Parameter Percentage Change The Number of Crashes If the Parameter Is 1 The Number of Crashes If the Parameter Is 0 Dscrete turn (GM) 16.72 6.37 7.65 Intersecton s angle (AN) 7.36 11.03 10.28 Bus stop (BS) 17.13 11.15 9.52 252
Modfcaton of ntersectons geometrc desgn to enhance the drver s vsblty of pedestrans who cross the street wdth. Apply ntellgent traffc systems to dentfy pedestrans and cyclsts and to alert vehcles drvers. Provde pedestran crash predcton models to nvestgate the effectve factors and reduce the number of crashes at ntersectons. Reducton of publc places n the vcnty of pedestran to reduce the pedestran volume. Another mportant pont s pedestran lanes pantng at ntersectons. Panted surfaces are very slppery and dangerous for pedestran durng ranfall. For ths reason, pedestran lanes panted nto two peces whch 2 meters away among them. So pedestran cross from ths created gap. 10. Conclusons and Recommendatons for Future Research Traffc accdents are one of the major publc health threat and a natonal dsaster. Thus reducng traffc accdents n developng countres s one of the most mportant ssues because the number of accdents ncreases n these countres. Most accdents happen n urban traffc networks so the role of ntersectons s very mportant. Due to convergng traffc flow, more accdents have been observed at ntersectons. Identfyng effectve factors on pedestran crashes and provdng pedestran crash predcton models can help to mprove pedestran safety and prevent pedestran crashes at ntersectons. Some models were shown to estmate pedestran crashes at ntersectons durng the research. Incomng vehcles volume on the man and secondary routs, number of transt stops and schools wthn the vcnty of ntersectons, number of lanes at man and auxlary road, area traffc plan, type of sgnal, one way streets, ntersecton s angle and pedestran volume have been extracted and used n pedestran crash estmaton models for 20 ntersectons. After examnng the correlatons some parameters were excluded n model. Among models ncludng: lnear regresson, Posson and negatve Bnomal to select the best pedestran crash predcton model from studed models wth conducted tests on them that can express characterstcs of pedestran crashes n the best way, negatve bnomal due to less dsperson, more correlaton and logcal answer between Posson and lnear regresson were consdered more approprate. ( 1.359 e EXP 0.0000009094 1 0.00000022046 2 0.000000022576 1 NOA = VP + VP + V + 0.00000001707V 2 + 0.183GM + 0.071AN + 0.147BS Whle the number of transt stops, shoppng malls, area traffc plan cause to reduce the pedestran crashes rate. Drvers tend to alert and pay more attenton to pedestran s safety because they typcally expect to encounter more pedestrans n these areas. The results of senstvty analyss show that the maxmum senstvty of pedestran crashes s related to bus stop whch nears to ntersecton and ncreases 17.13% of pedestran crashes. Ths happens because more pedestrans are crossng statons. Dscrete turn reduces 16.72% of pedestran crashes at ntersectons. Pedestran crashes due to drver vsblty reducton wll be ncreased when streets angle leadng to ntersecton s other than 90 degrees than when t s 90 degrees. 10% ncreases n pedestran volume n man route causes 2.63% ncrease n crashes rate and 10% decreases n pedestran volume n man route causes 2.56% decrease n crashes rate. Demographc, soco-economc, land use characterstcs can be effectve on the relatonshp between pedestran crashes, vehcles and pedestran volume. Aspects such as populaton by age group, automoble ownershp and transt rdershp (alghtng and boardng passengers at each transt stop) and weather condton were not consdered due to the lack of avalable data for the study perod. Descrbed methods n the prevous secton can great help to mprove pedestran safety and reduce pedestran crashes after determnng effectve factors and provdng pedestran crash predcton model at ntersectons. Recommendatons for Future Research Researchers nterested n reducng pedestran crashes to complete ths research can contnue ther studes n the followng subjects at ntersectons: Parameters such as demographc, soco-economc, land use characterstcs that have an mpact on the relatonshp between pedestran crashes, vehcles and pedestran volume, dfferent aspects ncludng populaton by age group, automoble ownershp, transt rdershp (alghtng and boardng passengers at each transt stop) and weather condton that due to the lack of avalable data were not consdered at ntersectons for the study perod could be consdered to estmate the pedestran crash predcton model n ther research. ) 253
Research can also be done on the optmzaton of traffc sgnals phase for safe passage of pedestrans. Cordon study 2 could used to lmt publc transt stops, commercal centers; schools and etc dstance to the ntersecton and provde accurate data to the locaton. References [1] Pulugurthaa, S.S. and Sambharab, V.R. (2011) Pedestran Crash Estmaton Models for Sgnalzed Intersectons. Accdent Analyss and Preventon, 43, 439-446. http://dx.do.org/10.1016/j.aap.2010.09.014 [2] Joksch, H.C. and Kostynuk, L.P. (1997) Modelng Intersecton Crash Counts and Traffc Volume. http://deepblue.lb.umch.edu/btstream/2027.42/1213/2/90762.0001.001.pdf [3] Brude, U. and Larsson, J. (1993) Models for Predctng Accdents at Junctons Where Pedestrans and Cyclsts Are Involved. How Well DO they Ft? Accdent Analyss and Preventon Journal, 25, 449-509. http://dx.do.org/10.1016/0001-4575(93)90001-d [4] Huang, H., Chn, H.C. and Haque, M.M. (2008) Bayesan Herarchcal Analyss of Crash Predcton Models. Transportaton Research Board 87th Annual Meetng Compendum of Papers DVD, Washngton, DC. [5] Lyon, C. and Persaud, B.N. (2002) Pedestran Collson Predcton Models for Urban Intersectons. Transportaton Research Record # 1818, 102-107. http://dx.do.org/10.3141/1818-16 [6] Wer, M., Wentraub, J., Humphreys, E.H., Seto, E. and Bhata, R. (2009) An Area-Level Model of Vehcle-Pedestran Collsons wth Implcatons for Land Use and Transportaton Plannng. Accdent Analyss & Preventon Journal, 41, 137-145. http://dx.do.org/10.1016/j.aap.2008.10.001 [7] Torbc, D.J., Harwood, D.W., Bokenkroger, C.D., Srnvasan, R., Carter, D.L., Zegeer, C.V. and Lyon, C. (2010) Pedestran Safety Predcton Methodology for Urban Sgnalzed Intersectons. Transportaton Research Board 89th Annual Meetng Compendum of Papers DVD, Washngton DC. [8] Lee, C. and Abdel-Aty, M.A. (2005) Comprehensve Analyss of Vehcle-Pedestran Crashes at Intersectons n Florda. Accdent Analyss & Preventon Journal, 37, 775-786. http://dx.do.org/10.1016/j.aap.2005.03.019 [9] Elvk, R. (2009) The Non-Lnearty of Rsk and the Promoton of Envronmentally Sustanable Transport. Accdent Analyss & Preventon Journal, 41, 849-855. http://dx.do.org/10.1016/j.aap.2009.04.009 [10] Harwood, D.W., Torbc, D.J., Glmore, D.K., Bokenkroger, C.D., Dunn, J.M., Zegeer, C.V., Srnvasan, R., Carter, D., Raborn, C., Lyon, C. and Persaud, B. (2008) Pedestran Safety Predcton Methodology. NCHRPWeb-Only Document 129: Phase. III. Transportaton Research Board, Washngton DC. [11] FHWA How to Develop a Pedestran Safety Acton Plan Traffc Safety Basc Facts (2005). [12] Pckerng, D., Hall, R.D. and Grmmer, M. (1986) Estmaton of Safety at Two-Way STOP-Controlled Intersectons on Rural Hghways. Transportaton Research Record, 1401, 83-89. [13] PASW. Statstcs18 lnk. Statstcs Software SPSS 18. [14] Mcrosoft Offce Excel ( 2007). Lnk. 2 Cordon study. 254