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Accident Analysis and Prevention 70 (2014) 258–266

Contents lists available at ScienceDirect

Accident Analysis and Prevention

jou rn al hom ep age: www.elsev ier .com/ locate /aap

afety performance models for urban intersections in Brazil

eloisa Barbosaa, Flávio Cuntob,∗, Bárbara Bezerrac, Christine Nodarid,aria Alice Jacquese

Universidade Federal de Minas Gerais, Belo Horizonte, BrazilUniversidade Federal do Ceará, Fortaleza, BrazilUniversidade Estadual Paulista, Bauru, BrazilUniversidade Federal do Rio Grande do Sul, Porto Alegre, BrazilUniversidade de Brasília, Brasília, Brazil

r t i c l e i n f o

rticle history:eceived 19 November 2013eceived in revised form 9 April 2014ccepted 14 April 2014

eywords:afety performance modelsoad safetyeneralized linear modelsbservational road safety studieseneralized Estimating Equations

a b s t r a c t

This paper presents a modeling effort for developing safety performance models (SPM) for urban inter-sections for three major Brazilian cities. The proposed methodology for calibrating SPM has been dividedinto the following steps: defining the safety study objective, choosing predictive variables and samplesize, data acquisition, defining model expression and model parameters and model evaluation. Amongthe predictive variables explored in the calibration phase were exposure variables (AADT), number oflanes, number of approaches and central median status. SPMs were obtained for three cities: Fortaleza,Belo Horizonte and Brasília. The SPM developed for signalized intersections in Fortaleza and Belo Hori-zonte had the same structure and the most significant independent variables, which were AADT enteringthe intersection and number of lanes, and in addition, the coefficient of the best models were in the samerange of values. For Brasília, because of the sample size, the signalized and unsignalized intersectionswere grouped, and the AADT was split in minor and major approaches, which were the most significantvariables. This paper also evaluated SPM transferability to other jurisdiction. The SPM for signalized inter-

sections from Fortaleza and Belo Horizonte have been recalibrated (in terms of the Cx) to the city of PortoAlegre. The models were adjusted following the Highway Safety Manual (HSM) calibration procedureand yielded Cx of 0.65 and 2.06 for Fortaleza and Belo Horizonte SPM respectively. This paper showedthe experience and future challenges toward the initiatives on development of SPMs in Brazil, that canserve as a guide for other countries that are in the same stage in this subject.

. Introduction

One of the primary goals for transportation researchers andractitioners is to ensure adequate safety performance of thearious transportation components for all road users given theesources available. Historically, safety has been defined and mea-ured in terms of the observed number of crashes in part becausef the intuitive and logical link between these two items. This typef approach relies heavily on the reliability and overall quality ofccident data systems as well as on statistical models aimed at esti-ating the expected number of crashes as a function of geometric

nd operational attributes of the traffic system components, also

nown as safety performance models (SPMs), safety performanceunctions (SPFs) or accident prediction models (APMs).

∗ Corresponding author. Tel.: +55 8533669488x219; fax: +55 8533669488x201.E-mail addresses: flaviocunto@det.ufc.br, fjcc07@gmail.com (F. Cunto).

ttp://dx.doi.org/10.1016/j.aap.2014.04.008001-4575/© 2014 Elsevier Ltd. All rights reserved.

© 2014 Elsevier Ltd. All rights reserved.

The occurrence of accidents in a given location is known to havea strong random component. In this context, SPM can contributeto measuring real safety performance by attenuating the effect ofrandomness in the observed crash frequency (Hauer, 2002). SPMsare developed based on police-reported crashes and geometric andoperational road attributes as covariates. These models have thepotential to improve road safety by comparing alternative roadprojects regarding expected relative safety performance (AASHTO,2010). Thus, it is possible to explicitly include road safety criterionin the decision-making process for selecting those projects that areexpected to have fewer accidents during a given operation period.

A great deal of the recent worldwide interest in developing SPMcan be credited to the release of the first edition of the HighwaySafety Manual – HSM (AASHTO, 2010). The HSM devotes much of itscontent to justification, premises, development and application of

SPM in the transportation systems planning process at the strategic,tactical and operational level.

Though SPMs have been explored for more than two decades incountries such as Canada, the USA, England and Sweden, in Brazil,

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H. Barbosa et al. / Accident Analy

his methodology is still in its infancy. Few scientific papers deal-ng with this topic come from under developing countries. Early

odeling efforts for the Brazilian environment can be accreditedo the doctoral research of Cardoso (2006) and summarized in theater work of Cardoso and Goldner (2007), in which urban arterialegments in the city of Porto Alegre were analyzed.

It is believed that this discrepancy can be attributed in part toroblems with the availability and quality of information on traf-c accidents associated with the relative scarcity of procedures foralibration and validation of such models nationwide. This situa-ion, along with the increase in crash frequencies in Brazilian urbanreas, has resulted in a joint research effort started in 2009 andponsored by the National Council of Technological and Scientificevelopment (CNPq). The research group consists of six Brazilianniversities and four international institutions, namely Universityf Waterloo and Ryerson University from Canada, Lund Universityrom Sweden and Universidade do Minho from Portugal.

This paper presents the modeling effort and initial results forhe development of safety performance models for urban streetsn Brazil that could be useful for worldwide practitioners in theame situation. Given the limited data available in most cities, thisroject also aimed at generating alternative solutions to obtainata and, at the same time, guide future developers on the bestpproach to define the functional form of the models, techniqueso be adopted in the calibration process and investigating modelpatial and temporal transferability.

. Road safety modeling with observational data

From the engineering perspective, methodologies for safetyssessments are heavily influenced by the way safety is definednd measured. Traditionally, the level of safety of a given entityas been defined as “the number of crashes by type and severity,xpected to occur on the entity during a specific period” (Hauer,002). Representing safety throughout crash events is therefore theatural domain of observational studies.

Observational studies can be viewed as a passive learning pro-ess in which the knowledge comes from meticulous analysis ofhe outcome of events that have not been formally designed toddress the problem. According to Davis (2004), an underlyingssumption of these studies is that crashes are individually unpre-ictable, although groups of crashes observed on a given locationan produce predictable statistical patterns. Basically, these groupsf crashes may be related to a single time period (number of crashelated to one or more years are considered globally) or may includeongitudinal data. In the latter situation, data belonging to differ-nt years for a given location can be treated and analyzed as timeeries events. In addition, the safety condition of different locationsay be related to each other. The presence of temporal or spatial

orrelations in the database imposes specific statistical consider-tions for model development (Lord and Persaud, 2000; Wang andbdel-Aty, 2006).

Under this paradigm, several methods for linking accidents andheir consequences to human, vehicle, roadway and environmen-al attributes have been proposed over the last two decades. Thesenclude the use of contingency tables, linear multivariate regres-ion models, logistic models, hierarchical loglinear models, inducedxposure models and generalized linear models, among others. Aroad review of these methodological alternatives for global crash-requency data can be found in Lord and Mannering (2010). Inddition, the work of Savolainen et al. (2011) presents a general

eview on methodological alternatives for specific analysis of crash-njury severities.

Because of the relative ability to address some aspects of thenherent stochastic rare random nature of crashes, such as the

Prevention 70 (2014) 258–266 259

regression to the mean phenomenon and the crash frequencyover dispersion, the generalized linear modeling approach (GLM)has recently become widely applied (Hauer, 2004; Sawalha andSayed, 2006; Hadayeghi et al., 2007; AASHTO, 2010). Further-more, a procedure derived from the GLM, called GeneralizedEstimating Equations (GEE), has been successfully applied in thepresence of longitudinal and/or spatial correlations in databases(Lord and Persaud, 2000; Wang and Abdel-Aty, 2006). The mostcommonly found general expression for SPM can be written as fol-lows (Hakkert and Hochermanand, 1996; Sawalha and Sayed, 2006;AASHTO, 2010):

Y =[∏

i

(Ai)ˇi

]· e˙j(�jBj) (1)

where Y, expected number of crashes over a specific time inter-val (year); A and B, predictive variables; ˛, ˇi and � j, model’scoefficients.

Initially, SPMs were developed assuming the error structure tobe compatible with the Poisson distribution; however, other stud-ies have produced better results by assuming the negative binomialdistribution (also known as Poisson-gamma) error structure incases where crash frequency presents a considerable dispersion(variance greater than average) among similar entities (Bonnesonand McCoy, 1993; Persaud and Mucsi, 1995). For all distributions,one important aspect that imposes difficulties for the modelingprocedure is the presence of many records of zero crashes in thedatabase. Different approaches have been adopted to address thissituation (Shankar et al., 1997; Lee and Mannering, 2002; Kumaraand Chin, 2003). However, some of them present limitations whenconsidered under the traffic engineering point of view (Lord et al.,2005, 2007).

SPM expressions have been used as one of the most importantcomponent of a methodology to improve crash estimations knownas the Empirical Bayes method (EB method), which applies conceptsof conditional probability to both the reference population (repre-sented by SPMs) and specific sites to produce a weighted value ofthe expected number of crashes. The EB estimate of crashes is givenby (Hauer, 2002) the following equation:

E(m|x) = w · E(m) + (1 − w) · x (2)

where E(m|x), the expected number of crashes for entity m giventhat x crashes have been observed for the same entity; E(m), crashestimate obtained from regression model developed using crashdata of similar sites (SPM); w, weight assigned to E(m) (0 = w = 1);x, observational crash data for the site.

The expression that yields the best estimate of w is given by

w = 11 + VAR(m)/E(m)

(3)

where VAR(m) is the variance associated with the regression modeldeveloped. Basically, the weight w in Eqs. (2) and (3) is a functionof the variability found in the data used to develop the crash pre-diction model. The lower the variation in these data, the higherthe weight placed on the model estimates of crashes, i.e., higherlevel of confidence in the model results. The EB method has beenlargely adopted in hot-spot identification (network screening) andin before-after analysis (AASHTO, 2010).

Despite the considerably large body of research on SPM devel-opment, a general methodology for SPM calibration is currentlynot available mostly due to a general lack of consensus regardingstrategic questions such as: (1) what would be the minimum sam-

ple size required to develop “acceptable” models?; (2) how shouldresearchers select the most important variables to be consideredin the model formulation?; (3) what is the most adequate modelstructure?; (4) how do researchers confirm the model usefulness

260 H. Barbosa et al. / Accident Analysis an

Definin g the Sa fety Stu dy Objecti ve

Accident Da ta System (ADS)

Geometric and Operational Attributes

Mode l Eval uation

Unsatisf.

Satisf .

Choosing Pr edicti ve Variables and Sa mple Size

Defining Model Express ion

Estimati on of Model Parameters

Mode l Acceptanc e

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Fig. 1. Procedure for developing SPM – Brazilian urban intersections.

nd acceptability (model validation); and (5) when is it appropriateo draw causal inferences as opposed to predictive inferences? Theollowing section describes the general methodology adopted forPM calibration for Brazilian urban intersections.

. Methodology

The literature review on the development of SPM based on his-orical crash data has shown a number of methodological steps inrder to improve model validity and predictive power. The criticalnalysis of these previous investigations allowed the establishmentf a procedure for calibrating SPM for Brazilian urban intersectionss shown in Fig. 1. These methodological steps will be discussed inetails in the following section.

.1. Safety study objective

Defining the main objective of the safety study is importanto guide the modeler throughout Accident data system – ADS

anagement (response variables and sample size) as well as therocess related to choosing covariates that are important to repre-ent changes in the response variables. For example, developingodels to predict the number of crashes involving motorcycles

t intersections requires ADS to provide separate information forotorcycles as well as to assume a criterion to assign the accident

o an intersection. For choosing the covariates one would certainlyeed exposure related information, i.e., AADT for motorcycles asell as other attributes, such as, number of lanes, lane width, type

f traffic control device, among others.

.2. Predictive variables and sample size

After the establishment of the safety study objective the mod-ler must define an initial set of predictive variable that will likelyo be significant to the construction of the SPF. Generally these vari-bles can be divided into factors that reflect the exposure of userso events that may cause accidents such as the period of analy-is, vehicle flow and segment length, and environmental factorshat influence the likelihood of being involved in traffic accidentsBonneson and McCoy, 1993; Hauer, 2004). Among the most com-

on environmental factors are number of lanes, lane width, trafficontrol device, intersection density, number of approaches, drive-ays density, median type, among others (Bonneson and McCoy,

993; Persaud and Mucsi, 1995; Hakkert and Hochermanand, 1996;reibe, 2003; Cardoso and Goldner, 2007).

It is observed that, in general, modelers choose predictive vari-bles using subjective criteria based on previous experience aboutts influence in traffic accidents or considering aspects regardinghallenges of obtaining certain attributes. The vast majority of SPM

d Prevention 70 (2014) 258–266

found in the literature uses some kind of measure of exposure suchas Annual Average Daily Traffic – AADT or segment length.

The minimum sample size for SPM development is one aspectlacking objective criteria. The over dispersion in traffic accidentsnormally causes the need of a large number of observations toobtain statistically significant values of the parameters. Larger sam-ples can be obtained either by adding entities or by increasing thestudy period (Bonneson and McCoy, 1993), however increasing thestudy period may bring side effects in case of a temporal depend-ency. Lord (2006) investigated the influence of sample size andsample mean value on the dispersion parameter (�) of the nega-tive binomial distribution using Monte Carlo simulation. The resultsindicated that the smaller the sample mean value the greater shouldbe the sample size and as a general rule, one should not try tocalibrate SPM with less than 100 observations.

3.3. Data acquisition

The calibration of reasonable SPM requires information relatedto the crash occurrence and several other factors that might haveinfluence on crash frequency. Unfortunately this information usu-ally is not structured into one single database. Frequently, modelersmake use of at least the general ADS and a database including trafficstudies that allow estimating the AADT.

One of the greatest challenges to the consolidation of obser-vational studies applied to road safety is associated to problemsrelated to the use of databases of traffic accidents as a primarysource of data. Among the most common problems found in theliterature related to accident database are: (i) low reportabilityrate, (ii) incomplete and inaccurate information and (iii) errorsduring data entry, among others (Davis, 2004; Hauer, 2002; Hirstet al., 2004). Therefore development of SPM depends directly onthe existence of reliable ADS including at least the following fields:precise location of the crash, type of crash, date, day of week, time,type of vehicle, severity, weather and light conditions.

In terms of the predictive variables, it worth notice that a dis-crepancy can be found between databases of vehicular flow fordifferent cities, due to the multiple collection methods (technology,frequency and scope) and data manipulation to estimate the AADT.This type of traffic studies are also relatively expensive which hasfostered a number of research efforts focused on establishing alter-native procedures to estimate reliable AADT for SPM developments(Lord and Persaud, 2000; Ferreira, 2010).

This research effort has focused primarily on estimating SPM forurban intersections mainly because of data availability regardingtraffic flow and other attributes considered important for the initialdefinition of homogeneous groups such as number of approaches,number of traffic lanes, intersection angle, central median config-uration, type of traffic control, land use, bus stops and parkingconfiguration. Some of the tools used in this step were aerialphotographs, using applications such as Google Earth©, maps andreports provided by the local traffic center, as well as specific leg-islation related to land use and functional classification of eachmunicipality.

3.4. Model expression and model parameters

According to Hauer (2004), defining the best expression forthe model is not a straightforward task. As a function of availablecovariates, the model expression may contain both multiplica-tive and additive components. Multiplicative components (variabletypes A and B in Eq. (1)) are recommended whenever the factor is

present along a road segment (number of lanes, median, shoulder,etc.) or to represent the exposure (AADT, length). Additive com-ponents must be applied to better represent the effects of isolatedfactors such as driveways, bridges and sharp curves).

H. Barbosa et al. / Accident Analysis and Prevention 70 (2014) 258–266 261

Table 1Sample size and predictive variables for homogeneous entities.

Jurisdiction Entity Group variables Predictive variables Sample size

Belo Horizonte Signalized Commercial land use, central median AADT, #lanes, #approaches, central median 220Brasília Intersections – Major/Minor AADT, #lanes/approach, type of traffic control;

red light enforcement; land use32

Fortaleza Signalized Mixed land use, four leggedintersections

Major/Minor AADT, total AADT, #lanes, #approaches, centralmedian

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The best model parameters estimates were usually obtainedy applying the maximum likelihood method using theewton–Rapson optimization algorithm. There are a numberf computational applications, such as SAS©, SPSS©, and R© thatave pre-established routines for the estimation of parametersepending on the structure assumed for the error (Poisson oregative binomial).

Because of the reduced sample size and consequent need for aongitudinal study, SPM can also be developed using a Generalizedstimation Equations (GEE) procedure, which represents an exten-ion of the Generalized Linear Models approach (Liang and Zeger,986; Halekoh et al., 2006). The GEE procedure allows for inves-igating different types of correlation structure in the longitudinalrash data, including the independence condition (Liang and Zeger,986; Wang and Abdel-Aty, 2006).

The calibration methodology applied to Fortaleza and Belo Hori-onte followed a sequential process of inserting variables suggestedy Hauer (2004). This process was initiated with a base modelhich the only predictive variable was AADT, representing the

xposure. Other predictive variables were subsequently introducedo the base model, until all variables (and its combination) wereested. It worth notice that the relatively low number of vari-bles (AADT, number of lanes, median configuration and numberf approaches) allowed developing and analyzing models with allossible combinations of the available variables.

Due to the reduced sample size, SPM for Brasília were developedsing a Generalized Estimation Equations (GEE). The investigatedodels were calibrated considering three possible working cor-

elation structures among the annual data for each location:ndependent, exchangeable and autoregressive.

An initial test using the dispersion parameter (�d) was con-ucted on base models to verify the most adequate assumptionegarding the error structure (Poisson or negative binomial –B). The dispersion parameter is obtained by the ratio of theeneralized Pearson statistic �2

p, and the difference between theumber of observations and number of model parameters. Inhis case, obtaining values close to 1 indicates that the vari-nce assumed in the model structure is similar to that observedn the data. In all jurisdictions, this test yielded �d valueslose to 1 therefore reinforcing the NB error structure assump-ion.

.5. Model evaluation

The goodness of fit analysis for candidate models was performedsing the following statistics: the generalized Pearson �2

p statistic,he scaled deviance �p and the Akaike Information Criterion (AIC).he Pearson �2

p statistic can be used for null hypothesis significanceesting regarding the equivalence of the variance assumed in the

odeling effort and the sample variance. The scale deviance is use-

ul for comparing the proposed model and the saturated model, andhe AIC compares different models based on the balance betweenhe bias and variance explained by them. For models developedsing the GEE approach (Brasília jurisdiction), a quasi-likelihood

Major/Minor AADT, total AADT, #lanes, central median 132

information criterion as presented by Pan (2001) was also appliedas a goodness of fit criterion.

The model performance over the entire range of predictive vari-ables was assessed throughout the Cumulative Residual Plot (CUREplot). According to Hauer (2004), for reasonably good models, theCURE plot should present a moderate random oscillation aroundzero (“random walk”). Constant up or downward trends in thegraph suggest areas (range of values) where the model can overor underestimate the predicted number of crashes. Additionally,Hauer (2004) recommends developing +2�d and −2�d confidenceintervals for the CURE plot to verify the model validity over its entiredomain. The following section discusses the major results from themodel calibration effort focusing on the estimated parameters andcorrespondent statistics as well as on overall performance of theproposed SPM.

4. SPM development

The application of the methodology concerning the identifi-cation of geometric and operational attributes for homogeneousgroups resulted in the predictive variables summarized in Table 1that also presents the sample size for each jurisdiction.

4.1. Average annual daily traffic (AADT) estimation

As previously mentioned, each city has adopted specific pro-cedures for the AADT estimation as a result of the availability ofdata. In Brasília, AADT was estimated from short counts of threehours in each intersection approach (V3 h). Expansion factors weredetermined from historical data collected by the nearest red lightsurveillance camera for three hours of observation at each site, tak-ing into account the day of the week, month and year of collection(2005–2010).

The AADT estimation for Belo Horizonte used the methodologyproposed by Roess et al. (2011) which allowed work with a sam-ple of 24 h for each intersection combined with data obtained frompermanent counting stations (loop detectors). Expansion factorswere obtained from a sample of five intersections located in thestudy area which presented consistent traffic volume databases.The weekly expansion factor was determined by dividing AverageDaily Traffic (ADT) by the estimated Annual Average Daily Traffic(AADTest) for each day of the week in the spot. The monthly expan-sion factor was obtained by dividing the Average Daily Traffic permonth by the AADTest.

In Fortaleza, daily flows were estimated from short durationcounts using daily expansion factors calculated for five homoge-neous groups of intersections depending on geographic locationand type of collection equipment (loop detectors for traffic sig-nals or red light enforcement). The expansion factors of shortdaily counts were estimated by surveys conducted in two intersec-

tions of Fortaleza for 24 h to obtain the daily traffic flow pattern.The 24 h estimates were subsequently expanded to AADT usingweekly and monthly factors obtained in the studies by Oliveira(2004).

262 H. Barbosa et al. / Accident Analysis and Prevention 70 (2014) 258–266

Table 2Variables description and basic statistics for the intersections studied.

Variable Description Averagea Sd. Min. Max.

Belo Horizonte: signalized intersectionsa

AADT AADT – all entering vehicles 42,459 24,014 2827 120,007#lanes Total number of lanes 6 2 14#app Number of approaches 3 0.7 2 5mconf 0, no median; 1, major; 2, major and minor 0.5 0.3 0 2YIF Injury + fatal crashes 4 3.0 0 24

Brasíliab

AADTmajor Major street AADT 34,039 28,769 10,204 248,161AADTminor Minor street AADT 7226 8312 202 37,669AADT AADT – all entering vehicles 41,265 33,765 10,416 285,830#lanes Total number of lanes major street 2.40 0.66 2 5Traffic Control 1, signalized intersection; 0, unsignalized intersection 0.50 0.5 0 1Red light surveillance camera 1, with camera; 0, without camera 0.40 0.49 0 1Yit Number of crashes for intersection i in time period t 2.22 3.16 0 13

Fortaleza: signalized intersectionsc

AADT AADT–all entering vehicles 35,319 10,438 15,887 65,618#lanes Total number of lanes 5.8 1.4 4 12#app Number of approaches 2.7 0.6 2 4mconf 0, no median; 1, major; 2, major and minor 0.7 0.6 0 2YT Total crashes 7.5 7.7 0 48YIF Injury + fatal crashes 1.5 1.6 0 7

Unsignalized intersectionsd

AADT AADT – all entering vehicles 17,424 8375 1040 41,984#lanes Total number of lanes 4.2 0.85 4 8mconf 0, no median; 1, major; 2, major and minor 0.02 0.25 0 1YT Total crashes 4.1 3.9 0 19

a Sample = 220 intersections. Year 2009.

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b Sample = 32 intersections Years from 2005 to 2010.c Sample = 101 intersections. Year 2009.d Sample = 132 intersections. Year 2007.

.2. Accident data systems

Different degrees of difficulty were encountered at each munic-pality concerning the format and the interpretation of the contentsf the accident database system (ADS). In Belo Horizonte andrasília, the database (ADS) does not record property damage onlyccidents. This procedure tends to reduce the total number of acci-ents in the intersections considered in the study.

The determination of the number of accidents from the databasenformation is not a direct activity because of the data storage pro-ess. For instance, for the Belo Horizonte jurisdiction, the attempto determine the number of accidents by creating a routine in MSxcel was not successful because of data format. Thus, the coordi-ates of the accident were used. An MS Excel database was used

n combination with Global Mapper software to plot on the cityap the occurrence of accidents using geographic coordinates. The

dentification of the number of accidents was then performed byanual counting.In general, crash reports and traffic flow information are avail-

ble from different databases, which make it difficult to manipulateatabases individually because of to the time spent to associatehe volume and number of accidents information in the samele. Table 2 presents a summary of the predictive and responseariables obtained from the available samples for the Belo Hori-onte, Brasília and Fortaleza jurisdictions.

.3. SPM for Fortaleza and Belo Horizonte

The model calibration effort for signalized intersections in For-aleza and Belo Horizonte has yielded a total of eight different

PM expressions for the total number of crashes (2009) and theet of predictive variables described in Table 2. Calibrated modeloefficients and other relevant statistics for all estimated expres-ions can be found in Tables 3 and 4.

A strict relative comparison using the generalized Pearson �2p

statistic, the scaled deviance Sp and the Akaike Information Crite-rion (AIC) would suggest model with all variables (AADT, numberof lanes, number of approaches and central median configuration)as the best model. However, differences among statistics are subtle,revealing no conclusive indicators to choose this expression as thebest model.

The analysis of the correlation matrix for predictive variablespointed out a high degree of correlation between number of lanesand central median (0.86) and between central median and num-ber of approaches (0.96). Considering the relatively low correlationbetween AADT and number of lanes (0.56), as well as improve-ments on Pearson �2

p statistic, the scaled deviance Sp and the AkaikeInformation Criterion (AIC) as compared to the base model (withAADT only), it was concluded that, although there is not a definitivepreference for a specific model, the expression with the variablesAADT and #lanes presents more adequate characteristics amongthe analyzed models.

Eqs. (4) and (5) represent the SPM for signalized intersectionsin Fortaleza and Belo Horizonte, respectively:

YT = 0.0059(AADT0.52) · e0.28·#lanes (4)

YIF = 0.0064(AADT0.51) · e0.14·#lanes (5)

where YT, total number of crashes in 2009; YIF, total number ofinjury and fatal crashes in 2009; AADT, annual daily traffic enter-ing the intersection; #lanes, total number of lanes (all intersectionlegs).

For the models using the frequency of injury and fatal crashes

duce significant coefficients for the set of independent variables.A visual analysis using a plot with AADT and the frequency ofinjury and fatal crashes revealed a considerably scattered pattern.It is possible that this over dispersed behavior, the inherently low

H. Barbosa et al. / Accident Analysis and Prevention 70 (2014) 258–266 263

Table 3Model parameters – Fortaleza city.

Variable Models

01 02 03 04 05 06 07 08

˛ ln (˛) −12.09 −5.13* −7.72 −5.65 −5.27 −7.49 −7.12 −7.23Coef. 5.61E−06 5.91E−03* 4.44E−04 3.52E−03 5.16E−03 5.61E−04 8.09E−04 7.22E−04�ˇ 2.59 2.52* 3.06 2.85 2.65 2.68 2.89 2.61

AADT Coef. 1.34 0.52* 0.90 0.59 0.53 0.70 0.60 0.55�ˇ 0.23 0.26* 0.30 0.14 0.28 0.26 0.29 0.26

#lanes Coef. – 0.28* – – 0.52 0.41 – 0.34�ˇ – 0.05* – – 0.14 0.08 – 0.08

mconf Coef. – – 0.31 – – −0.39 −0.66 −0.90�ˇ – – 0.14 – – 0.27 0.31 0.28

#app Coef. – – – 0.52 −0.03 – 1.16 0.74�ˇ – – – 0.14 0.20 – 0.33 0.31

� 2.92 4.47* 3.16 3.58 4.47 4.81 3.90 5.39−2� −575 −548* −570 −561 −548 −543 −556 −537AIC 581 556* 578 569 558 553 566 549

Note: All tested variables statistically significant ( = 0.05).* selected model.

Table 4Model parameters – Belo Horizonte city.

Variable Models

1 2 3 4 5 6 7 8

˛ ln(˛) −5.85 −5.06* −4.60 −5.24 −4.79 −4.35 −4.73 −4.48Coef. 0.0029 0.0064* 0.0100 0.0053 0.0083 0.0129 0.0088 0.0114� 1.34 1.37* 1.57 1.37 1.38 1.58 1. 57 1.58

AADT Coef. 0.68 0.513* 0.53 0.55 0.46 0.44 0.50 0.43� 0.13 0.14* 0.16 0.14 0.14 0.16 0.16 0.16

#lanes Coef. – 0.14* – – 0.12 .132 – 0.12� – 0.05* – – 0.05 .052 – 0.05

mconf Coef. – – 0.33a – – 0.20a 0.16a 0.10a

� – – 0.21 – – 0.22 0.23 0.24

#app Coef. – – – 0.26 0.17a – 0.22a 0.15a

� – – – 0.11 0.12 – 0.13 0.13

−2l −520 −516* −519 −518 −515 −516 −518 −515* 10

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AIC 1045 1038 1044

a Coefficients not significant ( = 0.05).* selected model.

ample mean and the relative small sample size (101 intersections)ontributed significantly to the problems observed for the injurynd fatal crashes model.

The cure plots (solid line) with ±2�d confidence intervalsdashed lines) for signalized models for Fortaleza and Belo Hori-onte (Fig. 2) indicated a reasonable performance over the entirexposure value range. The results for Belo Horizonte suggest thathere is a reasonably good fit until the total AADT of approximately0k vehicles per day, although the cumulative residuals tend to beegative. Beyond this AADT level, the model estimate strength iseduced given the relatively small number of observations in thisange.

The developed models for signalized intersections for Belo Hori-onte and Fortaleza pointed out very similar coefficients, whichay indicate that a modeling procedure could be tested aggre-

ating data of the two localities, despite the differences in theata collection systems and consequently differences in accidentatabases (damage property only accidents are not considered inelo Horizonte database).

For the unsignalized intersections in Fortaleza, the resultsTable 5) indicated that the number of lanes and central medianonfiguration were not significant in models 3 and 4. Model

(total number of crashes and AADT) was chosen basically

42 1038 1040 1043 1040

because of its simplicity and the smaller AIC, can be expressed asfollows:

YT = 0.049(AADT0.46) (6)

where YT, total number of crashes in 2007.The cure plot for the unsignalized models for Fortaleza (Fig. 3)

also indicated a reasonable performance over the entire exposurevalue range.

4.4. SPM for Brasília

SPM for Brasília were not calibrated using ordinary generalizedlinear models because of the reduced sample size (32 observations)and the number of years of available crash data (2005–2010). Thistype of data can be analyzed as a longitudinal study where timedependency should not be ignored. Therefore, models for Brasíliawere calibrated applying the Generalized Estimating Equations(GEE) procedure based on the work by Liang and Zeger (1986) andWang and Abdel-Aty (2006).

Three possible working correlation structures among the annualdata for each location were considered: independent, exchange-able and autoregressive. Negative binomial distributions for theestimative errors were assumed because the high dispersion on

264 H. Barbosa et al. / Accident Analysis and Prevention 70 (2014) 258–266

Fig. 2. Cure plots for signalized intersections

Table 5Calibrated models for total number of crashes – unsignalized intersections –Fortaleza.

Variable Models

1 2 3 4

˛ ln(˛) −3.02* −2.66 −3.00 −2.91Coef. 0.049* 0.070 0.050 0.055�ˇ

b 1.28* 1.34 1.29 1.59

AADTtotal Coef. 0.46* 0.46 0.46 0.46�ˇ 0.13* 0.13 0.13 0.13

#lanes Coef. – −0.09 – −0.02a

�ˇ – 0.10 – 0.22

mconf Coef. – – −0.33a −0.25a

�ˇ – – 0.34 0.73

� 1.55* 1.57 1.57 1.582L −656.85* −656.09 −650.10 −650.09�2

p.critico;0.05158 157* 157 155

�2p 59* 62 61 58

Sp 149* 149 150 149AIC 657* 658 658 660�d 1.15* 1.16 1.16 1.16

–: variable not used in the model.

taw

a

a Coefficients statistically NOT significant ( = 0.05).b Standard-error.* selected model.

he available crash data (many zero-observations). Other relevantspects considered for all estimated expressions can be found else-

here (Claude, 2012).

Based on the literature review, especially on the work of Lordnd Park (2008), five alternative model functions were investigated,

-150

-100

-50

0

50

100

150

Cum

ulat

ive

Res

idua

ls

AADT (x1000) 50 40 30 20 10

Fig. 3. Cure plot for unsignalized intersections – Fortaleza (2009).

– Fortaleza and Belo Horizonte (2009).

which are initially only based on exposure measures. They are pre-sented in Eqs. (7)–(11):

Model1 : ln �it = ˇ0 + ˇ1 ln(F1it + F2it) (7)

Model2 : ln �it = ˇ0 + ˇ1 ln(F1it + ˇ2 ln F2it) (8)

Model3 : ln �it = ˇ0 + ˇ1 ln(F1it × F2it) (9)

Model4 : ln �it = ˇ0 + ˇ1 ln(F1it + F2it)

+ ˇ2 ln(

F2it

F1it

)(10)

Model5 : ln �it = ˇ0 + ˇ1 ln F1it + ˇ2 ln F2it

+ ˇ3 ln(F1it × F2it) (11)

where ˇ0, ˇ1, ˇ2, and ˇ3 – parameters to be calibrated; �it –expected number of crashes for intersection i in time period t; F1itand F2it – AADT at intersection i in time period t for the approachesof road 1 (arterial) and 2 (minor road), respectively.

Models were evaluated by the following statistical tests: thecumulative residual test (CURE); the Akaike’s information criterion(AIC) in the GEE, which is called the quasi-likelihood informationcriterion (QIC), and the R2 statistic calculated based on standard-ized residuals. This evaluation for the models with only exposurevariables indicated that Models 1–3 are the most acceptable for fur-ther developments. Their parameters are statistically significant for

= 5%, and they revealed exchangeable work correlation among thedata and their CURE plots oscillate around zero and, for Model 3,inside the limits (±2�d) defined by the procedure. The R2 for Mod-els 2 and 3 (0.17 and 0.22, respectively) are significantly higher thanfor Model 1 (0.06).

These models were then further developed to test the inclusionof three other explanatory variables: traffic control (TC = 1, in caseof signalized intersections; TC = 0, otherwise), red light surveillancecamera (EF = 1, with camera; EF = 0, without camera), and numberof traffic lanes of the arterial road (NL), presenting minimum valueof 2 and maximum value of 5. Only the variable EF presented associ-ated regression coefficients that were significant when attached tothe original Models 2 and 3, which will further referred to as Models6 and 7, respectively. Both models are statistically acceptable basedon the statistical tests performed, and their R2 is similar (0.18 forModel 6 and 0.19 for Model 7). However, for Models 6 and 7, the

CURE plots were not inside the ±2�d limits for the whole range ofconsidered traffic volumes. Therefore, with caution, both of themcan be used and their final expressions are given in Eqs. (12) and(13). Compared with the models without the variable EF, it is clear

H. Barbosa et al. / Accident Analysis and Prevention 70 (2014) 258–266 265

and B

ts

M

M

M

tqfrt2

5

eiltcl

HttbfdSwpo

lrcoBbztt

oucaft

Fig. 4. Predicted × observed crashes using Fortaleza (a)

hat Model 3 presents the highest R2 value. Its final expression ishown in Eq. (14).

odel6 : �it=−10.0421 × F10.6160it × F20.5519

it × e−0.6001×EF (12)

odel7 : �it=−9.7609 × (F1it × F2it)0.5725 × e−0.6096×EF (13)

odel3 : �it=−7.8724 × (F1it × F2it)0.4583 (14)

Because of the small size of the considered intersection sample,he above models must be used with caution for predicting the fre-uency of crashes for intersections located in Brasília. However, theact that in both Models 6 and 7 the presence of red light cameraeduces this frequency gives an important indication of the poten-ial effect of this equipment on promoting traffic safety (Claude,012).

. Transferability analysis

The development of SPM has proven to be highly demanding infforts to obtain data on quantity and quality adequate for model-ng. Furthermore, developing and analyzing the model itself canimit the development of SPM in many jurisdictions. Thereforeransferring models developed in other jurisdictions may be a lessostly alternative, than the development of specific models for eachocation.

The SPM for signalized intersections from Fortaleza and Beloorizonte have been investigated in terms of their transferability

o the city of Porto Alegre. The models were adjusted followinghe Highway Safety Manual (HSM) calibration procedure which isased on the estimation of a Cx for different facility types. The trans-erability exercise also explored the effects of recalibrating the NBispersion parameter k based on the same procedure referred inawalha and Sayed (2006). Goodness of fit of the calibrated modelsere investigated using the z-score metrics (Vogt and Bared, 1998),redicted-versus-observed crashes and CURE plots. Further detailsf this procedure can be found in Cunto et al. (2013).

The calibration coefficients (Cx) for Porto Alegre using Forta-eza and Belo Horizonte SPM were found to be of 0.65 and 2.06espectively. A visual analysis of the predicted-versus-observedrashes plot shown in Fig. 4 suggests a greater dispersion betweenbserved and predicted values for both recalibrated Fortaleza andelo Horizonte SPM for entities with more than 15 acc./year. It cane observed that SPM calibrated for Porto Belo using Belo Hori-onte SPM (Fig. 4b) overestimates crashes for entities in the “lesshan 15 acc./yr” region and underestimates crashes for entities inhe “more than 15 acc./yr region”.

Based on these preliminary results, it is believed that the transferf SPM across different jurisdictions is an alternative that should besed parsimoniously. It is desirable to make efforts to develop spe-

ific models for each jurisdiction. Although the Cx has the purpose ofdjusting the differences in characteristics between cities/regionsor which the model was developed and calibrated, one is limitedo explain the accident rate based on the variablesadopted in the

elo Horizonte (b) SPM calibrated for Porto Alegre city.

original model. Thus, it is not possible to test new explanatory vari-ables that could be more efficient in predicting the accidents ofthese new jurisdictions.

6. Concluding remarks

This paper presented the initial joint effort for developing SPMfor urban intersections of three Brazilian cities. The SPM weredeveloped for signalized and unsignalized intersections in For-taleza, for signalized and unsignalized intersections (grouped) inBrasília and for signalized intersections in Belo Horizonte. Themethodology for calibrating SPM was divided into the followingsteps: defining the safety study objective, choosing predictive vari-ables and sample size, data acquisition, defining model expressionand model parameters and model evaluation.

This exercise has identified the most significant independentvariables to be used for calibrating SPM for Brazilian cities. Ini-tially, the exposure variable AADT for total entering flow (Fortalezaand Belo Horizonte) and AADT for minor and major flow (Brasília)were used as the base model. Other variables considered, numberof lanes, number of approaches and central median configuration,were then included in the SPM expression.

Although, for Fortaleza and Belo Horizonte jurisdictions, all vari-ables coefficients were found to be significant, an analysis of thecorrelation matrix and parameters coefficients pointed out to animportant correlation among most of the variables. Due to the rel-atively low correlation between AADT and number of lanes (0.56) aswell as improvements on Pearson �2

p statistic, the scaled devianceSp and the Akaike Information Criterion (AIC) as compared to thebase model (with AADT only), the expression with the variablesAADT and #lanes was indicated for Fortaleza and Belo Horizontejurisdictions.

In Brasília, 32 signalized and unsignalized intersections usedwere grouped and, therefore, a variable, the type of control, hasbeen added. In addition, two more variables used were red lightsurveillance camera and number of lanes. Due to the low sam-ple size and possible longitudinal correlation, SPM were developedusing Generalized Estimating Equations (GEE). The Brasilia modelsindicated that enforcement with red light cameras could make adifference in the number of accidents.

This paper also evaluated SPM transferability to other jurisdic-tion. The SPM for signalized intersections from Fortaleza and BeloHorizonte have been recalibrated (in terms of the Cx) to the cityof Porto Alegre. The models were adjusted following the HighwaySafety Manual (HSM) calibration procedure and yielded Cx of 0.65and 2.06 for Fortaleza and Belo Horizonte SPM respectively. Despitethe reasonable fit for the recalibrated models it is desirable to makeefforts to develop specific models for each jurisdiction.

Among the key challenges to enhance the development of SPMthere is a need for an integrated accident and traffic flow databaseand the need for a reliable and precise spatial crash location sys-tem. The study also has implications for establishing standards for

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66 H. Barbosa et al. / Accident Analy

xisting and proposed organizational accident database systemshat can easily be used to feed models used for road safety assess-

ent. This paper showed the experience and future challengesoward the initiatives on development of SPM in Brazil that canerve as a guide for other countries that are in the same stage inhis subject.

cknowledgment

The authors would like to acknowledge the Brazilian Council forcientific and Technological Development (CNPq) for supportinghis research.

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