Pedestrian at-fault crashes on rural and urban roadways in Alabama

Accident Analysis and Prevention 72 (2014) 267–276

Contents lists available at ScienceDirect

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

Pedestrian at-fault crashes on rural and urban roadways in Alabama Samantha Islam a,∗ , Steven L. Jones b a b

Department of Civil Engineering, University of South Alabama, 150 Jaguar Drive, Shelby Hall, Suite 3142, Mobile, AL 36688, United States Department of Civil, Construction & Environmental Engineering, University of Alabama, Room 213C Shelby Hall, Tuscaloosa, AL 35487, United States

a r t i c l e

i n f o

Article history: Received 22 February 2014 Received in revised form 2 June 2014 Accepted 3 July 2014 Keywords: Pedestrian at-fault crashes Logit models Random parameters Rural Urban

a b s t r a c t The research described in this paper explored the factors contributing to the injury severity resulting from pedestrian at-fault crashes in rural and urban locations in Alabama incorporating the effects of randomness across the observations. Given the occurrence of a crash, random parameter logit models of injury severity (with possible outcomes of major, minor, and possible or no injury) for rural and urban locations were estimated. The estimated models identified statistically significant factors influencing the pedestrian injury severities. The results clearly indicated that there are differences between the influences of a variety of variables on the injury severities resulting from urban versus rural pedestrian at-fault accidents. The results showed that some variables were significant only in one location (urban or rural) but not in the other location. Also, estimation findings showed that several parameters could be modeled as random parameters indicating their varying influences on the injury severity. Based on the results obtained, this paper discusses the effects of different variables on pedestrian injury severities and their possible explanations. From planning and policy perspective, the results of this study justify the need for location specific pedestrian safety research and location specific carefully tailored pedestrian safety campaigns. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Walking is the most fundamental form of transportation. It provides basic connectivity between origins and destinations as well as other transportation modes. As part of a balanced, multimodal transportation system, walking can help in reducing congestion and building sustainable communities. Walking is often promoted for its potential public health benefits derived from physical activity. Walking is also associated with negative public health outcomes associated with pedestrian–vehicle crashes. There were more than 76,000 fatal pedestrian crashes in the U.S. over the last fifteen years (Ernst and Shoup, 2009). Pedestrian fatalities in the U.S. rose 4% from 2009 to 2010 resulting in 4280 pedestrian deaths. Another 70,000 were injured in 2010 (NHTSA, 2012). In the past, researchers have explored the effects of a variety of factors, such as pedestrian and driver characteristics, road infrastructure and roadway characteristics, traffic characteristics, land use and temporal characteristics on the occurrence and severity of crashes involving pedestrians (Abdel-Aty, 2003; Lee and Abdel-Aty, 2005; Sze and Wong, 2007; Eluru et al., 2008; Moudon et al., 2011; Aziz et al., 2013; J.-K. Kim et al., 2008; Kim et al., 2010; K. Kim et al.,

∗ Corresponding author. Tel.: +1 251 460 6955; fax: +1 251 461 1400. E-mail address: [email protected] (S. Islam). http://dx.doi.org/10.1016/j.aap.2014.07.003 0001-4575/© 2014 Elsevier Ltd. All rights reserved.

2008; Ulfarsson et al., 2010). Few of the previous studies, however, focused specifically on crashes at which the pedestrian was deemed to be “at-fault”. Among the few previous studies of pedestrian at-fault crashes, K. Kim et al. (2008) developed several logistic regression models to explore the effects of age, gender and other factors on injury and fault for pedestrian related crashes in Hawaii. Whereas, Ulfarsson et al. (2010) estimated multinomial logit models to predict the probability of pedestrian, driver or both being at fault in pedestrian-related crashes in North Carolina. Cinnamon et al. (2011) indicated that fault can be attributed to the motorist, or the pedestrian, or both, and the distribution of fault among the parties involved in the crashes varies with local culture of safety and enforcement practices. In Alabama, pedestrians were recorded as at-fault in approximately 42% of the total pedestrian related crashes from 2006 to 2010 and fatality rates at rural locations were more than twice the rates at urban locations (CAPS, 2012). Therefore, greater understanding of the location specific factors associated with pedestrian at-fault crashes is required to develop effective safety countermeasures and safety campaigns. Another important issue related to injury severity analyses is that majority of the severity models from previous research are based on the restrictive assumption that the effect of various factors is equally-distributed across all observations. Few studies have considered the randomness or variability across observations while analyzing injury severity resulting from pedestrian

268

S. Islam, S.L. Jones / Accident Analysis and Prevention 72 (2014) 267–276

Table 1 Examples of previous studies analyzing crash-injury severities. Methodological approach

Previous studies

Multinomial logit

Carson and Mannering (2001), Ulfarsson and Mannering (2004), Khorashadi et al. (2005), Islam and Mannering (2006), Malyshkina and Mannering (2009) and Malyshkina and Mannering (2010) Milton et al. (2008), Anastasopoulos and Mannering (2011), Morgan and Mannering (2011), Haleem and Gan (2013) Shankar et al. (1996), Chang and Mannering (1999), Lee and Mannering (2002), Holdridge et al. (2005), Savolainen and Mannering (2007), Haleem and Abdel-Aty (2010) and Hu and Donnell (2011) Duncan et al. (1998), Khattak (2001), Khattak et al. (2002), Kockelman and Kweon (2002), Abdel-Aty (2003), Kweon and Kockelman (2003), Quddus et al. (2002), Lee and Abdel-Aty (2005), Clifton et al. (2009) and Kaplan and Prato (2012) Yamamoto and Shankar (2004)

Random parameters (mixed) logit Nested logit

Ordered probit

Bivariate ordered probit Heteroskedastic ordered logit Bayesian ordered probit Binomial logit Logistic regression

Wang and Kockelman (2005) Xie et al. (2009) Obeng (2007) Hill and Boyle (2006)

crashes. The consideration of such randomness has special significance for pedestrian safety, because the effect of randomness is likely more pronounced for vulnerable road users such as pedestrians (J.-K. Kim et al., 2008; K. Kim et al., 2008; Kim et al., 2010). In order to address the issue of variability, Kim et al. (2010) estimated a heteroskedastic logit model to analyze pedestrian injury severity for pedestrian-related crashes in North Carolina. They presented statistical evidence that the variance of unobserved pedestrian characteristics (physical and mental ability to react to circumstances) was not fixed across observations. Aziz et al. (2013) addressed the effect of randomness by estimating separate random parameter logit models for different locations in order to capture underlying factors affecting pedestrian crash severity. However, none of the previous studies have addressed the issue of randomness in the context of location-specific (urban and rural) injury severity analyses for pedestrian-related crashes. In this paper, we estimate random parameter logit models to explicitly examine the factors influencing the severity of pedestrian at-fault crashes in urban and rural locations in Alabama. 2. Methodology Previous researchers have used various approaches, particularly probit and logit model formulations, to explore crash risk factors and severity outcomes. Table 1 provides examples of past crash severity studies classified into groups of similar methodological approach employed. For a complete review of crash injury severity models and methodological approaches, please see Savolainen et al. (2011). The current research employed a mixed-logit model approach to capture the randomness associated with some parameters necessary to understand injury severities attributable to pedestrian at-fault crashes. This study used three injury-severity categories: possible/no injury, minor injury, and major injury (more discussions on the selection of these three categories are provided later in this paper). Given that three discrete outcomes were possible, an appropriate statistical modeling approach would be to use an ordered discrete probability model. This modeling approach would explicitly recognize the increasing severity of the three categories in the model estimation (from possible/no injury to major injury). Previously, researchers have applied this type of approach

Table 2 Equations used in mixed logit model formulation. Equation

Description Sin

Sin = ˇi Xin + εin

Xin

ˇi εin ˇ x Pn (i) = e i inˇ x

∀I



e i in

Pn (i|) =

eˇi xinˇ x ∀I

e i in

= severity function for category i in crash n = explanatory variables of pedestrian-injury severity category i in crash n = a vector of estimable parameters for pedestrian-injury severity category i = error term

Pn (i)

= probability of the ith outcome for the nth observation in a standard multinomial logit model (Washington et al., 2011) when error term is assumed to be generalized extreme value distributed (McFadden, 1981)

Pn (i|)

= probability in mixed logit injury severity analyses, i.e., probability of injury severity i conditional on f(ˇi |) = vector of parameters with known density function (McFadden and Train, 2000; Train, 2003)

f (ˇi |)dˇi 

to accident severity models (Kockelman and Kweon, 2002; AbdelAty, 2003). However, a major limitation of the traditional ordered models is that they can restrict the influence of explanatory variables on severity outcomes (Khorashadi et al., 2005; Kim et al., 2013; Yasmin and Eluru, 2013). These models restrict variables to either increase the highest severity category and decrease the lowest, or increase the lowest severity category and decrease the highest. For a complete discussion on the limitations of traditional ordered models, please see Washington et al. (2011). Although it is possible to use random parameter ordered models, the aforementioned limitation still exist (J.-K. Kim et al., 2013). Therefore, the traditional ordered models may not always be appropriate for accident severity data. As a result, this study used the more common unordered discrete outcome model approach. The current study followed the mixed logit model approach reported by Milton et al. (2008), Washington et al. (2011) and Morgan and Mannering (2011). Details of the mixed logit model formulation are summarized in Table 2. The mixed logit model is a generalization of the multinomial logit model, which allows the parameter vector ˇi to vary across each observation. In the mixed logit model, the injury outcome-specific constant and each element of the parameter vector ˇi can be either fixed or randomly distributed with fixed means. Accordingly, to allow for heterogeneity, random parameters are introduced with f (ˇi |), where  is a vector of parameters with chosen density function. As described by Train (2003), statistically significant variance in  indicates that injury severity will vary across observations with respect to X as defined by f (ˇi |). In this study, the mixed logit models were estimated using a simulation-based maximum likelihood method. Econometric and statistical software NLOGIT 4.0 was used for model estimation. The simulation points were sampled using Halton draws (Halton, 1960; Bhat, 2003; Train, 2003). Bhat (2003) and Hensher et al. (1999) demonstrated that Halton draws of a specific number produce results as accurate as ten times that number in pure random draws. The final results in the present study are based on 200 Halton draws, which have been found capable of producing accurate parameter estimates (Bhat, 2003; Milton et al., 2008, Gkritza and Mannering, 2008). To determine if a variable could be modeled as a random parameter and then the distribution of that random parameter, a stepwise iterative process was followed. Each variable was tested in the model as either fixed or random. Statistical testing of the

S. Islam, S.L. Jones / Accident Analysis and Prevention 72 (2014) 267–276

improvement in likelihood was used to determine the best fit. The process continued until the model was stable to changes. As a part of this study, several distributional forms (normal, lognormal, Weibull, etc.) were tested as potential distribution for model parameters. The normal distribution was found to provide the best estimation results. This finding is consistent with past research (Milton et al., 2008; Gkritza and Mannering, 2008), which found that the normal distribution generally establishes the best fit for injury severity data. In order to ensure that separate models were warranted for urban and rural conditions, likelihood ratio tests were performed as described by Washington et al. (2011). These tests indicated that separate urban and rural models were justified at a 95% confidence level. Beyond inspection of the mixed logit model, the concept of direct pseudo-elasticity (Washington et al., 2011) is often used to assess the impact of indicator variables (variables taking on values of 0 or 1) on crash severity predictions. The direct pseudo-elasticity of a variable with respect to a severity category represents the percent change in the probability of that injury category when the variable is changed from 0 to 1. The direct pseudo-elasticity of the kth independent variable xnk with respect to the probability Pni of individual n experiencing injury severity outcome i is computed as: EXPni = nk

Pni [given Xnk = 1] − Pni [given Xnk = 0] Pni [given Xnk = 0]

(1)

The direct pseudo-elasticity is calculated first for each individual observation. The average over the whole sample is computed then and reported as the average direct pseudo-elasticity. The interpretation of average direct pseudo-elasticity values is very simple; for example a 0.25 average direct pseudo-elasticity of a variable on a probability indicates that the probability increases by 25% on average when the variable is changed from 0 to 1. The current study employed average direct pseudo-elasticity values to complete the interpretation of the effects of various parameters on pedestrian injury severity. 3. Data and empirical setting In Alabama, crashes are reported and injury severities are categorized according to the KABCO injury scale: K = fatal injury, A = incapacitating injury, B = non-incapacitating injury, C = possible injury, and O = property damage only (PDO). Any injury that results in death within 30 days of occurrence is classified as a fatal injury. Incapacitating injury is defined as any injury other than a fatal injury, which prevents the injured person from walking, driving, or normally continuing the activities the person was capable of performing before being injured. Non-incapacitating injury is classified as any injury, other than a fatal injury or an incapacitating injury, which is evident to observers at the scene of the crash in which the injury had occurred. Possible or no injury is recorded as the injury category if the reported crash does not result in a fatal, incapacitating or non-incapacitating injury. One of the limitations of the dataset used in this study was that relatively small number of pedestrian at-fault accidents was available in several KABCO injury categories. As a result, the KABCO injury codes presented in the dataset were collapsed into three categories: major injury (KA), minor injury (B) and possible/no injury (CO). To overcome similar limitation, other researchers in the past (Milton et al., 2008; Chen and Chen, 2011) used three injury categories in accident severity analyses. If a crash involved more than one pedestrian, injury level was determined from the most severely injured person in the crash. Incorporating multiple injuries from the same crash greatly complicates the modeling structure. To avoid this, it is common in crash related injury severity studies to model the injury severity of the most severely injured individual in a crash (Mannering and Bhat,

269

2014). In this study, we followed similar approach. However, in this study, there were very few crashes that involved more than one pedestrian. In this study, the raw pedestrian at-fault crash data from 2006 to 2010 were filtered from the original police reported crash database using the Critical Analysis Reporting Environment (CARE) software system developed by the University of Alabama Center for Advanced Public Safety. There were a total of 1463 observations for urban and rural pedestrian at-fault accidents. In the Alabama accident database, accidents occurring in areas with populations of 5000 or more are classified as urban, with all other accidents classified as rural. Tables 3 and 4 show descriptive statistics of the urban and rural crash data, respectively.

4. Results Separate mixed logit models were estimated for analyzing injury severity of pedestrians resulting from pedestrian at-fault crashes in urban and rural locations. Models were conditional on a crash having occurred. As discussed earlier in Section 3 of this paper, three injury severity outcomes were considered in these models: major injury (included fatal and incapacitating injuries), minor injury (non-incapacitating injuries) and possible/no injury (included no visible injuries, no injuries and property damage only crashes). During model estimation, variables were included in the specification if they had t-statistics corresponding to the 90% confidence interval or above on a two-tailed t-test. However, the random parameters were included if their standard deviations had t-statistics corresponding to the 90% confidence interval or above. Detailed model estimation results for pedestrian at-fault crashes for urban and rural locations are presented in Tables 5 and 6 respectively. A wide variety of factors were found to affect the injury severity outcomes of pedestrian at-fault crashes. The effects of the variables on injury severity probabilities were also found to vary as measured by the magnitude of elasticities (Tables 7 and 8). Tables 5 and 6 show that the rural and urban mixed logit models have McFadden pseudo-2 values 0.30 and 0.51 respectively. Here the 2 ratios measure the improvements over the intercept models (models without variables, i.e., with constants only) by the full models in terms of their log-likelihood values. A value of 2 larger than 0.1 indicates meaningful improvement (Ulfarsson et al., 2010). Therefore, the McFadden pseudo-2 values in Tables 5 and 6 indicate good overall improvements in model goodness-of-fit. From a methodological point of view and application of the mixed logit model, a total of four parameter estimates were found to be statistically significant as random parameters for the two estimated models. The normal distribution provided the best statistical fit for all random parameters among variety of distributions (normal, lognormal, Weibull, etc.) tested. All of the random parameters in the severity models were found to be significantly different from zero (with more than 90% confidence). The effects of the rest of the factors were fixed across the populations for both urban and rural pedestrian at-fault crashes. In the rural model (Table 6), the parameter for clear weather (specific to minor injury) was found to be random. The normally distribution provided the best fit with a mean (−) 21.82 and standard deviation of 21.07. With these values, the normal distribution curve indicates that for 84.98% of the sample crashes occurring in clear weather, the probability of minor injuries is lower and for the rest of the sample the probability of minor injuries is higher. The commercial land use parameter in the estimated model for urban locations (specific to minor injury) was found to be random (normal distribution provided the best fit). With a mean (−) 1.51 and standard deviation of 2.35, the normal curve indicates that for 73.97% of the sample the presence of commercial land use

270

S. Islam, S.L. Jones / Accident Analysis and Prevention 72 (2014) 267–276

Table 3 Descriptive statistics – urban. Variable

Major injury

751 Total Demographic variables Age 122 <16 years old 626 ≥16 years old Gender 490 Male 261 Female Weather and temporal variables Time 57 6 am–9:59 am 115 10 am–2:59 pm 179 3 pm–5:59 pm 199 6 pm–8:59 pm 201 9 pm–5:59 am Weather conditions 512 Clear 166 Cloudy 6 Fog/smog/smoke 66 Rain Land use variables 297 Residential area 361 Commercial area 20 School area 16 Manufacturing area Open country area 43 Pedestrian behavior variables Pedestrian crossing street 429 Walking along roadway 101 Working in roadway 89 Other 132 Intersection, control and lighting variables Intersection and control conditions No traffic control 744 Traffic signal 5 2 Traffic sign 0 Human control Lighting conditions Daylight 323 Dawn or dusk 36 161 Dark-lighted Dark-unlighted 227 Roadway variables Freeway 27 US route 115 148 State route County road 16 439 Local street 4 Private property 2 Other

Minor injury

Possible/no injury

Total

67.3%

200

17.9%

165

14.8%

1116

55.5% 69.9%

61 139

27.7% 15.5%

34 131

15.5% 14.6%

220 896

65.7% 70.5%

141 59

18.9% 15.9%

115 50

15.4% 13.5%

746 370

57.0% 61.2% 62.2% 68.4% 80.7%

21 38 60 57 24

21.0% 20.2% 20.8% 19.6% 9.6%

22 35 49 35 24

22.0% 18.6% 17.0% 12.0% 9.6%

100 188 288 291 249

66.4% 67.5% 85.7% 73.3%

143 43 0 14

18.5% 17.5% 0.0% 15.6%

116 37 1 10

15.0% 15.0% 14.3% 11.1%

771 246 7 90

62.7% 71.8% 48.8% 84.2% 75.4%

105 71 10 1 9

22.2% 14.1% 24.4% 5.3% 15.8%

72 71 11 2 5

15.2% 14.1% 26.8% 10.5% 8.8%

474 503 41 19 57

68.0% 71.6% 69.0% 61.4%

111 21 20 48

17.6% 14.9% 15.5% 22.3%

91 19 20 35

14.4% 13.5% 15.5% 16.3%

631 141 129 215

68.2% 31.3% 22.2% 0.0%

192 5 3 0

17.6% 31.3% 33.3% 0.0%

155 6 4 0

14.2% 37.5% 44.4% 0.0%

1091 16 9 0

58.8% 66.7% 73.2% 78.8%

119 12 37 31

21.7% 22.2% 16.8% 10.8%

107 6 22 30

19.5% 11.1% 10.0% 10.4%

549 54 220 288

79.4% 73.2% 74.0% 66.7% 63.9% 33.3% 100.0%

5 18 31 6 137 3 0

14.7% 11.5% 15.5% 25.0% 19.9% 25.0% 0.0%

2 24 21 2 111 5 0

5.9% 15.3% 10.5% 8.3% 16.2% 41.7% 0.0%

34 157 200 24 687 12 2

decreases the probability of minor injuries and for the rest of the sample it increases the probability of minor injuries. In the urban model, accident occurring at intersection was found to be another random parameter (specific to major injury). The normal distribution provided the best fit for this parameter as well with a mean 0.51 and a standard deviation 0.66. Using the normal curve and these values, it can be stated that for 78.02% of the sample, crashes occurring at intersections increase the probability of major injuries and for 21.98% of the sample they decrease the probability of major injuries.

5. Discussion Based on the results obtained from the present study, this section of the paper discusses the effect of different variables on pedestrian injury severities. It should be noted that this study used a relatively small database of pedestrian at-fault accidents available from Alabama. A larger database, possibly from multiple states with similar pedestrian population, could yield additional

significant factors that are unavailable in the present study. For ease of interpretation, the variables with similar attributes are grouped together and the results are discussed for each of them in the following subsections. 5.1. Demographic variables Several age groups were classified in the data: Group 1: 12 years and younger; Group 2: 13–15 years; Group 3: 16–20 years; Group 4: 21–25 years; Group 5: 26–64 years; Group 6: 65 years and older. The parameter estimates for three age groups are found statistically significant. The age group ranging from 26 to 64 is found to increase the probability of major injuries in urban locations. To interpret this result one should keep it in mind that Group 5 (26–64 years) contains a substantially large number of observations compared to the other age groups. This is because no finer segregation could be achieved for this age group based on the original data. Results also show that the age group 12 years and younger increases the probability of minor injuries both in urban and rural locations. The increased likelihood of this group to experience less severe injury

S. Islam, S.L. Jones / Accident Analysis and Prevention 72 (2014) 267–276

271

Table 4 Descriptive statistics – rural. Variable

Major injury

279 Total Demographic variables Age 198 <16 years old 81 ≥16 years old Gender 490 Male 261 Female Weather and temporal variables Time 23 6 am–9:59 am 27 10 am–2:59 pm 46 3 pm–5:59 pm 78 6 pm–8:59 pm 105 9 pm–5:59 am Weather conditions 207 Clear 48 Cloudy 4 Fog/smog/smoke 20 Rain Land use variables 41 Residential area 29 Commercial area 2 School area 2 Manufacturing area Open country area 204 Pedestrian behavior variables Pedestrian crossing street 98 Walking along roadway 79 Working in roadway 52 Other 50 Intersection, control and lighting variables Intersection and control conditions No traffic control 279 Traffic signal 0 0 Traffic sign 0 Human control Lighting conditions Daylight 80 Dawn or dusk 10 135 Dark-lighted Dark-unlighted 53 Roadway variables Freeway 16 US route 58 48 State route County road 156 1 Local street 0 Private property 0 other

Minor injury

Possible/no injury

Total

80.4%

44

12.7%

24

6.9%

347

78.9% 84.4%

33 11

13.1% 11.5%

20 4

8.0% 4.2%

251 96

65.7% 70.5%

141 59

18.9% 15.9%

115 50

15.4% 13.5%

746 370

74.2% 73.0% 83.6% 83.0% 80.8%

6 6 8 9 15

19.4% 16.2% 14.5% 9.6% 11.5%

2 4 1 7 10

6.5% 10.8% 1.8% 7.4% 7.7%

31 37 55 94 130

80.9% 77.4% 100.0% 80.0%

30 11 0 3

11.7% 17.7% 0.0% 12.0%

19 3 0 2

7.4% 4.8% 0.0% 8.0%

256 62 4 25

78.8% 80.6% 100.0% 100.0% 80.3%

7 3 0 0 34

13.5% 8.3% 0.0% 0.0% 13.4%

4 4 0 0 16

7.7% 11.1% 0.0% 0.0% 6.3%

52 36 2 2 254

81.7% 73.1% 81.3% 90.9%

15 18 9 2

12.5% 16.7% 14.1% 3.6%

7 11 3 3

5.8% 10.2% 4.7% 5.5%

120 108 64 55

80.9% 0.0% 0.0% 0.0%

43 0 1 0

12.5% 0.0% 100.0% 0.0%

23 0 0 1

6.7% 0.0% 0.0% 100.0%

345 0 1 1

80.0% 71.4% 86.0% 70.7%

14 3 13 14

14.0% 21.4% 8.3% 18.7%

6 1 9 8

6.0% 7.1% 5.7% 10.7%

100 14 157 75

84.2% 79.5% 80.0% 80.8% 50.0% 0.0% 0.0%

3 8 9 24 0 0 0

15.8% 11.0% 15.0% 12.4% 0.0% 0.0% 0.0%

0 7 3 13 1 0 0

0.0% 9.6% 5.0% 6.7% 50.0% 0.0% 0.0%

19 73 60 193 2 0 0

in an accident can be explained by the fact that young pedestrians are more likely to be struck on roads with low speed limits (e.g., residential streets, school zone, on-street parking, etc.) (Leaf and Preusser, 1999; Dissanayake et al., 2009). Finally, the estimate for the age group ranging from 16 to 20 years demonstrates higher probability of no injury in urban locations. The gender parameter indicating female pedestrians is found to have an increased likelihood of major injuries in urban locations. This may be attributed largely to the greater fragility of females than males due to their physiological differences, in terms of height and weight, as well as differences in resistance of the body to withstand impact (Ulfarsson and Mannering, 2004). 5.2. Weather and temporal variables In rural locations (Table 6), the parameter for clear weather (specific to minor injury) is found to be random in nature. It is intuitive that clear weather would offer better visibility for the drivers to notice the pedestrians, which would lead to reduced

probabilities of more severe injuries for the pedestrians. On the other hand, pedestrian activities are expected to be more prevalent during clear weather, which would lead to increased probabilities of conflict between pedestrians and motor vehicles. This explains the random nature of the clear weather parameter. The model estimated for rural locations also indicated that inclement weather like rain increases the probability of minor injuries. The model estimated for urban locations indicates that pedestrian at-fault crashes occurring during winter and summer seasons have increased probability of major injuries. It is intuitive that pedestrian activities are more prevalent during summer time, which justifies the results. Parameter for winter also indicates an increased probability of no injuries in urban locations. Crashes occurring in daylight are found to have increased probability of minor injuries. This finding is consistent with the results of previous studies (Aziz et al., 2013; K. Kim et al., 2008), which indicated crashes occurring in darkness result in more severe injuries. Results also indicates that there is an increased probability of major injuries during the weekend in urban locations.

272

S. Islam, S.L. Jones / Accident Analysis and Prevention 72 (2014) 267–276

Table 5 Mixed logit severity model estimation results for pedestrian at-fault accidents in urban locations. Variables Defined for major injury Manufacturing or industrial location (1 if true; 0 otherwise) Dark – roadway not lighted (1 if true; 0 otherwise) Weekend (1 if true; 0 otherwise) Female pedestrian (1 if true; 0 otherwise) At intersection (1 if true; 0 otherwise) Standard deviation of at intersection (normal distribution) Pedestrian age 26–64 (1 if true; 0 otherwise) Winter (1 if true; 0 otherwise) Summer (1 if true; 0 otherwise) Defined for minor injury Pedestrian darting (1 if true; 0 otherwise) No traffic control present (1 if true; 0 otherwise) Pedestrian age 0–12 (1 if true; 0 otherwise) 3-lanes (1 if true; 0 otherwise) Shopping or business location Standard deviation of shopping/business location (normal distribution) Defined for possible/no injury Constant Lying or sitting in roadway (1 if true; 0 otherwise) Pedestrian age 16–20 (1 if true; 0 otherwise) Winter (1 if true; 0 otherwise) Daylight (1 if true; 0 otherwise) 2-Lane Roadway (1 if true; 0 otherwise) Model statistics Number of observations Log-likelihood at constants Log-likelihood at convergence McFadden 2

Table 7 Elasticity values from pedestrian injury severity model for urban locations. Variables

Coefficient t-Statistic 1.23

1.59

0.51 0.42 0.44 0.51 0.66

2.17 2.13 2.43 4.16 3.13

0.28 0.78 0.47

1.60 2.25 2.13

0.71 0.70 0.52 2.30 −1.51 2.35

1.62 2.33 1.94 1.96 −1.52 1.77

−0.81 0.81 0.69 1.02 0.57 0.79

−3.80 1.85 2.33 2.81 2.65 2.54 1116 −1276 −896 0.30

Elasticity/pseudo elasticity Major injury

Defined for major injury Manufacturing or industrial location (1 if true; 0 otherwise) Dark – roadway not lighted (1 if true; 0 otherwise) Weekend (1 if true; 0 otherwise) Female pedestrian (1 if true; 0 otherwise) At intersection (1 if true; 0 otherwise) Pedestrian age 24–64 (1 if true; 0 otherwise) Winter (1 if true; 0 otherwise) Summer (1 if true; 0 otherwise) Defined for minor injury Pedestrian darting (1 if true; 0 otherwise) No traffic control present (1 if true; 0 otherwise) Pedestrian age 0–12 (1 if true; 0 otherwise) 3-lane roadway (1 if true; 0 otherwise) Shopping or business location Defined for possible/no injury Lying or sitting in roadway (1 if true; 0 otherwise) Pedestrian age 16–20 (1 if true; 0 otherwise) Winter (1 if true; 0 otherwise) Daylight (1 if true; 0 otherwise) 2-Lane roadway (1 if true; 0 otherwise)

Minor injury

Possible/no injury

0.2%

−1.5%

−1.5%

2.1%

−7.0%

−8.8%

2.6% 3.3%

−6.5% −7.1%

−7.9% −8.6%

14.4%

−26.4%

−22.3%

2.6%

−6.3%

−8.0%

3.2% 2.2%

−6.5% −5.1%

−8.0% −6.2%

−0.6%

1.0%

−0.8%

−1.8%

4.9%

−2.5%

−1.5%

4.0%

−2.4%

−0.6%

0.4%

−0.8%

−1.5%

11.0%

−0.1%

−0.7%

−0.9%

2.0%

−1.3%

−1.7%

4.2%

−2.8% −4.5% −1.5%

−3.7% −5.9% −1.9%

12.8% 20.4% 4.9%

5.3. Land use variables The manufacturing or industrial land use is found to be a significant variable for major injuries in urban locations. Results in Table 5 indicate that, industrial land use is associated with higher

Table 6 Mixed logit severity model estimation results for pedestrian at-fault accidents in rural locations. Variables Defined for major injury Constant Open Country, Lighting condition: dark (1 if true; 0 otherwise) Walking against traffic (1 if true; 0 otherwise) Used safety equipment (1 if true; 0 otherwise) County road (1 if true; 0 otherwise) Defined for minor injury Pedestrian age 0–12 years (1 if true; 0 otherwise) 2-Lane Roadway (1 if true; 0 otherwise) Clear weather (1 if true; 0 otherwise) Standard deviation of clear weather (normal distribution) Open country Raining (1 if true; 0 otherwise) Defined for possible/no injury Constant Standard deviation of constant (normal distribution) Pedestrian not visible, i.e. dark cloth (1 if true; 0 otherwise) Non-intersection (1 if true; 0 otherwise) Model statistics Number of observations Log-likelihood at constants Log-likelihood at convergence McFadden 2

Coefficient

t-Statistic

8.29 1.73

2.41 1.76

−5.05 −3.27 1.75

−2.04 −2.20 1.83

8.35 5.09 −21.82 21.07

2.06 3.19 −1.45 1.66

4.63 2.17

1.59 1.63

−13.24 9.65

−1.28 1.83

10.39

1.76

8.58

1.55 347 −381 −185 0.51

probability of major injuries in urban locations. The commercial land use (shopping/business) variable in the estimated model for urban locations is found have a random parameter (specific to minor injury). The random nature of the commercial land use Table 8 Elasticity values from pedestrian injury severity model for rural locations. Variables

Elasticity/pseudo elasticity Major injury

Defined for severe injury Open Country, Lighting condition: dark (1 if true; 0 otherwise) Walking against traffic (1 if true; 0 otherwise) Used safety equipment (1 if true; 0 otherwise) County road (1 if true; 0 otherwise) Defined for minor injury Pedestrian age 0–12 years (1 if true; 0 otherwise) 2-Lane roadway (1 if true; 0 otherwise) Clear weather (1 if true; 0 otherwise) Open country Raining (1 if true; 0 otherwise) Defined for possible injury (no injury) Pedestrian not visible, i.e. dark cloth (1 if true; 0 otherwise) Non-intersection (1 if true; 0 otherwise)

Minor injury

Possible/no injury

5.7%

−22.7%

−17.6%

−5.1%

8.9%

4.4%

−6.9%

24.1%

13.7%

5.8%

−25.9%

−20.8%

−7.6%

4.6%

−3.4%

−12.9%

16.4%

−3.9%

−2.2%

27.6%

−3.3%

−20.2% −1.9%

90.2% 12.5%

−6.5% −0.4%

−1.5%

−0.7%

3.0%

−12.4%

−6.4%

131.2%

S. Islam, S.L. Jones / Accident Analysis and Prevention 72 (2014) 267–276

273

(shopping/business) parameter can be due to the fact that people in general drive slowly and more carefully in commercial (shopping/business) locations but on the other hand, pedestrian activities (including walking while intoxicated) are more prevalent in these locations which lead to increased probability of pedestrian–vehicle conflicts. In addition, the model for rural location in Table 6 indicates that there are increased probabilities of major and minor injuries if crashes occur in open areas.

However, the results show that in rural areas, two-lane roads have higher probability of minor injuries. Finally, for rural locations, crashes occurring on county roads are found to increase the probability of major injuries. The posted speed limits on county roads are typically higher at rural locations compared to those at urban locations. Therefore, pedestrian–vehicle crashes on rural county roads are more likely to result in more severe injuries as compared to similar crashes in urban locations.

5.4. Pedestrian behavior variables

5.7. Elasticity values and policy implications

For model estimated for urban locations, results in Table 5 show that there is an increased probability of minor injuries if pedestrians cross the streets rapidly and abruptly, or in other words dart across the streets. An increased probability of no injuries is observed for parameter associated with pedestrian sitting or lying on the roadway. According to the model estimated for rural locations (Table 6), there is a reduced probability of major injuries if pedestrians walk against the traffic. Results also indicate that pedestrians using reflective clothing, lights or any such safety equipment have a reduced probability of major injuries in rural areas. Low pedestrian visibility due to pedestrians wearing dark clothes is found to have an increased probability of no injuries in rural areas.

The study also identified important factors that significantly impact injury severity of pedestrians based on the estimated values of average pseudo-elasticity as shown in Tables 7 and 8. The pseudo-elasticity values are useful for alternative safety policy selection, especially in cases not all of the recommended policy can be implemented due to budget constraint (Aziz et al., 2013). Direct pseudo-elasticity values of different significant variables and their policy implications are discussed in the following paragraphs. Based on the average direct pseudo-elasticity values presented in Table 7, the following factors are found to increase the probability of major (severe) and minor injuries of pedestrians in urban areas: crashes occurring at intersections (increase the probability of severe injury by 14.4%), shopping or commercial areas (increase the probability of minor injury by 11.0%), no traffic control present (increases the probability of minor injury by 4.9%), pedestrian being a female (increases the probability of severe injury by 3.3%), winter and summer months (increase the probabilities of severe injury by 3.2% and 2.2% respectively), weekend (increases the probability of severe injury by 2.6%), and pedestrians of age 24–64 years (increase the probability of severe injury by 2.6%). In addition, lying or sitting on the roadway, and pedestrians 16–20 years of age are found to increase the probability of no injuries in pedestrian atfault crashes in urban locations. Therefore, for urban locations, pedestrian–vehicle crashes at intersections should be looked at more carefully to improve pedestrian safety. Priority should be given to reducing pedestrian accidents associated with commercial areas. For urban areas, it might also be appropriate to introduce awareness campaigns that would educate people about hazards of pedestrian crashes during weekends, and during holiday seasons and summer months. Based on the average direct pseudo-elasticity values presented in Table 8, the following factors are found to increase the probability of major and minor injuries of pedestrians in rural areas: county roads (increase the probability of severe injury by 5.8%), open country with dark lighting condition (increases the probability of severe injury by 5.7%), and inclement weather (rain) (increases the probability of minor injury by 12.5%). Important variables that decrease the probabilities of major injuries for pedestrians at rural locations are: pedestrians using safety equipment while walking on the streets (decrease by 6.9%) and pedestrians walking against traffic (decrease by 5.1%). Furthermore, non-intersection related crashes and low pedestrian visibility (due to wearing dark clothes) result in increased probability of no injury crashes. Therefore, roadway and pedestrian access design issues should receive heightened attention in open country locations in rural areas. Stricter speed reinforcements should be in place for rural county roads to improve pedestrian safety. Also, as suggested in the models, campaigns and awareness programs designed for rural areas should emphasize on walking against the traffic and using safety equipment, such as wearing reflective clothing, using lights, etc.

5.5. Intersection and control variables The estimated injury severity model for urban location in Table 5 shows that crash occurring at an intersection is a random parameter (specific to major injury). Various factors, such as posted speed limit, presence of traffic control device, presence of aggressive drivers etc. can affect the injury severity of the pedestrians involved in the crashes differently and hence justify the random nature of the parameter in the estimated model. For example, if an aggressive driver wants to drive through a signalized intersection with a relatively high posted speed limit, probability of major injuries would be high. However, regular drivers typically exert more caution and drive relatively slowly if there is no traffic control present at the intersection. Accordingly, crashes taking place at such an intersection would have reduced probability of major injuries. Table 5 also indicates that in urban locations with no traffic control present, crashes are associated with an increased probability of minor pedestrian injuries. In addition, Table 6 indicates that non-intersection related crashes in rural locations have an increased probability of no injuries. 5.6. Roadway and roadway lighting variables Tables 5 and 6 show several significant variables related to roadway characteristics that affect injury severities of pedestrians involved in pedestrian at-fault crashes in urban and rural locations respectively. Results show that dark roads (defined by light condition indicator) increase the probability of major injuries of pedestrians in both urban and rural locations. This supports the findings by Sullivan and Flannagan (2011), which also indicated higher probability of fatalities associated with dark road conditions. The number of lanes on a roadway is found to be a significant factor that influences the injury severity of pedestrians resulting from pedestrian-motor vehicle crashes. Results indicate that crashes on three-lane roads have greater probability of minor injuries in urban locations. Further, results show that crashes on two-lane roads have higher probability of no-injury in urban areas. These findings are consistent with the results of previous studies (Aziz et al., 2013; Poch and Mannering, 1996), which indicated that crashes occurring on multilane roads have higher probability of severe crashes.

5.8. Summary of results The aforementioned results indicate that there is difference between the influence of a variety of variables on the injury

274

S. Islam, S.L. Jones / Accident Analysis and Prevention 72 (2014) 267–276

Table 9 Model comparisons. Variables

Urban Major

Manufacturing or industrial location Weekend Female pedestrian At intersection Pedestrian age 24–64 Winter Summer Pedestrian darting No traffic control present 3-lane roadway Shopping or business location Lying or sitting in roadway Pedestrian age 16–20 Daylight Walking against traffic Used safety equipment County road Pedestrian age 0–12 years 2-Lane roadway Clear weather Open country Raining Non-intersection Dark – roadway not lighted or Drak Cloth Pedestrian age 0–12 2-Lane roadway

Rural Minor

↑ ↑ ↑ ↑ ↑ ↑ ↑

Possible/no

Major

Minor

Possible/no

↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↓ ↓ ↑ ↑ ↑ ↑ ↑ ↑

↑

↑ ↑

↑ ↑ ↑

↑ ↑

↑ indicates increase in the probability of an injury severity category. ↓ indicates decrease in the probability of an injury severity category.

severities resulting from urban and rural pedestrian at-fault accidents. Details of these differences are presented in Table 9. Some variables are found to be significant only in one location (urban or rural) but not in other location. For example, 14 variables are found significant only in the urban model but not in the rural model. Similarly, 9 variables are found significant only in the rural model. Finally, only 3 variables are found significant in both urban and rural models.

6. Model specification test In the past, researchers used the likelihood-ratio tests to check the suitability of joint models (Ulfarsson and Mannering, 2004; Washington et al., 2011; Aziz et al., 2013). In this study, we used similar test to statistically justify the development of separate models for urban and rural locations. The test statistics, likelihood-ratio (LR), was calculated using the following equations: LR = −2[LL(ˇall ) − LL(ˇurban ) − LL(ˇrural )] where LL(ˇall ), LL(ˇurban ), LL(ˇrural ) are the log-likelihood at convergence of the models estimated with all data, urban data and rural data respectively. The test statistics are 2 distributed with the degrees of freedom equal to the summation of the estimated parameters in all the separate models minus the number of estimated parameters in the corresponding total data model. The result of the likelihood ratio test revealed that the test statistic (LR = 46) is higher than the corresponding 2 value (2 = 39.13) with n degrees of freedom (n = 12) at 99.99% confidence level (p = 0.0001). Therefore, we can reject the null hypotheses that the joint model does not have a log-likelihood value that is significantly different from that of the corresponding separate models and conclude that the specification of separate models is appropriate.

7. Conclusion This research analyzed pedestrian injury severity at a disaggregate level for pedestrian at-fault crashes in Alabama. Separate models for urban and rural locations identified different sets of factors that can lead to effective policy decisions aimed at improving pedestrian safety for respective locations. Several parameters were found to be random in nature indicating their varying influences on the injury severity of the pedestrians resulting from pedestrian at-fault crashes. The results of this study clearly indicated differences between urban and rural pedestrian at fault accidents (Table 9). The study found some variables to be significant only in one location (urban or rural) but not in other location. Only three variables were found to impact pedestrian injury severities regardless of the location of the accident: dark lighting conditions, 2-lane roadways, and pedestrians 12 years of age or younger. These results indicate that there is a need for campaigns focused on making pedestrians more aware of the fact that it is difficult for drivers to see for them in dark lighting conditions. This inference reiterates the recommendations of Ulfarsson et al. (2010) and K. Kim et al. (2008). Also, these results suggest that younger persons (those 12 years of age and younger) should be a top target for safety education and promotional materials as was suggested in Wang and Kockelman (2013). Educational institutions can partner with state and local agencies to make such campaigns more effective. Further, the results demonstrate a need for campaigns more focused on improving pedestrian behavior on 2-lane roadways while walking or crossing the streets irrespective of urban or rural location. The results of this study provide useful insights into the injury severities of pedestrians resulting from pedestrian at-fault crashes in urban and rural locations. However, similar to most past studies, the present study also has some limitations, such as it used a relatively small database from a single state. Future studies of pedestrian at-fault accidents using databases from multiple states

S. Islam, S.L. Jones / Accident Analysis and Prevention 72 (2014) 267–276

could yield additional statistically significant factors that would better explain pedestrian crash risk and severity. The knowledge of location specific pedestrian accident risk and severity differences from such comprehensive studies would help designing effective pedestrian safety policies and pedestrian safety awareness programs addressing the type of accidents pedestrians are more likely to be at fault. Acknowledgements The authors would like to thank the Center for Advanced Public Safety at the University of Alabama for assistance with the CARE software. They would also like to thank Dr. Akhter Hossain of Alabama Department of Transportation for his assistance in model development and statistical analyes. Gratitude is also extended to Dr. Saravanan Gurupackiam and Mr. Daniel Dye for their help in extracting and organizing the crash data. References Abdel-Aty, M., 2003. Analysis of driver injury severity levels at multiple locations using ordered probit models. J. Saf. Res. 34 (5), 597–603. Anastasopoulos, P., Mannering, F., 2011. An empirical assessment of fixed and random parameter logit models using crash- and non-crash-specific injury data. Accid. Anal. Prev. 43 (3), 1140–1147. Aziz, H.M.A., Ukkusuri, S., Hasan, S., 2013. Exploring the determinants of pedestrian–vehicle crash severity in New York City. Accid. Anal. Prev. 50, 1298–1309. Bhat, C., 2003. Simulation estimation of mixed discrete choice models using randomized and scrambled Halton sequences. Transp. Res. B 37 (1), 837–855. Carson, J., Mannering, F., 2001. The effect of ice warning signs on ice-accident frequencies and severities. Accid. Anal. Prev. 33 (1), 99–109. Chang, L.-Y., Mannering, F., 1999. Analysis of injury severity and vehicle occupancy in truck- and non-truck-involved accidents. Accid. Anal. Prev. 31 (5), 579–592. Chen, F., Chen, S., 2011. Injury severity of truck drivers in single- and multi-vehicle accidents on rural highways. Accid. Anal. Prev. 43, 1677–1688. Center for Advanced Public Safety (CAPS), 2012. 2011 Alabama Traffic Crash Facts, Alabama Crash Facts Book. University of Alabama, Tuscaloosa, Alabama. Cinnamon, J., Schuurman, N., Hameed, S.M., 2011. Pedestrian injury and human behaviour: observing road-rule violations at high-incident intersections. PLoS ONE 6 (6), e21063, http://dx.doi.org/10.1371/journal.pone.0021063. Clifton, K., Burnier, C., Akar, G., 2009. Severity of injury resulting from pedestrian–vehicle crashes: what can we learn from examining the built environment? Transp. Res. D: Transp. Environ. 14 (6), 425–436. Dissanayake, D., Aryaija, J., Wedagama, D.M.P., 2009. Modelling the effects of land use and temporal factors on child pedestrian casualties. Accid. Anal. Prev. 41 (2009), 1016–1024. Duncan, C., Khattak, A., Council, F., 1998. Applying the ordered probit model to injury severity in truck-passenger car rear-end collisions. Transp. Res. Rec. 1635, 63–71. Eluru, N., Bhat, C., Hensher, D., 2008. A mixed generalized ordered response model for examining pedestrian and bicyclist injury severity level in traffic crashes. Accid. Anal. Prev. 40 (3), 1033–1054. Ernst, M., Shoup, L., 2009. Dangerous by design: solving the epidemic of preventable pedestrian deaths (and making great neighborhoods). Transportation for America and Surface Transportation Policy Partnership. Gkritza, K., Mannering, F.L., 2008. Mixed logit analysis of safety-belt use in singleand multi-occupant vehicles. Accid. Anal. Prev. 40, 443–451. Haleem, K., Abdel-Aty, M., 2010. Examining traffic crash injury severity at unsignalized intersections. J. Saf. Res. 41 (4), 347–357. Haleem, K., Gan, A., 2013. Effect of driver’s age and side of impact on crash severity along urban freeways: a mixed logit approach. J. Saf. Res. 46 (September), 67–76. Halton, J., 1960. On the efficiency of evaluating certain quasi-random sequences of points in evaluating multi-dimensional integrals’. Numerische Mathematik 2 (1), 84–90. Hensher, D., Louviere, J., Swait, J., 1999. Combining sources of preference data. J. Econom. 89, 197–221. Hill, J., Boyle, L., 2006. Assessing the relative risk of severe injury in automotive crashes for older female occupants. Accid. Anal. Prev. 38 (1), 148–154. Holdridge, J., Shankar, V., Ulfarsson, G., 2005. The crash severity of fixed objects. J. Saf. Res. 36 (2), 139–147. Hu, W., Donnell, E., 2011. Severity models of cross-median and rollover crashes on rural divided highways in Pennsylvania. J. Saf. Res. 42 (5), 375–382. Islam, S., Mannering, F., 2006. Driver aging and its effect on male and female single vehicle accident injuries: some additional evidence. J. Saf. Res. 37 (3), 267–276. Kaplan, S., Prato, C.G., 2012. Risk factors associated with bus accident severity in the United States: a generalized logit model. J. Saf. Res. 46 (September), 67–76. Khattak, A., 2001. Injury severity in multi-vehicle rear-end crashes. Transp. Res. Rec. 1746, 59–68.

275

Khattak, A., Pawlovich, D., Souleyrette, R., Hallmark, S., 2002. Factors related to more severe older driver traffic crash injuries. J. Transp. Eng. 128 (3), 243–249. Khorashadi, A., Niemeier, D., Shankar, V., Mannering, F., 2005. Differences in rural and urban driver-injury severities in accidents involving large trucks: an exploratory analysis. Accid. Anal. Prev. 37 (5), 910–921. Kim, K., Brunner, I.M., Yamashita, E., 2008. Modeling fault among accident-involved pedestrians and motorists in Hawaii. Accid. Anal. Prev. 40 (6), 2043–2049. Kim, J.-K., Ulfarsson, G.F., Shankar, V.N., Mannering, F.L., 2010. A note on modeling pedestrian injury severity in motor-vehicle crashes with the mixed logit model. Accid. Anal. Prev. 42, 1751–1758. Kim, J.-K., Ulfarsson, G.F., Shankar, V.N., Kim, S., 2008. Age and pedestrian injury severity in motor-vehicle crashes: a heteroskedastic logit analysis. Accid. Anal. Prev. 40, 1695–1702. Kim, J.-K., Ulfarsson, G.F., Kim, S., and Shankar, V.N. 2013. Driver-injury severity in single-vehicle crashes in California: A mixed logit analysis of heterogeneity due to age and gender. Accident Analysis & Prevention 50, pp. 1073-1081. Kockelman, K., Kweon, Y.-J., 2002. Driver injury severity: an application of ordered probit models. Accid. Anal. Prev. 34 (4), 313–321. Kweon, Y.-J., Kockelman, K., 2003. Overall injury risk to different drivers: combining exposure, frequency, and severity models. Accid. Anal. Prev. 35 (3), 414–450. Leaf, W.A., Preusser, D.F., 1999. Literature review on vehicle travel speeds and pedestrian injuries among selected racial/ethnic groups. U.S. Department of Transportation National Highway Traffic Safety Administration, Final Report (DOT HS 809 021). Lee, C., Abdel-Aty, M., 2005. Comprehensive analysis of vehicle–pedestrian crashes at intersections in Florida. Accid. Anal. Prev. 37 (4), 775–786. Lee, J., Mannering, F., 2002. Impact of roadside features on the frequency and severity of run-off-roadway accidents: an empirical analysis. Accid. Anal. Prev. 34 (2), 149–161. Malyshkina, N., Mannering, F., 2009. Markov switching multinomial logit model: an application to accident-injury severities. Accid. Anal. Prev. 41 (4), 829–838. Malyshkina, N., Mannering, F., 2010. Empirical assessment of the impact of highway design exceptions on the frequency and severity of vehicle accidents. Accid. Anal. Prev. 42 (1), 131–139. Mannering, F.L., Bhat, C.R., 2014. Analytic methods in accident research: methodological frontier and future directions. Anal. Methods Accid. Res. 1 (2014), 1–22. McFadden, D., 1981. Econometric models of probabilistic choice. In: Manski, D., McFadden (Eds.), A Structural Analysis of Discrete Data with Econometric Applications. The MIT Press, Cambridge, MA. McFadden, D., Train, K., 2000. Mixed MNL models for discrete response. J. Appl. Econom. 15 (5), 447–470. Milton, J., Shankar, V., Mannering, F., 2008. Highway accident severities and the mixed logit model: an exploratory empirical analysis. Accid. Anal. Prev. 40 (1), 260–266. Morgan, A., Mannering, F., 2011. The effects of road-surface conditions, age, and gender on driver-injury severities. Accid. Anal. Prev. 43 (5), 1852–1863. Moudon, A.V., Lin, L., Jiao, J., Hurvitz, P., Reeves, P., 2011. The risk of pedestrian injury and fatality in collisions with motor vehicles, a social ecological study of state routes and city streets in King County, Washington. Accid. Anal. Prev. 43 (1), 11–24. National Highway Traffic Safety Administration (NHTSA), 2012. Traffic Safety Facts 2010. U.S. Department of Transportation, Washington, DC. Obeng, K., 2007. Some determinants of possible injuries in crashes at signalized intersections. J. Saf. Res. 38 (1), 103–112. Poch, M., Mannering, F., 1996. Negative binomial analysis of intersection-accident frequencies. J. Transp. Eng. 122 (2), 105–113. Quddus, M., Noland, B., Chin, H., 2002. An analysis of motorcycle injury and vehicle damage using ordered probit models. J. Saf. Res. 33 (4), 445–462. Savolainen, P., Mannering, F., 2007. Probabilistic models of motorcyclists’ injury severities in single- and multi-vehicle crashes. Accid. Anal. Prev. 39 (5), 955–963. Savolainen, P., Mannering, F., Lord, D., Quddus, M., 2011. The statistical analysis of crash-injury severities: a review and assessment of methodological alternatives. Accid. Anal. Prev. 43 (5), 1666–1676. Shankar, V., Mannering, F., Barfield, W., 1996. Statistical analysis of accident severity on rural freeways. Accid. Anal. Prev. 28 (3), 391–401. Sullivan, J.M., Flannagan, M.J., 2011. Differences in geometry of pedestrian crashes in daylight and darkness. J. Saf. Res. 42 (1), 33–37. Sze, N.N., Wong, S.C., 2007. Diagnostic analysis of the logistic model for pedestrian injury severity in traffic crashes. Accid. Anal. Prev. 39, 1267–1278. Train, K., 2003. Discrete Choice Methods with Simulation. Cambridge University Press, Cambridge, UK. Ulfarsson, G., Mannering, F., 2004. Differences in male and female injury severities in sport-utility vehicle, minivan, pickup and passenger car accidents. Accid. Anal. Prev. 36 (2), 135–147. Ulfarsson, G.F., Kim, S., Booth, K.M., 2010. Analyzing fault in pedestrian–motor vehicle crashes in North Carolina. Accid. Anal. Prev. 42 (6), 1805–1813. Wang, X., Kockelman, K., 2005. Occupant injury severity using a heteroscedastic ordered logit model: distinguishing the effects of vehicle weight and type. Transp. Res. Rec. 1908, 195–204. Wang, Y., Kockelman, K.M., 2013. A conditional-autoregressive count model for pedestrian crashes across neighborhoods. In: Proceedings of the 92nd Transportation Research Board Annual Meeting, Washington, DC, January.

276

S. Islam, S.L. Jones / Accident Analysis and Prevention 72 (2014) 267–276

Washington, S.P., Karlaftis, M.G., Mannering, F.L., 2011. Statistical and Econometric Methods for Transportation Data Analysis, second ed. Chapman &Hall/CRC, Boca Raton, Florida. Yamamoto, T., Shankar, V., 2004. Bivariate ordered-response probit model of driver’s and passenger’s injury severities in collisions with fixed objects. Accid. Anal. Prev. 36 (5), 869–876.

Yasmin, S., Eluru, N., 2013. Evaluating alternate discrete outcome frameworks for modeling crash injury severity. Accid. Anal. Prev. 59 (No. 1), 506–521. Xie, Y., Zhang, Y., Liang, F., 2009. Crash injury severity analysis using Bayesian ordered probit model. J. Transp. Eng. 135 (1), 18–25.