Single-vehicle crashes along rural mountainous highways in Malaysia: An application of random parameters negative binomial model

Accident Analysis and Prevention 102 (2017) 153–164

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Single-vehicle crashes along rural mountainous highways in Malaysia: An application of random parameters negative binomial model Rusdi Rusli a,d,∗ , Md. Mazharul Haque a,b , Mark King a , Wong Shaw Voon c a Queensland University of Technology (QUT), Centre for Accident Research and Road Safety—Queensland (CARRS-Q), 130 Victoria Park Road, Kelvin Grove, QLD 4059, Australia b Queensland University of Technology (QUT), Civil Engineering and Built Environment, Science and Engineering Faculty, 2 George St., S Block, Room 701, Brisbane, QLD 4000, Australia c Malaysian Institute of Road Safety Research (MIROS), Jalan TKS1, Taman Kajang Sentral, 43000 Kajang, Selangor, Malaysia d Politeknik Sultan Mizan Zainal Abidin, Jalan Paka, 23000 Dungun, Terengganu, Malaysia

a r t i c l e

i n f o

Article history: Received 27 October 2016 Received in revised form 5 February 2017 Accepted 2 March 2017 Keywords: Mountainous roads Single-vehicle crashes Random parameters model Vertical gradient Horizontal curve Developing country

a b s t r a c t Mountainous highways generally associate with complex driving environment because of constrained road geometries, limited cross-section elements, inappropriate roadside features, and adverse weather conditions. As a result, single-vehicle (SV) crashes are overrepresented along mountainous roads, particularly in developing countries, but little attention is known about the roadway geometric, traffic and weather factors contributing to these SV crashes. As such, the main objective of the present study is to investigate SV crashes using detailed data obtained from a rigorous site survey and existing databases. The final dataset included a total of 56 variables representing road geometries including horizontal and vertical alignment, traffic characteristics, real-time weather condition, cross-sectional elements, roadside features, and spatial characteristics. To account for structured heterogeneities resulting from multiple observations within a site and other unobserved heterogeneities, the study applied a random parameters negative binomial model. Results suggest that rainfall during the crash is positively associated with SV crashes, but real-time visibility is negatively associated. The presence of a road shoulder, particularly a bitumen shoulder or wider shoulders, along mountainous highways is associated with less SV crashes. While speeding along downgrade slopes increases the likelihood of SV crashes, proper delineation decreases the likelihood. Findings of this study have significant implications for designing safer highways in mountainous areas, particularly in the context of a developing country. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction According to the WHO Global Road Safety Report, about 1.2 million people die and up to 50 million people sustain road traffic injuries on the world’s roads every year (WHO, 2015). Unfortunately, low and middle-income countries account for nearly 90% of these road fatalities and injuries. Malaysia as a middle-income country and with a traffic death rate of 24 per 100,000 inhabitants is the second worst country in Southeast Asia in terms of road safety. To tackle this, Malaysian Government has recently launched a 15 year Road Safety Plan (MOT, 2016). However, existing research to date is not sufficient to inform government agencies and road authorities on the best ways to initiate targeted countermeasures. The scarcity of scientific research is more acute for rural regions

∗ Corresponding author. E-mail addresses: [email protected], [email protected] (R. Rusli). http://dx.doi.org/10.1016/j.aap.2017.03.002 0001-4575/© 2017 Elsevier Ltd. All rights reserved.

of Malaysia than for urban areas. This research aims to investigate single-vehicle (SV) crashes along rural mountainous roads in Malaysia, which is a step towards addressing this significant research gap. Constrained topography and complex road geometries are among major issues in designing and constructing roads in mountainous regions to meet appropriate roadway standards. This problem is worse in the context of resource-constrained developing country. Substandard cross-section elements and dangerous roadside environments coupled with adverse weather conditions in mountainous areas differentiate mountainous roads from those in flatter areas and generally represent a risky road traffic situation. Ma et al. (2015) have reported that steep gradients and sharp curves along mountainous roads induce different driving behavior compared to roads in flatter areas. Recent research (e.g., Rautela and Shikher Pant, 2007; Rusli et al., 2015) reported that the fatality index—the ratio of fatalities to road injuries—is higher for mountainous roads compared to non-mountainous roads in developing

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countries like Malaysia and India. In China, up to 76% of crashes with high number of fatalities (10–30 deaths in the same crash) and serious injuries (50–100 injuries in the same crash) occurred in mountainous areas between 2007 and 2013 (Chen et al., 2016a). Due to their complicated geometry and topographical conditions, crash blackspots are commonly located along mountainous roads (Lin et al., 2013). Despite this elevated crash risk, research examining the effects of road traffic parameters on mountainous road safety is relatively scant. Mountainous highways in western countries (e.g. mountainous section of I-70 freeway in Colorado, USA) also suffer from high crash rates (Yu et al., 2015). Curve segments are generally associated with increased number of road traffic crashes (Yu et al., 2015; Zhang et al., 2010). Road traffic crashes along mountainous highways are reported to increase with the increase in curve deflection angle (Ma et al., 2015), decrease in curve radius (Bauer and Harwood, 2013), and decrease in horizontal curve length (Bauer and Harwood, 2013). Mountainous road segments with a higher degree of curvature, however, are associated with lower crash rates (Ahmed et al., 2012, 2011). Longitudinal grades along mountainous roads also represent a significant crash risk factor (Chen et al., 2011; Yu and Abdel-Aty, 2013) and are reported to increase the crash rate exponentially (Fu et al., 2011). In particular, steep downgrade sections of mountainous roads are associated with elevated crash risks (Ahmed et al., 2012, 2011; Weeratunga and Somers, 2015; Yu and Abdel-Aty, 2013; Yu et al., 2015). In addition to road alignments, cross-section elements and roadside features play a vital role in road safety, but much remains unknown about their effects for mountainous roads. Among the few cross-sectional factors studied, the number of lanes is found to be associated with a lower number crashes, and the presence of a wide median is reported to improve safety (Ahmed et al., 2011; Yu and Abdel-Aty, 2013). The presence of guardrails and better road surface are reported to reduce both fatal and serious injury crashes along a mountainous freeway in Southwest China (Zhou et al., 2005). Speed is one of the most important parameters of road safety and has a direct relationship with crash occurrence. Posted speed limits are often used as a proxy measure of traffic speed along road segments, but the posted speed limit may not be a good indicator, particularly along mountainous roads because traffic speed on these roads may be dominated by roadway geometric characteristics and driver perceptions of comfort and safety (Castro et al., 2012). In fact, Ahmed et al. (2011) reported that crash frequencies along mountainous roads are not significantly associated with posted speed limit. In contrast, Yu and Abdel-Aty (2013) reported that the average speed recorded by downstream detectors is significantly associated with vehicle crashes along mountainous roads. Instead of using posted speed limit or average speed, Ma et al. (2015) used the speed gap—the difference between the posted speed limit and the mean traffic speed—and found that an increase in speed gap leads to a higher crash rate. Weather in mountainous areas plays a vital role in road safety. A recent study on the relationship between real-time weather and crash occurrences along a mountainous freeway in the United States demonstrated that depending on weather conditions, the same traffic parameters along a mountainous road section might influence driver behavior (and this safety) differently (Ahmed et al., 2012). In a subsequent study that examined hazardous factors involved in single- and multi-vehicle crashes along the same freeway (I-70) in the United States, Yu and Abdel-Aty (2013) reconfirmed that the crash occurrence along mountainous roads is highly influenced by weather conditions and suggested adoption of different active management strategies across different seasons. In particular, real-time visibility and precipitation—measured as average visibility or precipitation 30 min before and after the

crash—were reported to increase crash risks along mountainous section of I-70 (Yu et al., 2015). Ma et al. (2015) also reported that poor visibility along mountainous roads increases the crash risk. All of these studies have been conducted in the US, and their findings may not be generally applicable to Malaysia, which is located in the equatorial region and has a tropical rainforest climate. SV crashes are a dominant crash type along mountainous highways. For example, about 58% of crashes on I-70 in Colorado, US were reported to be SV crashes (Yu and Abdel-Aty, 2013). The safety performance function for these SV crashes identified that the SV crashes are associated with vertical gradients, width of the median, number of lanes, and segment length (exposure parameter) (Yu and Abdel-Aty, 2013). In a subsequent study considering real-time weather and traffic data, Yu and Abdel-Aty (2013) reported that real-time weather variables such as average visibility within the segment and precipitation rates and real-time traffic variables such as average speed during 5–10 min prior to the crash are associated with SV crashes along mountainous freeways in the United States. A preliminary research study comparing crashes along mountainous and non-mountainous roads in Sabah state Malaysia showed that the propensity of single-vehicle (SV) crashes is about 2.6 times higher along mountainous roads, and about 97% of ‘out-of-control’ collision types on mountainous roads involve a single vehicle only (Rusli et al., 2015). In light of the above review, there remain significant research gaps where scientific research is warranted. The overall aim of this study is to investigate the effects of roadway geometries, traffic characteristics, real-weather condition, cross-sectional elements, roadside features, and spatial characteristics on SV crashes along rural mountainous roads in the context of a developing country. This is achieved by developing a safety performance function (SPF) for SV crashes along rural mountainous highways. The contribution of this study is third-fold. First, this study addresses an important road safety issue in a developing country—SV crashes along rural mountainous highways. While there has been considerable research on this topic in western countries, only a little is known in the context of a developing country. According to the recent crash statistics, SV crashes represent nearly 65% of road crashes along rural mountainous roads in Malaysia (Rusli et al., 2015). The findings from western countries may not be directly applicable, as there are differences in roadway designs, roadside environment, presence of roadside furniture, traffic mix, enforcement practices, and most importantly driver behavior in developing countries compared to developed countries. Second, road engineers often face challenges in designing and ensuring adequate cross-sectional elements (e.g. shoulder, overtaking lane, etc.) due to constrained road reserves along mountainous roads. A proper understanding of their effects on safety is much needed in this regard. Third, the development of an SPF for SV crashes along rural mountainous highways represents a unique contribution of this study. In addition to common roadway and traffic factors, the SPF of this study includes a wide range of roadway factors including cross-sectional elements, roadside features and spatial characteristics (e.g. adjacent land use factors) mainly representing the context of a developing country. The developed SPF would provide insights into SV crash occurrences along rural mountainous highways in developing countries in general and in Malaysia in particular.

2. Data description The dataset for this study was collected for four highways passing through rural mountainous areas in Sabah, Malaysia, including 1) Kimanis – Keningau highway, 2) Penampang – Tambunan highway, 3) Tamparuli – Ranau highway, and 4) Ranau – Sandakan highway. These highways were mainly two-lane two-way roads

R. Rusli et al. / Accident Analysis and Prevention 102 (2017) 153–164

(approximately 99% of total highway length), and the posted speed limit along these roads was mainly 90 km/h. Topographical information for these highways was obtained from the Digital Terrain Model (DTM) provided by the Department of Survey and Mapping Malaysia. The global information system (GIS) software, ArcGIS was used to overlap road maps with topographical information. Following the geometric design guideline of Malaysia, mountainous highways sections were selected as those located in areas where the average natural ground slope is more than 25% (REAM, 2002). The identified sections were then segmented mainly based on guidelines provided by AASHTO (2011). Three main criteria for segmentation include (1) presence of major intersections, (2) changes in number of lanes, and (3) changes in longitudinal grades of more than 2%. These resulted in about 375 mountainous road segments along the four highways in Sabah. Mountainous highways in Sabah are full of different types (e.g. simple, compound, reverse, brokenback) of horizontal curves with large variations in curve radius. Horizontal alignment was not used as a criterion for segmentation because it may lead to segments with very short lengths. Using a randomly assigned draw number, 102 out of these 375 segments were selected for detailed data collection through field surveys. Five years of road crash data from 2008 to 2012 were obtained from Malaysian Institute of Road Safety Research – Road Accident Analysis and Database System (M-ROADS) (MIROS, 2014). During this period, a total of 715 SV crashes (including injury and property damage only crashes) occurred along the selected segments. To account for monthly variation in traffic volume and ensure the accuracy of real-time weather information, SV crashes on each segment were counted at monthly intervals. This led to a panel dataset of 6120 observations for 102 mountainous highway segments. The most challenging task for conducting scientific research in the context of developing countries is the availability of reliable data. In addition to utilizing existing data sources, an extensive road survey was carried out to collect roadway and traffic data for each segment. Table 1 presents the descriptive statistics of the explanatory variables included in this study. The explanatory variables are broadly categorized into eight categories, including exposure variables, real-time weather condition, traffic characteristics, horizontal alignment, longitudinal grades, cross-sectional elements, roadside features, and spatial characteristics. The two exposure variables used for SV crashes were average traffic volume (ADT) and length of road segment. Traffic volume data was collected from the Road Traffic Volume Malaysia (RTVM) database (HPU, 2013) maintained by the Public Works Department in Sabah and the Highway Planning Unit, Ministry of Works Malaysia. This database includes historical traffic volume data for some predefined census locations along the roads and may not have exact volume data for the selected segments. To circumvent this problem, two-hour vehicle counts were conducted for each segment, and the ADT for each segment was estimated by using hourly expansion factors and seasonal variation factors following the procedure mentioned in Garber and Hoel (2009). Traffic volume data from RTVM was divided into two seasons; January to June (census in March) and July to December (census in September) for each year. In these two seasons, RTVM provided the details of traffic survey for a 16-h period at the selected survey stations. This 16-h census data was then transformed into 24-h data using factors provided by the Public Works Department in Sabah (HPU, 2013). From this 24-h traffic volume, the hourly expansion factors (HEF) for each census station were calculated. Using these seasonal HEFs, the two-hour vehicle counts of each segment were converted to ADT. Hourly rainfall and visibility information for the same five year period were collected from the Department of Irrigation and Drainage, Sabah Malaysia and National Centers for Environmental Information (NOAA). While the rainfall data were available from twelve rainfall stations next to the study location, the

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visibility data were available from only two weather stations. Using proximity measures in AutoCAD – Geolocation, hourly weather information for crashes on each road segment was obtained following the aggregation procedure developed by Yu et al. (2015). In this aggregation procedure, the reported crash times were first matched with weather information recorded at the nearest weather stations. Real-time weather information (e.g. rainfall, visibility at the time of crash) was then converted into a segment level variable following three criteria: exact value if a segment had only one crash, an average value if a segment had more than one crash and annual average if a segment had no crash. Using the same procedure, the time stamp of every crash in this study was matched with the meteorological dataset to extract the corresponding weather information. Real-time weather data was converted to the segment level by using exact values if the segment had only one crash. An average value (a single value for each segment) was used if the segment had more than one crash. The monthly average weather information was used if the segment had no crash in that month. As reported in Table 1, real-time weather information included average visibility at the time of crash, and average hourly rainfall at time of crash. As posted speed limit may not be a good indicator of driving speed, a two-hour spot speed study was conducted for each highway segment. Two speed related variables were created from this speed survey data: upgrade and downgrade speeding indicators. For instance, downgrade speeding indicator refers to a condition when the 85th percentile speed along a downgrade segment is greater than the posted speed limit. Roadway geometric, cross-sectional elements, roadside features and spatial characteristics data were mainly collected by field surveys, as these data were not readily available. To capture the data for horizontal and vertical alignments, the survey team took GPS coordinates (x, y, and z) every five meters along the road segment using a handheld GPS device (Garmin Etrex 10). GPS coordinates at two lateral points were recorded every five meters along the segment (See Fig. 1). These coordinates were used to construct the whole road segment in AutoCAD. To crosscheck accuracy, the constructed segments were overlapped with the map available in Google Earth (Google, n.d). Cross-section elements like road width and shoulder width were measured by measurement wheels, and longitudinal distances of these elements were extracted from GPS coordinates. In addition, both directions of each segment were driven and filmed with a video camera. Video data were extremely helpful, not only for collecting data on roadside features like pavement marking, signs, and guardrails, but also for crosschecking data accuracy for almost all variables. Spatial characteristic data like number of houses and commercial developments was manually collected and crosschecked with the aerial view in Google Earth. As reported in Table 1, variables related to horizontal alignment included proportion of segment length with horizontal curve, proportion of segment that was simple curve, compound curve, reverse curve, or broken back curve, maximum and minimum degrees of curvature, curve radius, length of circular curve and length of tangent. While variables related to horizontal alignments are shown in Fig. 1, the details of horizontal curve types in a typical mountainous highway segment are illustrated in Fig. 2. As shown in Fig. 1, the length of the tangent refers to the distance along the tangent from the Point of Intersection (point where the back and forward tangents intersect) to the point where the circular curve begins. Deflection angle or intersecting angle is the amount of angle change from the first tangent line to the second tangent line. The proportion of segment length with horizontal curve is representing the length of highway segment with horizontal curve over the total length of the segment. Variables for longitudinal grades included proportion of segment with longitudinal grades greater than zero, intensity of changes in vertical alignment (number of vertical curves per km) and indicators for different levels of longitudinal grades ranging

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Table 1 Summary statistics of explanatory variables included in the model. Variables

Mean

Std. dev.

Min, Max

Counta

Percentagea

Exposure Variables ADT (veh/day) Segment length (m)

1682.70 881.58

856.10 384.89

297.60, 5728.92 30.00, 2039.00

– –

– –

Real– time weather condition Average hourly rainfall at time of crash (mm) Average visibility at the time of crash (km)

0.49 12.15

1.60 1.395

0, 90.00 1.50, 28.00

– –

– –

–

–

–

539

8.81

–

–

–

479

7.83

0.52 0.40 0.06 0.04 0.03 17.54 64.23 0.84 0.23 0.15 0.09 0.12 0.04

0.17 0.20 0.13 0.09 0.12 17.44 42.15 0.96 0.50 0.08 0.07 0.13 0.03

0, 1 0, 1 0, 0.66 0, 0.45 0, 0.61 0, 104.00 0, 330.00 0, 5.99 0, 3.66 0, 0.40 0, 0.38 0, 1.10 0, 0.17

– – – – – – – – – – – – –

– – – – – – – – – – – – –

0.65 4.32 – –

0.34 3.96 – –

0, 1 0.54, 33.33 – –

– – 360 900

– – 5.90 140.70

–

–

–

960

15.70

–

–

–

1200

19.60

–

–

–

2700

44.12

0.09 0.03 0.14 0.73 0.21 0.65 0.14 0.72 0.01 0.01 0.01 –

0.20 0.10 0.23 0.31 0.33 0.39 0.28 0.32 0.04 0.05 0.02 –

0, 1 0, 0.52 0, 1 0, 1 0, 1 0, 1 0, 1 0, 1 0, 0.24 0, 0.5 0, 0.12 –

– – – – – – – – – – – 900

– – – – – – – – – – – 14.70

0.80 0.06 2.98 0.84 23.86 1.52 0.17 0.02 0.62 0.16 0.49 0.05 – –

1.25 0.24 8.51 1.37 23.82 4.32 0.17 0.05 0.34 0.24 0.32 0.09 – –

0, 7.00 0, 1 0, 58.67 0, 7.81 0, 122.81 0, 28.83 0, 0.72 0, 0.34 0, 1 0, 1 0, 1 0, 0.39 – –

– – – – – – – – – – – – 600 2520

– – – – – – – – – – – – 9.80 41.20

12.87

18.84

0, 113.87

–

–

0.75 0.10 0.14

0.30 0.21 0.20

0, 1 0, 1 0, 1

– – –

– – –

Traffic characteristics Upgrade speeding indicator (1 if 85th percentile vehicle operating speed greater than the posted speed limit) Downgrade speeding indicator (1 if 85th percentile vehicle operating speed greater than the posted speed limit) Horizontal alignment Proportion of segment with horizontal curve Proportion of segment with simple curve Proportion of segment with reverse curve Proportion of segment with compound curve Proportion of segment with broken back curve Maximum degree of curvature (◦ ) Minimum degree of curvature (◦ ) Maximum radius of curvature (km) Minimum radius of curvature (km) Maximum length of circular curve (km) Minimum length of circular curve (km) Maximum length of tangent (km) Minimum length of tangent (km) Longitudinal grades Proportion of segment with longitudinal grades greater than zero Number of vertical curves per km Maximum longitudinal grade <2% indicator (1 if maximum longitudinal grade <2%, 0 otherwise) Maximum longitudinal grade 2–4% indicator (1 if maximum longitudinal grade 2–4%, 0 otherwise) Maximum longitudinal grade 4–6% indicator (1 if maximum longitudinal grade 4–6%, 0 otherwise) Maximum longitudinal grade 6–8% indicator (1 if maximum longitudinal grade 6–8%, 0 otherwise) Maximum longitudinal grade >8% indicator (1 if maximum longitudinal grade >8%, 0 otherwise) Cross-sectional elements Proportion of segment with concrete shoulder Proportion of segment with bitumen shoulder Proportion of segment with gravel and earth shoulder Proportion of segment with turf shoulder Proportion of segment with one side shoulder width >1.5 m Proportion of segment with both sides shoulder width >1.5 m Proportion of segment with both sides shoulder width <1.5 m Proportion of segment with broken centre line Proportion of segment with rumble strip Proportion of segment with marginal strip >0.5 m Proportion of segment with edge drop-offs >100 mm Presence of overtaking lane (1 if there is an overtaking lane along the segment, 0 otherwise) Roadway and roadside features Number of minor intersections Number of appropriate emergency stop areas Number of trees per km Number of culverts per km Number of electric poles per km Number of roadway lighting poles per km Proportion of segment with guardrails along one side Proportion of segment with guardrails along both sides Proportion of segment with embankments along one side Proportion of segment with embankments along both sides Proportion of segment with cliffs along one side Proportion of segment with cliffs along both sides Presence of bridge (1 if there is a bridge along the segment, 0 otherwise) Presence of road delineation (1 if there are road delineations such as guide posts and chevron signs along the segment, 0 otherwise) Spatial characteristics Number of houses/shops/commercial buildings within 100 m buffer zone from the each road edge in the road segment per km Proportion of segment with forest within 10 m of the road edge Proportion of segment with farm/agricultural activity within 10 m of the road edge Proportion of segment with houses/shops/commercial buildings within 10 m of the road edge a

Count and percentage are reported for indicator variables.

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157

Fig. 1. A typical horizontal curve along a mountainous road segment.

Fig. 2. Different types of horizontal curves in a typical road in mountainous areas.

from 2% to 8%. A similar range of longitudinal grades was also used in Ahmed et al. (2011). Explanatory variables related to cross-section elements included proportion of segment length with a wide shoulder, proportion of segment with a concrete shoulder, bitumen shoulder or unpaved shoulder, proportion of segment with broken centre lines, rumble strips, marginal strips more than 0.5 m (area between edge line and edge drop of pavement), edge drop-offs more than 100 mm and presence of overtaking lane. In the context of two-lane two-way mountainous highways in Sabah, an additional lane is only provided occasionally for overtaking, so number of lanes is not included as an additional variable. Roadside features included number of minor intersections, trees, roadside culverts, or lighting poles per km, proportion of segment with embankments, cliffs, or guardrails, presence of bridge and presence of road delineation, spatial characteristics included proportion of segment with

forest, farm/agricultural land, or roadside housing and commercial premises. In addition, number of houses or commercial premises within a 100 m from road edge of the road segments was also captured to examine if there is any adjacent land use effect on mountainous road safety. 3. Model development Count data modelling techniques were applied to establish the relationship between observed SV crashes and explanatory variables like road geometries, traffic characteristics, real-time weather conditions, cross-sectional elements, roadside features, and spatial characteristics of rural mountainous roads. As crash counts at transportation entities are often over-dispersed, the Negative Binomial (NB) regression model is generally preferable to the Poisson regression model.

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Let Yit represent SV crash counts on the ith highway segment in the tth time period. Following the Poisson process, the probability of segment i and period t having Yit crashes is expressed as follows: y

P (yit ) =

EXP (−it ) itit yit !

, i = 1, 2, . . ., N and t = 1, 2, . . ., T

(1)

where it is the Poisson mean for highway segment i in time period t. In Negative Binomial (NB) regression model, the Poisson mean is specified as follows: it = exp(X it  ˇ + εit )

(2)

where Xit = (1, Xit,1 , . . .. . ., Xit,k ) is a vector of covariates representing segment-specific attributes of mountainous highways, ␤ = (ˇ0 , . . .. . ., ˇk ) is a vector of unknown regression parameters, and εit is the model error that is independent of all covariates. The stochastic component, εit allows for over-dispersion in the crash data. The NB model assumes that exp(εit ) is Gamma distributed with mean 1 and variance . The parameter  is often referred as an over-dispersion parameter, which leads to following probabilistic distribution for observed crashes on mountainous highways segments: P (yit ) =



   1/ + yit  

 1/ yit !

1/ 1/ + it

1/ 



it



1/ + it

yit

(3)

where  (·) is a gamma function. The simplistic mean structure in Eq. (2) cannot take into account possible non-linear relationships between exposure (e.g. traffic flow) and crashes. It also does not ensure that in the absence of exposure there should not be any crash. To address these fundamental issues, logarithmic transformations of major and minor road traffic flows have been used in the development of safety performance functions for intersection crashes (Mitra and Washington, 2007; Tulu et al., 2015; Washington and Haque, 2013). Following the same principle, the mean of SV crashes along highway segments is structured as follows: it = ˛0 Fit ˛1 Li ˛2 exp(X it  ˇ + εit )

(4)

where Fit represents traffic flows in Average Daily Traffic (ADT) along ith highway segment in tth time period, Li is the length of segment i, and ˛0 , ˛1 and ˛2 are regression parameters to be estimated. Unobserved heterogeneities represent a major challenge in developing SPFs. Heterogeneities could be structured or unstructured depending on the sources they arise from. In the context of this study, structured heterogeneities may result from data clustering or because of temporal correlations, as the same road segment was observed for multiple time periods. The above NB model cannot take into account location specific effects and potential serial correlation associated with the use of time-series cross-sectional panel data for SV crashes in this study. This may lead to incorrect inferences of model parameters as the estimated standard errors of regression coefficients may be underestimated. On the other hand, unstructured heterogeneities may arise from model misspecification, uncertainty in exposure and covariates, and omitted variables. Although an extensive effort has been made to collect relevant data that may influence SV crashes along rural mountainous roads in Malaysia, there may remain some unobserved variables. For example, driver behavior factors like aggressiveness and risk-taking have a strong relationship with traffic crashes but they are unobserved in this study. In the absence of driver behavior factors, it may be unrealistic to assume that the effects of available explanatory variables are fixed across all observations. This misspecification may lead to biased and inconsistent parameter estimates, and erroneous inferences (Mannering et al., 2016). To account for these unobserved heterogeneities, this paper has applied a random parameters Negative Binomial model (RPNB) for

SV crashes along rural mountainous roads. The random constant term of RPNB model act as a location-specific parameter and allows for structured heterogeneities or within-subject correlations. The randomness specification of regression parameters allows parameters to vary across road segments to account for unstructured heterogeneities. The regression coefficients in RPNB model can be expressed as follows: ˇit = ˇ + ωit

(5)

where ωit is a randomly distributed term (e.g. a normally distributed term with mean zero and variance  2 ). With this equation, the negative binomial parameter becomes it |ωit = EXP(ˇit Xit + εit ), and the corresponding log likelihood function can be expressed as follows: LL =

 ln

g (ωit ) P (yit |ωit ) dωit

(6)

ωit

∀it

where g (·) is the probability density function of ωit . Theoretically, a wide range of probability distributions could be specified for ωit . In this study, regression parameters are specified to be normally distributed as this is often found to be suitable in SPFs. As the log-likelihood function in Eq. (6) is computationally cumbersome with random parameters, simulation-based maximum likelihood techniques are typically employed with Halton draws (Bhat, 2003; Milton et al., 2008; Train, 1999). A parameter was defined as random if the estimated standard deviation was significantly different from zero; otherwise it was estimated as a fixed parameter. To obtain the parsimonious model with the best subset of regression parameters, preliminary multicollinearity and backward stepwise technique were employed in this study. To estimate the effects of estimated regression parameters on SV crashes, two types of elasticities were computed: elasticities for continuous variables (Eq. (7)) and pseudo-elasticities for indicator variables (Eq. (8)). Exiki = PExiki

∂i

=

i

X

xik

∂xik

= ˇk xik

   

EXP ˇk − 1 EXP ˇk

(7)

(8)

where E represents the elasticity, PE represents pseudo-elasticity, xik is the value of the independent variable for observation i, ˇk is the estimated parameter for the kth independent variable, and i is the expected SV crash frequency for observation i. Elasticity for a continuous variable indicates the percentage in expected SV crash frequencies for a percent change in the continuous variable while holding all other variables at their mean. The pseudo-elasticity for an indicator variable indicates the percentage change in SV crash counts for the condition change (0–1) in the indicator variable while holding all other variables at their mean (Washington et al., 2010). 4. Model results The RPNB model estimates of SV crashes along rural mountainous highways are presented in Table 2. Reported random parameters were estimated using 200 Halton draws. A likelihood ratio test comparing the log likelihood values between the fitted model and the null model indicates the overall significance (LR statistic = 384.92, p-value < 0.001) of the fitted model in explaining SV crashes. Akaike Information Criteria (AIC) were used in the backward stepwise technique to derive the parsimonious model by removing insignificant variables one by one. The over-dispersion parameter was significant (95% CI: 0.49, 4.40) at a 5% significance level, suggesting the greater appropriateness of the Negative Binomial regression model than the Poisson regression model. The

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Table 2 RPNB model estimates of SV crashes along rural mountainous highways. Variables

Estimate

Std. Err.

z

Prob. |z| >Z

[95% conf. interval]

Constant term Standard deviation of distribution

−14.259 0.313

0.955 0.041

−14.93 7.69

0.000 0.000

[−16.131, −12.388] [0.233, 0.393]

Exposure Variables Log ADT Log of segment length

0.451 1.071

0.091 0.109

4.94 9.84

0.000 0.000

[0.272, 0.631] [0.857, 1.284]

Real-time weather information Average hourly rainfall at time of crash (mm) Average visibility at the time of crash (km)

0.116 0.083

0.014 0.013

8.30 6.40

0.000 0.000

[0.089, 0.143] [0.058, 0.109]

Traffic Characteristics Downgrade speeding indicator (1 if 85th percentile vehicle speed along downgrade greater than the posted speed limit, 0 otherwise)* Standard deviation of distribution

0.604

0.120

5.03

0.000

[0.369, 0.839]

0.536

0.117

4.57

0.000

[0.307, 0.766]

Horizontal alignment Maximum radius of curvature (km)

−0.183

0.060

−3.07

0.002

[−0.301, −0.066]

0.086 0.789 0.216

0.155 0.065 0.087

0.55 12.10 2.49

0.582 0.000 0.013

[−0.219, 0.390] [0.661, 0.916] [0.046, 0.387]

−2.363 −0.540

0.695 0.191

−3.40 −2.82

0.001 0.005

[−3.725, −1.001] [−0.915, −0.165]

0.525 −0.477

0.175 0.094

3.00 −5.07

0.003 0.000

[0.182, 0.878] [−0.661,−0.292]

Spatial characteristics Number houses/shops/commercial buildings per kma Standard deviation of distribution

0.004 0.014

0.002 0.002

2.12 7.33

0.034 0.000

[0.000, 0.010] [0.010, 0.018]

Dispersion parameter negative binomial distribution Log likelihood at zero Log likelihood convergence AIC Chi-sq./DF P-value

2.445 −2194.91 −2002.45 4042.90 384.92/4 0.000

0.997

2.45

0.014

[0.490, 4.399]

Longitudinal grades Proportion of segment with longitudinal grades greater than zeroa Standard deviation of distribution Maximum longitudinal grade >8% indicator (1 if maximum longitudinal grade >8%, 0 otherwise) Cross-sectional elements Proportion of segment with bitumen shoulder Proportion of segment with one side shoulder width >1.5 m Roadway and roadside features Proportion of segment with embankments along one side Presence of road delineation (1 if there are road delineations such as guide posts and chevron signs along the segment, 0 otherwise)

a

Random parameter.

statistical significance of the variance of location-specific effect (95% CI: 0.23, 0.39) suggests the existence of strong structural temporal correlation (structured heterogeneity) in the dataset. The parsimonious model identified 13 explanatory variables influencing SV crashes along rural mountainous highways—all have plausible signs and magnitudes. Ten of them were estimated as fixed parameters, and the other three turned out to be random parameters. Variables estimated as fixed parameters include (1) ADT, (2) segment length, (3) average hourly rainfall at time of crash, (4) average visibility at the time of crash, (5) maximum radius of curvature, (6) maximum longitudinal grade, (7) proportion of segment with bitumen shoulder, (8) proportion of segment with wide shoulder, (9) proportion of segment with roadside embankment, and (10) presence of road delineation. The standard deviations of three parameters were found to significantly differ from zero and thus they were estimated as random parameters. They include (1) downgrade speeding indicator, (2) proportion of segment with longitudinal grades greater than zero, and (3) number of houses, shops or commercial buildings per km. The presence of random parameters indicates the existence of unobserved heterogeneities around these parameters in explaining SV crashes, and thus further indicates the appropriateness of the RPNB model in the context of this study. Elasticity estimates of significant variables in the SPF are presented in Table 3. Both exposure variables, annual daily traffic (95% CI: 0.27, 0.63) and segment length (95% CI: 0.86, 1.28), are significant and positively associated with SV crashes along rural mountainous highways.

Elasticity estimates suggest that a 1% increase in log of ADT is associated with about a 3.29% increase in SV crashes. SV crashes are also found to increase by about 7.11% for a 1% increase in log of segment length. The average hourly rainfall at time of crash is positively associated (95% CI: 0.09, 0.14) with SV crashes along rural mountainous highways. SV crashes are found to increase by 0.06% for a 1% increase in average rainfall. Average visibility at the time of crash is found to be positively associated with SV crashes (95% CI: 0.06, 0.11). The elasticity estimate suggests that a 1% increase in visibility is associated with about 1.01% increase in SV crashes. The parameter estimate for the variable downgrade speeding indicator is found to be a normally distributed random parameter with mean 0.60 and standard deviation 0.54, suggesting that the coefficient for this variable is positive for 87% of road segments and negative for the other 13% of samples. The corresponding elasticity estimate indicates that SV crashes increase by about 45% if the 85th percentile driving speed along a mountainous highways segment is higher than the posted speed limit. The maximum radius of curvature is negatively associated (95% CI: −0.30, −0.07) with SV crashes along rural mountainous roads. Results suggest that a one percent increase in radius of curvature is associated with about a 0.15% decrease of SV crashes on mountainous highways. The parameter estimate for proportion segment length with longitudinal grades greater than zero was found to be normally

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Table 3 Elasticity and pseudo-elasticity estimates of significant variables in SPF. Variables

Elasticity/Pseudo-elasticity (%)

Log ADT Log of segment length Average hourly rainfall at time of crash Average visibility at the time of crash Downgrade speeding indicator (1 if 85th percentile vehicle speed along downgrade greater than the posted speed limit) Maximum radius of curvature Proportion of segment with longitudinal grades greater than zero Maximum longitudinal grade >8% indicator (1 if maximum longitudinal grade >8%, 0 otherwise) Proportion of segment with bitumen shoulder Proportion of segment with one side shoulder width >1.5 m Proportion of segment with embankments along one side Presence of road delineation (1 if there are road delineations such as guide posts and chevron signs along the segment, 0 otherwise) Number houses/shops/commercial buildings within 100 m buffer zone at each end of road segment per km

3.294 7.106 0.057 1.008 45.34 −0.154 0.056 19.43 −0.071 −0.113 0.326 −61.12 0.064

distributed with mean 0.09 and standard deviation 0.79, implying that the corresponding relationship is positive for 54% of highway segments and negative for the rest 46%. On average SV crashes are found to increase by about 0.06% for every percent increase in segment length with longitudinal grades greater than zero. Among the indicator variables for magnitudes of longitudinal grade along mountainous roads, a highway segment with the maximum longitudinal grade higher than 8% is positively associated (95% CI: 0.05, 0.39) with SV crashes. Pseudo-elasticity estimate of this variable indicates that a steep highway segment with longitudinal grade more than 8% increases SV crashes as much as 19% compared to segments with milder gradients. Among the cross-sectional elements, proportion of segment length with bitumen shoulder is a significant (95% CI: −3.72, −1.00) predictor in the SPF and negatively associated with SV crashes. Elasticity suggests that SV crashes decrease by 0.07% for one percent increase in proportion of segment length with bitumen shoulder. Proportion of segment length with wide shoulder (>1.5 m ) along one side is negatively associated (95% CI: −0.92, −0.17) with SV crashes. SV crashes are found to decrease by 0.11% for one percent increase in proportion of segment with wide shoulder along a side. Proportion of segment length with embankment along a side is significant (95% CI: 0.18, 0.88) in explaining SV crashes along rural mountainous roads. A 1% increase in proportion of segment with one side embankment is associated with about 0.33% increase in SV crashes. The presence of road delineation like chevron signs and guide posts is a significant predictor (95% CI: −0.66, −0.29) and positively associated with safety. The presence of road delineation along rural mountainous highways has been found to reduce as much as about 61% SV crashes. Among the spatial factors, number of houses, shops or commercial buildings per km within 100 m within road edge of mountainous highway segments is significant in explaining SV crashes. The parameter estimate has been found to be normally distributed with mean 0.004 and standard deviation 0.01, implying that SV crashes increase with increase in density of houses or commercial buildings for 61% of samples but decrease for the other 39% of road segments. 5. Discussion SV crashes along rural mountainous highways are associated with a wide range of factors, including horizontal and vertical alignment, real-time weather condition, traffic characteristics, cross-sectional elements, roadside features, and spatial characteristics. Effects of these variables are comprehensively discussed and contrasted with the findings from developed countries in the following subsections.

Average daily traffic (ADT) and the length of segment are positively associated with SV crashes. The corresponding elasticity estimates suggest that they are respectively associated with about 3.29% and 7.11% of SV crashes, implying that the risk of SV crashes increases with exposure. In general traffic crashes are positively associated with exposure (e.g., Ceder and Livneh, 1982; Chang, 2005), but the relationship between SV crashes and exposure is not very straightforward. For a set of two-lane rural highway segments (non-mountainous), Ivan et al. (2000) found SV crashes are higher along segments with low volume/capacity ratios and along segments with a better level of service (e.g., LOS A). Using hourly traffic volume data from a set of non-mountainous road segments in the United States, Qin et al. (2006) demonstrated that the relationship between exposure and SV crashes may change from positive to negative depending on the time of day. However, exposure measured as average annual daily traffic (AADT) was not significantly associated with SV crashes along mountainous freeways in the United States (Yu and Abdel-Aty, 2013). In contrast, the relationship between SV crashes and exposure (i.e., ADT and segment length) along rural mountainous highways in Malaysia, as is the case in this study, is positive and non-linear. As the relationship between exposure and SV crashes is complex and different levels of traffic volume along mountainous roads may lead to different responses and adaptations by local drivers, a proper understanding of other factors in relation to SV crashes is required. Mountainous areas are well known for their adverse weather conditions. This study has identified that average rainfall at the time of crash increases the likelihood of SV crashes, with 1% increase in the average rainfall increasing SV crashes by 0.06%. Similar findings are also reported elsewhere (Ma et al., 2015; Yu and Abdel-Aty, 2013; Yu et al., 2015). Wet pavements offer less skid resistance (Colonna et al., 2016a), and the effects of wet pavements may be more prominent for SV crashes along mountainous highways as vehicles are harder to control while negotiating curves or driving along steep slopes. Visibility is another important weather factor in mountainous areas as a number of studies in the United States reported that visibility is negatively associated with crashes on mountainous roads (Ahmed et al., 2012; Ma et al., 2015; Yu and Abdel-Aty, 2013; Yu et al., 2015) and elsewhere (Ahmed et al., 2014). It is argued that poor visibility increases the total crash rate along mountainous roads mainly because of drivers facing difficulty in car-following or lane-changing maneuvers, which may lead to rear-end or sideswipe collisions. In contrast, this study has found that visibility is positively associated with SV crashes along rural mountainous highways in Malaysia. There are two explanations for this condition. First, this may suggest that better visibility encourages higher speed along rural roads, which may in turn increase the likelihood of SV crashes. In general, driving speed increases with visibility (Colonna et al., 2016b). A separate frequency analysis on the

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161

0.09

Expected crash frequency

Bitumen shoulder Road shoulder width>1.5m 0.07

0.05

0.04

0.02

0.00 0

25

50 Proportion of segment length

75

100

Fig. 3. The relationship between SV crash frequencies and road shoulders.

relationship between visibility and SV crashes has indicated that about 93% of speeding-related SV crashes occurred when visibility was higher than 10 km. Second, this finding may be related to the exposure variable ADT. It is possible that traffic volume decreases as visibility goes down and vice versa. This could explain why the finding of this research is different from other research where realtime traffic together with real-time weather was considered (e.g., Ahmed et al., 2014; Chen et al., 2016a; Yu and Abdel-Aty, 2013). This possibility could be better examined if real-time traffic data were available for this study. The likelihood of SV crashes is found to be about 45% higher for those highway sections where the 85th percentile driving speed is higher than the posted speed limit. As such, downgrade speeding represents a significant safety concern for rural mountainous highways. Drivers generally increase their speed along rural roads because of low traffic volume (Lee et al., 2015), and the higher speed may more common along downgrade sections. Therefore, appropriate countermeasures should be targeted to control driving speed along downgrade sections of rural mountainous highways. This variable is also estimated as a random parameter in the model, suggesting that this parameter is negative for some road segments. This may suggest the presence of unobserved heterogeneities around this parameter, perhaps indicating the fact that some road segments are well designed to accommodate speeds higher than the posted speed limit. This study has identified that the likelihood of SV crashes is lower for horizontal road segments with a large radius of curvature, with 1% increase in maximum radius of curvature associated with about 0.15% decrease in SV crashes. This is expected as a curve with large radius of curvature represents a less complex situation than curves with small radii. Other studies elsewhere have also reported that a road section with uniform horizontal curve radius is safer than a road with varying radii (Li et al., 2014; Wang et al., 2010). The proportion of segment length with longitudinal grades greater than zero and the presence of a longitudinal grade higher than 8% are associated with increased SV crashes. These findings are consistent with other research conducted in mountainous areas elsewhere. For example, Ahmed et al. (2011) reported that a downgrade segment with slope 6–8% is the most hazardous compared to other gradients such as 4–6% and 2–4%. Similarly, Yu et al. (2015) reported that the presence of a steep downgrade slope increases the crash risk. There are at least two possible reasons for the increased likelihood of SV crashes along steep gradients. First, speed is likely to be higher for vehicles travelling down along downgrades. Second, continuous braking along downgrades of mountainous roads is

likely to increase the temperature of brake pads which may eventually degrade the efficiency of vehicle brakes and may increase crash risk. Results also suggests that the variable ‘proportion of segment length with longitudinal grades greater than zero’ is a normally distributed random parameter, and thus has an opposite safety effect for about 46% of highway segments. This might again indicate the presence of unobserved heterogeneities around this variable. For example, drivers may be cautious while driving down along longitudinal grades; however, the SPF of this study does not capture any driving behavior related factors. Investigating the driving behavior along longitudinal grades of mountainous highways could be a worthwhile research topic. Among the cross-sectional elements, the presence of a bitumen shoulder and the presence of wide shoulders along rural mountainous highways have a positive effect on road safety and are respectively associated with about 0.07% and 0.11% less SV crashes. To examine the overall effect of road shoulders, the expected crash frequencies of SV crashes are plotted against the proportion of segment length with bitumen shoulder or wide shoulders (≥1.5 m) and presented in Fig. 3. It appears that SV crashes decrease with the increase in proportion of segment length with a bitumen shoulder, and the SV crash frequencies could be about 85% lower if bitumen shoulders were present along 100% of mountainous highways given all other variables being equal. Sealed shoulders allow drivers to recover and redirect their errant vehicle back onto the travelling lanes. In Australia, sealed shoulders are reported to reduce casualty crashes (Jurewicz et al., 2015). The safety effect of wide shoulders is also evident as Fig. 3 clearly shows that the likelihood of SV crashes is about 29% lower if a wide shoulder is present along the entire highway segment. Similar safety effects of wide shoulders along non-mountainous highways are reported elsewhere (e.g., Ivan et al., 1999). To further understand the combined effect of shoulder type and width on SV crashes along rural mountainous highways in Malaysia, a cross-table frequency analysis (Table 4) was conducted accounting for shoulder type (turf, paved, gravel & earth) and shoulder width (narrow vs. wide). It appears that the odds of SV crashes along mountainous highway segments with narrow shoulders (less than 1.5 m) is about 41% lower (OR 0.59, 95%CI 0.04–0.87) for paved shoulders compared to turf or unpaved shoulders. These results suggest the safety benefits of paved shoulders along constrained road geometries of mountainous highways, which often do not allow sufficient space for wider shoulders. The presence of embankments along the mountain side is a typical feature of rural mountainous roads, but they represent a safety concern as the proportion of segment length with embankments is positively associated with SV crashes, with an elasticity

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Table 4 Cross-tabulation analysis of shoulder type and width for SV crashes. Road Shoulder Type

Turfa Paved Gravel & earth a

Shoulder width Narrow (<1.5 m)

Wide (≥1.5 m)

119 (48.0) 39 (15.7) 90 (36.3)

548 (42.7) 304 (23.7) 431 (33.3)

OR (95% CI)

Chi-sq., p-value

1.00 0.59 (0.40–0.87) 0.96 (0.71–1.30)

2.66, p < 0.01 0.26, p = 0.799

Reference category.

estimate of 0.33%. First, an embankment along a highway segment may decrease the sight distance of the drivers if they are particularly located along curved road sections. Second, surface run-off is higher over the pavement next to an embankment, which may pose additional risks because of hydroplaning or less skid resistance. This finding merits further investigation. The presence of road delineations such as chevron signs and guide posts decreases the likelihood of SV crashes by about 61% along rural mountainous highways. Proper curve delineations through chevron signs, curve warning signs, and repeater arrows are well-established treatment options for improving safety along non-mountainous roads (Charlton, 2007; Montella, 2009). The safe benefit of these treatments might be more acute in mountainous areas where road geometries are very tight and the visibility remains a major issue because of mountainous weather. The number of houses or commercial buildings within the 100 m from the road edge is heterogeneously associated with SV crashes, with positive association for 66% of segments and negative association for the other 34%. This is an interesting finding which may have captured the randomness of driver behavior unobserved in this study. This requires further investigation of driving behavior and traffic movements through residential or commercial developments in mountainous areas. 6. Contributions to scientific knowledge and implications This study represents the first study, to the authors’ best knowledge, considering statistical modelling of SV crashes along rural mountainous highways in the context of developing countries. By collecting an extensive dataset though site surveys and utilizing existing databases of traffic crashes and weather information, this research successfully modelled SV crashes as a function wide range variables including road geometries, traffic characteristics, real-time weather condition, cross-sectional elements, roadside features, and spatial characteristics. A significant contribution of this study includes understanding of different factors affecting SV crashes along mountainous highways in the context of developing countries. Constrained topographic conditions along mountainous highways represent a safety concern for SV crashes as the results indicate that steep longitudinal grades and tight horizontal curves increase the likelihood of SV crashes. Downgrade speeding—measured as the 85th percentile of free flow speed higher than the posted speed limit—is also found to be associated with higher likelihood of SV crashes. This finding has significant implications for mountainous road safety and would be helpful for road engineers to design new highways in mountainous areas or redesign existing downgrade road sections identified as blackspots. The road shoulder is identified as one of the critical elements for mountainous road safety, as both paved shoulders (bitumen) compared to unpaved shoulders and wide shoulders compared to narrow ones are associated with reduced likelihood of SV crashes. A subsequent investigation into their effects identifies that the likelihood of SV crashes along highway sections with narrow shoulders is significantly less for paved compared to unpaved shoulders. This implies that as constrained geometric conditions often do not allow

an increase in the road reserve to accommodate wide shoulders, the safety along mountainous highway segments with narrow shoulders could be improved by paving the road shoulders or extending the bituminous road pavements to cover narrow shoulders. The presence of road delineations (e.g. chevron signs, guide posts, etc.) along mountainous highways is associated with reduced likelihood of SV crashes. These low-cost treatment options represent a viable option for improving mountainous road safety, particularly in resource-constrained developing countries. Real-time weather factors like rainfall and visibility are linked with SV crashes in mountainous areas. As rainfall is quite common in mountainous areas, authorities should prioritize frequent pavement management and maintenance programs to ensure sufficient pavement quality. It is found that speed related SV crashes are more frequent in better visibility conditions. Given that the speed is an important factor for mountainous road safety as identified through several explanatory variables used in this research, engineering countermeasures for blackspots along mountainous roads should target controlling driving speed, perhaps in free-flow conditions.

7. Conclusions This study applied a random parameters negative binomial (RPNB) model to examine factors contributing to SV crashes along rural mountainous highways in the context of developing countries. Treating the data as time series cross-section panels, the RPNB model was found to be suitable and appropriate to model SV crashes. The presence of three random parameters further ensured the appropriateness of RPNB model to the development of safety performance functions for SV crashes. From more than 55 explanatory variables, the parsimonious model identified 13 variables significantly associated with SV crashes along rural mountainous roads in Malaysia. Variables positively associated with SV crashes included traffic flow, segment length, average hourly rainfall at time of crash, average visibility at the time of crash, downgrade speeding indicator, proportion of segment length with longitudinal grades greater than zero, the presence of steep grade (>8%), proportion of segment length with embankment along one side and number of houses/shops/commercial buildings. On the other hand, variables negatively associated with SV crashes included maximum radius of curve, proportion of segment length with bitumen shoulder, proportion of segment length with wide shoulder (≥1.5 m ) and the presence of road delineation. Among these variables, downgrade speeding indicator, proportion of segment length with longitudinal grades greater than zero and number of houses/shops/commercial buildings were identified as random parameters capturing unobserved heterogeneities in explaining SV crashes around these factors. The findings of this study shed considerable light on the factors affecting SV crashes along rural mountainous highways in Malaysia. These findings would be helpful for road engineers, road safety professionals and relevant authorities to design appropriate countermeasures as discussed in the last section. The developed safety performance function will also help to identify blackspots or high-risk sites in mountainous areas.

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A major challenge in conducting road safety research in the context of developing countries is the availability of reliable and accurate data. In this study, an extensive effort has been made to collect relevant data through site surveys. Despite these significant efforts, there remain some limitations. First, traffic volume data for the selected segments were collected with brief traffic counts. Although appropriate hourly expansion factors and seasonal variation factors were used to convert these traffic counts to Annual Daily Traffic, the use of Average Annual Daily Traffic (AADT) collected through year round counts with loop detectors may be more appropriate to capture the relationship between exposure and SV crashes. Moreover, manual traffic counts may be subject to error, and were used only because they were the best alternative available for this research given resource and time constraints. Second, visibility information was obtained only from two weather stations because there are only two weather stations in Sabah which record hourly visibility information. Third, although, spiral transition curves were reported to have safety benefits on mountainous roads (Council, 1998), it was not possible to capture this variable because of the unavailability of road geometry design data from the road authority and limitations on the reconstruction of highway segments using GPS coordinates. While GPS coordinates were collected with a handheld GPS (Garmin eTrex10) at 5 m intervals, the accuracy of this device is +/− 3 m (Garmin, 2011). This degree of uncertainty did not allow the identification of spiral transition curves. Ai and Tsai (2014) also mentioned this shortcoming of using GPS data to capture spiral transition curves. Fourth, despite the fact that the pavement condition of mountainous roads may have a significant relationship with safety, the dataset does not include variables related to road surface condition (e.g. skid resistance, rutting, international roughness index, etc.). The pavement condition and surface run-off after rainfall are two important factors for traffic safety along rural mountainous highways in general, and for SV crashes in particular. Future research should target investigating these factors in relation to road safety in mountainous areas. Acknowledgements The first author acknowledges the support of the Queensland University of Technology (QUT), Australia to carry out his Ph.D. We would also like to thank a number of relevant agencies in Malaysia for providing support and help to facilitate the data collection through site surveys. They include Malaysian Institute of Road Safety Research (MIROS), Road Safety Department Sabah (JKJR), and Public Works Department (JKR) Sabah. References AASHTO, 2011. A Policy on Geometric Design of Highways and Streets, 6th ed. American Association of State Highway and Transportation Officials (AASHTO), Washington, DC, USA. Ahmed, M., Huang, H., Abdel-Aty, M., Guevara, B., 2011. Exploring a Bayesian hierarchical approach for developing safety performance functions for a mountainous freeway. Accid. Anal. Prev. 43 (4), 1581–1589. Ahmed, M., Abdel-Aty, M., Yu, R., 2012. Assessment of interaction of crash occurrence, mountainous freeway geometry, real-time weather, and traffic data. Transp. Res. Rec.: J. Transp. Res. Board 2280, 51–59. Ahmed, M.M., Abdel-Aty, M., Lee, J., Yu, R., 2014. Real-time assessment of fog-related crashes using airport weather data: a feasibility analysis. Accid. Anal. Prev. 72, 309–317, http://dx.doi.org/10.1016/j.aap.2014.07.004. Ai, C., Tsai, Y., 2014. Automatic horizontal curve identification and measurement method using GPS data. J. Transp. Eng. 141 (2), 04014078. Bauer, K., Harwood, D., 2013. Safety effects of horizontal curve and grade combinations on rural two-lane highways. Transp. Res. Rec.: J. Transp. Res. Board 2398, 37–49. Bhat, C.R., 2003. Simulation estimation of mixed discrete choice models using randomized and scrambled Halton sequences. Transp. Res. Part B: Methodol. 37 (9), 837–855, http://dx.doi.org/10.1016/S0191-2615(02)00090-5. Castro, M., Sanchez, J.F., Sanchez, J.A., 2012. Operating speed models for two-lane rural highways. Proc. Inst. Civ. Eng.—Transp. 165 (2), 107–118, http://dx.doi. org/10.1680/trans.2012.165.2.107.

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