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shimultilevelbayesiansafety2016.md

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category: literaturenote citekey: shimultilevelbayesiansafety2016 title: Multi-level Bayesian safety analysis with unprocessed Automatic Vehicle Identification data for an urban expressway authors: "Shi, Qi; Abdel-Aty, Mohamed; Yu, Rongjie" year: 2016 date: 2016-00-00 2016 doi: 10.1016/j.aap.2015.12.007 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2015.12.007" zotero_key: KSJCE53D zotero_storage: M95JPTKK collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Shi, Qi"

status: converted

Contents lists available at ScienceDirect

Accident Analysis and Prevention

jour nal home page: www.elsevier.com/locate/aap

Multi-level Bayesian safety analysis with unprocessed Automatic Vehicle Identification data for an urban expressway

Qi Shi a,∗, Mohamed Abdel-Atya, Rongjie Yub

  • a Department of Civil, Environmental and Construction Engineering, University of Central Florida, Engineering II-215, Orlando, FL 32816, United States
  • b School of Transportation Engineering, Tongji University, 4800 Cao'an Road, 201804 Shanghai, China

a r t i c l e i n f o

Article history: Received 10 October 2013 Received in revised form 8 December 2015 Accepted 10 December 2015 Available online 23 December 2015

Keywords: Urban expressway safety Automatic Vehicle Identification Multi-level model Random parameters Bayesian inference

a b s t r a c t

In traffic safety studies, crash frequency modeling of total crashes is the cornerstone before proceeding to more detailed safety evaluation. The relationship between crash occurrence and factors such as traffic flow and roadway geometric characteristics has been extensively explored for a better understanding of crash mechanisms. In this study, a multi-level Bayesian framework has been developed in an effort to identify the crash contributing factors on an urban expressway in the Central Florida area. Two types of traffic data from the Automatic Vehicle Identification system, which are the processed data capped at speed limit and the unprocessed data retaining the original speed were incorporated in the analysis along with road geometric information. The model framework was proposed to account for the hierarchical data structure and the heterogeneity among the traffic and roadway geometric data. Multi-level and random parameters models were constructed and compared with the Negative Binomial model under the Bayesian inference framework. Results showed that the unprocessed traffic data was superior. Both multi-level models and random parameters models outperformed the Negative Binomial model and the models with random parameters achieved the best model fitting. The contributing factors identified imply that on the urban expressway lower speed and higher speed variation could significantly increase the crash likelihood. Other geometric factors were significant including auxiliary lanes and horizontal curvature.

© 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Road safety is a major concern of transportation professionals. To gain better insights into crash occurrence mechanisms, extensive research has been conducted at both the macro- and micro-levels. Micro-level traffic safety studies investigate motorvehicle crashes with relatively small number of occurrences within specific locations (e.g., roadway segment, intersection), but use information in a great amount of detail. Traffic flow, roadway geometric characteristics, weather conditions and drivers characteristics, have been incorporated in micro-level safety analysis. Most existing studies at this level can be generalized as aggregate analysis (e.g., crash frequency analysis, crash rate analysis) and disaggregate analysis (e.g., real-time crash prediction). For aggregate analysis, identification of risk factors of total crash frequency is of prime importance before taking crash type and severity into consideration.

This study explored the contributing factors of traffic crashes on a 21-mile urban expressway segment of State Road 408 (SR 408), operated by the Central Florida Expressway Authority (CFX). The toll road extends through downtown Orlando and is heavily used with CFX (2013) reporting 125,000–135,000 vehicles travel along the expressway daily. Due to large volume of commuter traffic, the expressway of interest has significantly higher volume on weekdays than weekend as illustrated in Fig. 1 using traffic count by the AVI detector on SR 408 eastbound near the interchange with Interstate-4. Moreover, crash data indicated that around 80% of all crashes occurred on weekdays. According to Mirshahi et al. (2007), traffic incidents caused 25% of congestion in the United States. By improving safety condition on the expressway, higher freeway efficiency would be achieved. The large traffic volume and crash concentration on weekdays necessitate the safety evaluation on the expressway.

On the studied expressway, an Automatic Vehicle Identification (AVI) system is installed for Electronic Toll Collection (ETC) and anonymous travel time estimation. The AVI detectors for travel time estimations are installed on the mainline of the expressway near interchanges with other roads. Traveling speed between two adjacent mainline AVI detectors is processed and archived by CFX

∗ Corresponding author.

E-mail addresses: shiqi@knights.ucf.edu (Q. Shi), m.aty@ucf.edu (M. Abdel-Aty), yurongjie@tongji.edu.cn (R. Yu).

on 1-min intervals. Previous studies (Abdel-Aty et al., 2012; Ahmed and Abdel-Aty, 2012) on this road have discussed the possibility of using the processed AVI data for real-time crash predictions. One notable disadvantage of the processed AVI data is that the speed is capped at speed limit during the processing. Therefore the distribution of speed from processed AVI data would be misleading. The use of processed and unprocessed AVI traffic data in traffic safety analysis was compared for crashes occurring on weekdays to take into account the traffic characteristics and crash occurrence on SR 408. While the unprocessed AVI data are rarely available in existing studies, its advantages against processed AVI data are obvious. By measuring its performance in safety evaluation, there will be hope that unprocessed AVI data could be archived routinely in the future and could extend the usage of AVI system in traffic operation and safety.

In this paper, the unprocessed AVI traffic data of which speed is not capped were collected for crash frequency analysis along with roadway geometric information. The combination oftraffic (43 segments) and roadway geometric characteristics (196 segments) data meant that multiple segments based on geometric characteristics would be nested within one AVI segment, thus exhibiting hierarchical data structure. The data structure indicated that multi-level modelframework shouldbe consideredfor traffic safety evaluation. Multi-level models and random parameters multi-level models were constructed and compared with the classic Negative Binomial model. The three model formulations were evaluated within the Bayesian inference framework to determine the most efficient model in terms of model fitting and identifying the contributing factors to crashes and hence suggesting the corresponding safety countermeasures.

2. Background

Since crash frequencies are non-negative integer values, Poisson and Negative Binomial (NB) distributions are commonly used to represent the crash frequency distribution. Although easy to estimate, both models have fixed parameters. In a model with fixed parameters, the effects of explanatory variables are constant over observations and unobserved variations across sites are overlooked. Several extensions of crash frequency models have been developed. Lord and Mannering (2010) summarized the issues associated with crash-frequency data and the advantages and disadvantages of the existing models. When the data structure exhibits hierarchical characteristics, multi-level models should be the appropriate modeling approach to handle the temporal, spatial and other correlations among groups of observations. In the meanwhile, the random parameters approach is valued for its flexibility in accounting for unobserved heterogeneity, which the fixed-parameters approach fails to capture.

Huang and Abdel-Aty (2010) highlighted the use of multi-level modeling approach in traffic safety analysis to accountfor the structured disturbances. The authors stated that the commonly used generalized linear regression models (GLMs) hold the assumption thatthe residuals fromthemodel exhibitindependence, whichmay not hold true under multi-level data structure. Xie et al. (2013) conducted a corridor-level signalized intersection safety analysis for 195 intersections of 22 corridors in Shanghai, China. Corridorlevel data and intersection-level data were employed to construct a multi-level NB model. They organized their data in the multi-level structure because signalized intersections located along the same corridor share similar traffic flow, geometric design, land use and signal control timing (Guo et al., 2010). However, the parameters of intersection-level variables were fixed parameters. Therefore, unobserved heterogeneity among the intersections could not be captured.

Several crash-frequency studies have implemented the random parameters approaches. Anastasopoulos and Mannering (2009) used random-parameters NB model to study the crash mechanisms on 322 rural interstate highway segments in Indiana. The effects of pavement characteristics, roadway geometric characteristics, and truck percentages on crash frequencies were examined. El-Basyouny and Sayed (2009) employed the Poisson-lognormal (PLN) model with random parameters for 392 urban road segments belonging to 58 corridors in Vancouver, British Columbia. Corridor

Fig. 1. Hourly volume by AVI detector on SR 408 eastbound near the interchange with Interstate-4.

variations were modeled by fitting a different regression curve for each corridor. Urban road geometric characteristics contributing to crash occurrence were identified. Venkataraman et al. (2011, 2013) analyzed 1153 directional segments of the seven Washington State interstates with nine-year's crash data. In their study, several geometric variables suchas curvature effects, roadway lighting,left and right side shoulder width were studied. They also implemented a randomparameters approachto estimate crashfrequency by severity, number of vehicles involved and location types.

The existing random parameters crash-frequency studies for freeways normally studied multiple freeway corridors over large geographic area. The effects of roadway geometric characteristics have been well covered. Yet the traffic flow variables were seldom incorporated. In most cases only AADT was available. The lack of the speed or more detailed volume information could be because the time span or the geographic scope of the study area made it impossible to have detectors installed for traffic data collection. However, roadway safety can be affected by various factors such as driver characteristics, roadway geometry, traffic condition and weather (Huang and Abdel-Aty, 2010; Yu and Abdel-Aty, 2013a). In this paper, both traffic and geometric information was collected at very detailed level. In addition, unlike previous studies in which multi-level structures were implemented due to the geographic clusters of the freeway segments, in this study the multi-level data structure exists because of the segmentation criteria of traffic and geometry data.

With the development of Intelligent Transportation System (ITS), researchers have benefited from different traffic detection systems providing traffic data at microscopic level. Loop detectors are the most widely used traffic data sources (Pande and Abdel-Aty, 2006; Golob et al., 2008; Xu et al., 2012). Loop detectors have the advantage of being accurate when operating correctly. However, their performance is sensitive to environmental conditions such as rain or snow (Minge et al., 2010). Recent years see the utilization of new nonintrusive detection devices such as Remote Traffic Microwave Sensors (RTMS) (Akin et al., 2011; Ahmed and Abdel-Aty, 2013; Yu et al., 2013), Video Detectors (Hourdos et al., 2006), and Automatic Vehicle Identification (AVI) sensors (Ahmed et al., 2012) to be used for traffic data collection. These detection systems are less sensitive to inclement weather and easier for maintenance and repair. As more states consider the use of tolls on freeways/expressways to raise infrastructure funding, AVI systems have gained substantial attention for its use in ETC and traffic monitoring. While the loop detectors, RTMS, and Video Detectors measure time mean speed at specific locations, the AVI sensors calculate space mean speed for a segment where AVI detectors are installed at both ends of the segment.

Previous studies using loop detectors or microwave radar detectors collect speed, volume and lane occupancy aggregated into specific time interval (normally 1-min interval). However, for toll roads without loop or radar detectors, existing studies could only use the processedAVI data aggregated into each minute and capped at the speed limit. As for the expressways on the CFX system from where the traffic data were obtained in this study, to leverage the existing population of AVI toll tags for generation of anonymous travel time information, a network of dedicated travel time AVI detectors was deployed at each interchange on the system. The travel time system encrypts the AVI tag identification number then uses tag matches between consecutive AVI detectors to generate segment-based traveltimes. Per CFX Policy,traveltimes are capped at the speed limit. If a vehicle travels through the AVI segment at a speed higher than the speed limit, the speed will only be recorded as equal to speed limit. As a consequence, traffic information at high speed is incomplete and the speed variation of a segment can be distorted. When analyzing the safety condition of a corridor equipped with AVI detectors, unprocessed AVI data, which store the uncapped speed information, is therefore more desirable. However, such data are rarely available. In this study, unprocessed AVI data were archived. The fact that unprocessed AVI data keep information at vehicle level enables researchers have more accurate estimation of speed variation compared with that used in previous research. In addition, if AVI system is the only vehicle detection system installed, unprocessed AVI data could provide part ofthe traffic volume and more importantly how the volume changes along time.

3. Data description and preparation

Three sets of data were prepared for the crash frequency analysis, (1) one-year processed and unprocessed weekday AVI data for SR 408 from September 2012 to August 2013 provided by CFX, (2) crash data on the same roadway for the corresponding time period, (3) roadway geometric characteristics data downloadedfromFlorida Department of Transportation(FDOT)Roadway Characteristics Inventory (RCI) database. A descriptive statistics summary of variables from the three data sources is provided in Table 1.

Although environmental effects on crash occurrence have been examined in some previous studies (Shankar et al., 1995; Ahmed et al., 2011), weather information was not available in this study. In addition, the urban expressway of interest is located in Orlando, Central Florida area where climate is mild all year round. Thunderstorms or fog, while they can pose threats to drivers, exert their effects only during short time intervals and can be random, making them more appropriate in real-time rather than frequency models. In this crash frequency study, risk factors of traffic condition and roadway geometry are explored.

The 21-mile urban expressway segment of SR 408 is mostly used by commuter traffic (Ahmed and Abdel-Aty, 2012). Upon request, CFX has kept unprocessed AVI data since September 2012 for the purpose of this study. The unprocessed AVI data contains the original time stamps of vehicle tag readings. The encrypted transponder (tag) ID of each vehicle, the date and time when the vehicle is detected, the AVI detector ID and the location (milepost) of the detectors are available. Providing data in terms of encrypted transponder IDs protects the privacy of CFX customers. The authors developed an algorithm to calculate the average speed per AVI segment. The encrypted vehicle information was used to filter out the time stamps when the same vehicle was detected at different AVI detectors. Based on the mileposts of two adjacent AVI detectors and the time interval between successive time stamps, the average speed of the vehicle at this segment can be calculated. Extreme speed records were removed according to the definition of abnormal data offered by CFX.

As noted, not all vehicles traveling on the toll road are equipped with transponders. According to toll system's Traffic Data and Statistics manual (CFX, 2011), the E-Pass usage on SR 408 is between 70% and 80% at each toll plaza. Based on the unprocessed AVI data,the E-Pass usage is lower than the reported value as shown in Table 2. One contributing factor would be that the information of a portion of vehicles was not archived in the first place, for which the reason is unknown. Other possible factors are discussed in Table 2. Nevertheless, the sample size is still sufficient enough to make the speed information from AVI recordings reliable to reflect the real traffic condition on the road. The processed AVI speed distribution in Fig. 2 indicates that speed limit of 55 and 65 mph are enforced on the expressway segment. However, unprocessedAVI speed suggests thatin reality the speed is more normally distributed in Fig. 3. The reasons behind the bell-shaped speed distribution could be that peak-hour congestions resultin low traveling speed while during non-congested hours, drivers tend to drive at speed that are comfortable for them rather than complying with

Table 1 Statistic summary of variables for the final model.

Variables Description Number Mean Std. dev. Min Max
Dependent variable
Crash.ct Crash counts per segment on 196 2.08 3.04 0 19
weekdays
Independent variables
RCI segment level variables
Loglength Logarithmic of segment length 196 −1.65 0.47 −2.60 -0.27
Isldwdth Inside shoulder width 196 6.94 3.48 0 12
Auxlane 1 if segment has auxiliary lane; 196 0.34 0.48 0 1
0 if not
Hrzdgcrv Horizontal degree of curvature 196 0.48 0.89 0 5.25
AVI segment level variables
LogAADT Logarithmic of directional 43 10.43 0.40 9.18 10.99
AADT
Pavi avgspd Average speed based on 43 57.91 4.26 52.25 64.60
processed AVI data on
weekdays
Pavi stdspd Standard deviation of speed 43 3.31 1.79 1.01 8.85
based on processed AVI data on
weekdays
Logvol Logarithmic of median traffic 43 9.34 0.53 8.11 10.58
count per segment based on
unprocessed AVI data on
weekdays
Uavi avgspd Average speed based on 43 64.41 5.14 53.33 64.60
unprocessed AVI data on
weekdays
Uavi stdspd Standard deviation of speed 43 6.48 2.00 4.13 11.27
based on unprocessed AVI data
on weekdays

Fig. 2. Speed distribution of processed AVI data on SR 408.

the speed limit. There are in total 43 AVI segments on SR 408, of which 23 are Eastbound (EB) and 20 are the Westbound (WB).

As stated, SR 408 is a toll road and mostly used by commuter traffic. The time period when the road is heavily used rather than when it is lightly traveled is assumed to uncover the relationship between crash and traffic flow more accurately. Accordingly, average and standard deviation of speed per segment on SR 408 for weekday traffic are calculated.

Crash data on weekdays of the same twelve months (Sep. 2012–Aug. 2013) on SR 408 were prepared. The crash reporting agencies on CFX facilities are the Florida Highway Patrol (FHP) and the Orlando Police Department (Orlando PD). However, more than half (142 out of 274) of the crash records reported by the Orlando PD coded the crash time at midnight. The original crash reports were then inspected to correct this error. In Florida, two types of crash reports are used by the above agencies; namely long form and shortform crash reports. To have the complete crash data, both long and short form crash data were incorporated in this research. To investigate in the contributing factors affecting traffic safety on the mainline of expressway, crashes occurring on the ramps and

Fig. 3. Speed distribution of unprocessed AVI data on SR 408.

Table 2 Comparison between AADT and unprocessed AVI volume.

| Data | AADT | Unprocessed AVI volume | | | |------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--|--| | Strength | • Reflect the total traffic
volume
• AADT is widely used in
traffic analysis | • Reflect the traffic volume
pattern for each AVI
segment
• Give detailed volume
pattern for specific time
interval of interest | | | | Weakness | • AADT is the combined
traffic for both directions
• Volume for each direction
is assigned by a fixed
directional factor
• Could not reflect volume
pattern at more detailed
level | • The volume captured by
AVI detector is only for the
vehicles equipped with toll
tags
• The true percentage of
the AVI volume to the total
volume is hard to be
determined | | | | Comparison | The volume at each AVI detector accounts for
40–60% of AADT volume for that segment | | | |

at manual or coin toll plazas were excluded. In total 500 crashes were identified occurring on the mainline of SR 408 in the one year period, of which 405 crashes occurred on weekdays (81% of total).

Roadway geometric characteristics data were collected from FDOT RCI database. The roadway geometric information collected included the number of lanes, type and width of auxiliary lane, left-/right-shoulder, median, horizontal degree of curvature, speed limit, pavement condition, sectional AADT, average directional factor of AADT (D factor), etc. The roadway is divided into homogeneous segments based on these geometric characteristics. When one ofthe values ofthese geometric factors changes, a new RCI segment will be generated. If a RCI segment is shorter than 0.1 mile, it is combined with adjacent RCI segments with higher similarity. The motivation and an example of combining these small segments were addressed in a previous study (Ahmed et al., 2011). A total of 196 RCI segments for SR 408 were generated (98 segments for each direction). The AADT data stored in the FDOT RCI database is the total AADT for both directions. The directional D factor must be used to derive AADT for each direction. In RCI database, a constant D factor of 52.7% was assigned to represent the percentage of AADT of the bound with higher volume on SR 408. On the other hand, the unprocessed AVI data keeps the information at each vehicle level, making it possible to calculate traffic volume during specific time interval. A preliminary comparison between these two types of volume was conducted as shown in Table 2.

The comparison implied that the volume by AVI detector was not equivalent to AADT. The ratio between AVI traffic volume and AADT could only partially reveal the relationship between the tagequipped traffic and the total traffic since even within the segment of a constant AADT, the traffic volumes vary across locations. The comparison here is intended to show the potential that a surrogate measure of disaggregate volume is worth investigation and could be used as an alternative to aggregate volume indicators such as AADT. To understand their performance in safety analysis, both AADT and AVI traffic volume were incorporated in the modeling process. Considering that there are part of vehicles that are not detected by the AVI sensors could lead to lower values of traffic counts, the median value of AVI traffic volumes was chosen as the traffic volume indicator at each AVI detector locations. Average speed and its standard deviation for both unprocessed and processed data were calculated based on the traffic data aggregated at 1-min interval.

When the three data sets were combined together, the data showed significant multi-level structure features. Crashes were aggregated at the RCI segment level. The 196 RCI segments corresponded to 43 AVI segments. As a result, multiple RCI segments were covered by one AVI segment, and shared the same traffic data. Besides, the traffic counts and speed from unprocessed AVI data were used in traffic safety analysis for the first time. Evaluation of their performance was needed against the conventionally used AADT and processed AVI speed data.

4. Model specification

In light of the limitations of GLMs discussed above and the hierarchical data structure in this study, Bayesian multi-level NB models and random parameters multi-level models were proposed in this paper. The Bayesian inference is a statistical method appropriate for this goal as it could deal with multi-level data structure and complex estimation process. Poisson and NB regressions are mostly used in crash frequency studies as a starting point. The NB model is a variation of Poisson model in which a gammadistributed error term is included to account for over-dispersion. Consequently, NB model is also known as Poisson-gamma model. In this study, multi-level and random parameters NB regressions were implemented.

Two types of Bayesian models,(1) multi-level model which estimate AVI and RCI at different levels and (2) random parameters multi-level model at both AVI and RCI levels. Moreover, the classic NB model was constructed and compared. Since unprocessed AVI data was introduced in safety analysis, comparisons between the use of AADT, processed AVI speed and unprocessed AVI speed and volume (AVI transactions) were conducted in type (1) multi-level model framework.

The structure of the NB (Poisson-gamma) model can be shown as:

$$Y{ij} \sim Poisson(\lambda{ij} \varepsilon_{ij})$$ (1)

where Yij is the crash count at RCI segment i(i = 1, . . ., 196) belonging to AVI segment j(j = 1, . . ., 43) which follows Poisson distribution with expected crash frequency of ij with gamma distributed error term εij.

For classic single-level NB model,

$$\lambda{ij} = e{ij}^{\delta} \exp(\alpha + \mathbf{X}_{ij}\mathbf{\beta}) \tag{2}$$

where eij is the exposure variable. In crash-frequency studies, vehicle miles traveled (VMT) (VMT = Traffic volume × Segment length) is often used as an exposure factor. In case of this study, the segment length was RCI level exposure variable and traffic volume AVI level variable. Xij stands for candidate factors atthe RCI andAVI segment levels; is vector of regression coefficients with ˛ indicating intercept.

For multi-level model type (1), the expectation ij for NB distribution could be expressed as

$$\lambda{ij} = e{ij}^{\delta} \exp(\alpha + a{j[i]} + \mathbf{X}{ij}\mathbf{\beta})$$ (3)

To account for their effect properly, they were used separately at the two different levels.

At RCI segment level:

$$\log(\lambda_{ij}) = \alpha + \delta_l \text{Loglength}i + a{j[i]} + \mathbf{X}_{ij} \boldsymbol{\beta}$$ (4)

At AVI segment level:

$$a_j = \delta_v \text{Logvolume}_j + \mathbf{U}_j \boldsymbol{\gamma} \tag{5}$$

Uj is travel flow related factors at AVI segment j(j = 1, . . ., 43). is vector of regression coefficients atAVI segmentlevel. ıl and ıv stand for coefficients of exposure variables Loglength and Logvolume.

For the random parameters model type (2) at both AVI and RCI segment level variables, the model specification should be updated accordingly, at RCI segment level:

$$\log(\lambda_{ij}) = \alphai + \delta{l_i} \text{Loglength}i + a{j[i]} + \mathbf{X}_i \mathbf{\beta}_i$$ (6)

At AVI segment level:

$$aj = \delta{\nu_j} \text{Logvolume}_j + \boldsymbol{U}_j \boldsymbol{\gamma}_j$$ (7)

where ˛i, ıl , i, ıvj , j are coefficients of random parameters. Other parameters have the same meaning as in the model type (1). For ˛, ˛i, -, i, ıl, ıl , ıv, ıvj , , and j, non-informative priors of N(0, 106) were assigned. aj follows a normal distribution with mean determined by Eqs. (5) and (7); and variance follows gamma(10−3, 10−3). The error term εij follows gamma distribution gamma(,) with mean 1 and variance 1/ (Lord and Mannering, 2010), where = elog() and log() ∼ N(0, 106).

Full Bayesian inference using Markov Chain Monte Carlo (MCMC) algorithm was implemented to construct the multi-level models. The Bayesian model's structure is inherently hierarchical. The prior distribution f(|a) of the model parameter with prior parameters a can be considered one level of hierarchy, with the likelihood f(y|) as the final stage of a Bayesian model. The posterior distribution is f(|y) ∝ f(y|)f(|a) via the Bayes theorem (Ntzoufras, 2011). The model calibrations were done in WinBUGS software. Three chains of 20,000 iterations were run for each model, of which 5000 iterations were fed as burn-in.

The deviance information criteria (DIC) introduced by Spiegelhalter et al. (2002) was used as a Bayesian measure of model complexity and fit. DIC can be viewed as the combination of measure of model fitting (D¯ ) and penalization of number of effective variables (pD) in the model. When the difference in DIC between two models is more than 10, it is assured that the model with smaller DIC is better. The difference of DIC between 5 and 10 is considered substantial. Otherwise it is hard to make a definitive judgment (Spiegelhalter et al., 2003). Bayesian Credible Interval (BCI) was used for variable estimation, and the 95% BCI was measured to test the significance of variables. If the BCI does not contain 0, then the effect of variable is significant.

5. Modeling results and discussion

5.1. Processed AVI data vs. unprocessed AVI data

Traffic variables have been confirmed as important risk factors for crash occurrence. AADT, processed AVI data, and unprocessed AVI data were all available in this study. Considering these traffic variables, several data issues arise: (1) directional AADT is calculated based on segment AADT for both directions and a constant D factor; (2) traffic counts based on unprocessed AVI data can reflect the traffic pattern during the time span of interest (weekday) but only the vehicles with tags are captured; (3) speed derived from processed AVI data is capped at the speed limit while unprocessed AVI data does not suffer from this problem. As a result, whether the adoption of unprocessed AVI data will improve the estimation and our understanding of the risk factors of crashes and generate better model fitting was evaluated.

Three combinations of traffic data, (1) AADT and processed AVI speed, (2) AADT and unprocessed AVI speed, (3) unprocessed AVI traffic counts and speed were used and compared. The three combinations were evaluated in the multi-level random parameters framework in which RCI and AVI level variables were evaluated with random parameters. Based on the variable significance and whether the standard deviations of their parameter distributions were statistically significant from 0, it was then decided whether to keep the variable in the model and assign the variable with random parameters. The parameter estimation and modeling results are shown in Table 3. Variables at the AVI segment level and RCI segment level were estimated simultaneously. Mean value of the estimated coefficients, standard deviation, 95% BCI, and t-values were calculated.

The effects of RCI segment variables of the three models generally agreed with each other. The effects of logarithmic segment length were found significant with random parameters. The larger the logarithmic segment length, the more crashes would occur on the segment. This explained the impact of exposure variable on crashes. RCI segments with wider inside shoulder width were associated with fewer crashes. On the urban expressway, wider inside shoulder could allow drivers on the inner lane some leeway for driving errors.

The existence of auxiliary lanes increased the chance of crashes on through travel lanes. The effect of auxiliary lanes as illustrated

Table 3 Parameter estimation and model fitting for different traffic data in multi-level random parameters framework.

AADT and processed AVI speed AADT and unprocessed AVI speed Unprocessed AVI volume and speed
Mean SD 95% BCI t-value Mean SD 95% BCI t-value Mean SD 95% BCI t-value
RCI level variables
Intercept 5.576 3.466 (−0.313,9.693) 1.609 2.996 3.040 (−1.599,7.320) 0.986 2.219 1.361 (0.084,4.368) 1.630
Loglength 0.954 0.157 (0.660,1.292) 6.082 1.033 0.155 (0.737,1.322) 6.682 1.051 0.148 (0.767,1.335) 7.087
SD of Loglength 0.282 0.114 (0.064,0.459) 2.476 0.296 0.126 (0.024,0.488) 2.358 0.314 0.113 (0.029,0.488) 2.788
Isldwdth −0.078 0.032 (−0.141,−0.016) −2.436 −0.040 0.034 (−0.100,0.033) −1.183 −0.070 0.034 (−0.136,−0.008) −2.033
Auxlane 0.300 0.169 (−0.018,0.642)* 1.770 0.367 0.172 (0.048,0.714) 2.134 0.348 0.176 (0.017,0.694) 1.985
Hrzdgcrv −0.298 0.106 (−0.517,−0.100) −2.818 −0.285 0.107 (−0.513,−0.083) −2.662 −0.285 0.109 (−0.491,−0.080) −2.625
AVI level variables
LogAADT 0.410 0.308 (−0.107,0.914) 1.330 0.234 0.317 (−0.465,0.853) 0.736 – – – –
SD of LogAADT 0.050 0.013 (0.026,0.075) 3.973 0.057 0.016 (0.026,0.087) 3.653 – – – –
Logvol – – – – – – – – 0.457 0.231 (−0.022,0.955)* 1.982
SD of Logvol – – – – – – – – 0.059 0.016 (0.028,0.090) 3.759
Pavi avgspd −0.129 0.029 (−0.180,−0.075) −4.404 – – – – – – – –
Pavi stdspd 0.017 0.066 (−0.109,0.142) 0.256 – – – – – – – –
Uavi avgspd – – – – −0.064 0.036 (−0.111,0.030) −1.783 −0.078 0.026 (−0.129,−0.028) −3.014
Uavi stdspd – – – – 0.143 0.073 (0.005,0.286) 1.961 0.156 0.072 (0.015,0.308) 2.153
Model performance
D¯ 560.358 560.715 560.073
pD 80.840 83.013 81.982
DIC 641.198 643.728 642.055

* Significant at 90% BCI.

Fig. 4. Auxiliary lanes on expressway from the RCI Handbook (FDOT, 2012).

in Fig. 4 has not been adequately discussed before. According to the FDOT RCI Handbook (FDOT, 2012), auxiliary lanes are required to provide turning movements and speed changes at critical locations such as ramps. On the segment with auxiliary lanes, more lane-changing behaviors are expected in close proximity; speed difference might also be significant among through travel lanes. The turbulence of traffic flow on mainline segments with auxiliary lanes could then result in more crashes.

The effects of horizontal degree of curvature should be reviewed carefully. Previous research has found mixed effect of horizontal curves. Hauer (1999), Abdel-Aty and Radwan (2000) and Bonneson et al. (2007) suggested sharper curvature would increase the crash likelihood. On the other hand, Milton and Mannering (1998), Haynes et al.(2007) andAhmed et al.(2011)found that sharper horizontal curves were negatively related to crash frequency. It should be interpreted as that shaper curvature might be risky considering its engineering effect, but drivers might drive more slowly and cautiously on curves. In case of this study, the horizontal degree of curvature was negatively related with crash frequency. On the one hand, the maximum horizontal degree of curvature on the expressway is 5.25◦ per 100 feet, which is not too sharp. On the other hand, commuter traffic constitutes a large proportion of the total traffic, indicating the drivers are familiar with the roadway geometry. As a consequence, drivers are more likely to adapt their behavior according to the roadgeometric characteristics andalsobe more careful when driving on curves. The combined effects of road geometric features and driver behavior could result in the negative effect of sharper horizontal curvature on crash occurrences.

The effects of AADT were insignificant in the first two models incorporating AADT. This could be the data issue that was mentioned at the beginning of this section. A constant D factor lacks the capability to determine the direction with higher traffic volume for each segment. Standard deviation of speed based on processed AVI data was insignificant. The processed AVI speed information was capped at the speed limit, thus the real variation could not be reflected objectively. In contrast, traffic counts with random parameters and speed (average and standard deviation) from unprocessed AVI data were proven to be significant for weekday crashes. Their effects indicated higher volume and turbulence (larger standard deviation of speed) would increase the crash likelihood. The speed was negatively associated with crash frequency in this research. Some previous studies suggested a positive relationship between speed and crash counts (Taylor et al., 2002; Elvik et al., 2004) because higher speed requires longer stopping distance. The negative relationship found in this study might be attributed to that the expressway of interest is located in the urban area and accommodates high percentage of commuter traffic. According to the crash data, almost half ofthe crashes (188) occurred during the morning (7:00–9:00 a.m.) and evening (17:00–19:00 p.m.)peakhoursduring whichspeed was expectedto be lower due to congestion. In addition, 206 out of the 405 crashes were rear-end crashes that would be more likely to occur under

Table 4 Parameter estimation and model comparison for NB, multi-level, and multi-level random parameters models.

| | Simple Negative Binomial | | | | Multi-level Negative Binomial | | | | Multi-level Random Parameters Negative
Binomial | | | | | |---------------------|--------------------------|-------|-----------------|---------|-------------------------------|---------|-----------------|---------|----------------------------------------------------|---------|-----------------|---------|--| | | Mean | SD | 95% BCI | t-value | Mean | SD | 95% BCI | t-value | Mean | SD | 95% BCI | t-value | | | RCI level variables | | | | | | | | | | | | | | | Intercept | −2.619 | 1.291 | (−4.905,0.086)* | −2.029 | −0.208 | 3.821 | (−4.978,6.093) | −0.054 | 2.219 | 1.361 | (0.084,4.368) | 1.630 | | | Loglength | 0.736 | 0.105 | (0.543,0.957) | 7.035 | 0.962 | 0.1255 | (0.714,1.213) | 7.665 | 1.051 | 0.148 | (0.767,1.335) | 7.087 | | | SD of Loglength | – | – | – | – | – | – | – | – | 0.314 | 0.113 | (0.029,0.488) | 2.788 | | | Isldwdth | −0.039 | 0.019 | (−0.078,−0.002) | −2.022 | −0.073 | 0.02598 | (−0.127,−0.023) | −2.819 | −0.070 | 0.034 | (−0.136,−0.008) | −2.033 | | | Auxlane | 0.090 | 0.107 | (−0.114,0.297) | 0.840 | 0.165 | 0.1209 | (−0.079,0.402) | 1.365 | 0.348 | 0.176 | (0.017,0.694) | 1.985 | | | Hrzdgcrv | −0.217 | 0.073 | (−0.357,−0.072) | −2.981 | −0.255 | 0.07562 | (−0.402,−0.116) | −3.369 | −0.285 | 0.109 | (−0.491,−0.080) | −2.625 | | | AVI level variables | | | | | | | | | | | | | | | Logvol | 0.851 | 0.115 | (0.659,1.093) | 7.406 | 0.695 | 0.3025 | (0.123,1.160) | 2.297 | 0.457 | 0.231 | (−0.022,0.955)* | 1.982 | | | SD of Logvol | – | – | – | – | – | – | – | – | 0.059 | 0.016 | (0.028,0.090) | 3.759 | | | Uavi avgspd | −0.058 | 0.016 | (−0.091,−0.030) | −3.609 | −0.073 | 0.0294 | (−0.131,−0.018) | −2.482 | −0.078 | 0.026 | (−0.129,−0.028) | −3.014 | | | Uavi stdspd | 0.092 | 0.026 | (0.039,0.141) | 3.502 | 0.142 | 0.06406 | (0.018,0.26) | 2.218 | 0.156 | 0.072 | (0.015,0.308) | 2.153 | | | Model performance | | | | | | | | | | | | | | | D¯ | 859.452 | | | 656.193 | | | 560.073 | | | | | | | | pD | 8.529 | | | 35.206 | | | 81.982 | | | | | | | | DIC | 867.981 | | | | | 691.399 | | | | 642.055 | | | |

* Significant at 90% BCI.

stop-and-go traffic conditions. As a result, the negative effects of speed on crash frequency in this study could imply that congestion would lead to more crashes on urban expressways, such conclusion was consistent with some previous real-time safety analysis conducted on the same expressway system (Ahmed and Abdel-Aty, 2012; Shi and Abdel-Aty, 2015). The goodness-of-fit of the three models were also compared. According to Table 3, the DIC values were highly comparable (the differences within 5). However, comparing the significance of variables, the model with unprocessed AVI data significantly outperformed the other two models.

5.2. Negative Binomial, multi-level and multi-level random parameters models comparison

Multi-level model and random parameters multi-level model were used to compare the performances against traditional NB model. Multi-level approaches have the advantages of evaluating the variables at their own levels. Random parameters multi-level models are more flexible to handle the unobserved heterogeneity among observations. In some of the previous random-parameters studies, the parameters vary across observations (Anastasopoulos and Mannering, 2009; Dinu and Veeraragavan, 2011; Venkataraman et al., 2013). In El-Basyouny and Sayed's (2009) study, 392 urban road segments belong to 58 corridors and the parameters vary across corridor groups. In this section, three models, namely the NB model, multi-level model, and random parameters multi-level model were constructed using unprocessed AVI data. The segment of SR 408 in this study was divided into 43 AVI segments and 196 RCI segments, indicating multiple RCI segments shared a common AVI segment. Table 4 summarizes the modeling results for weekday crashes.

The parameter estimations of the traffic and roadway geometric characteristics variables were consistent for the three models. In general, the effects of the variables in the three models agree with each other. Logarithmic segment length and logarithmic AVI volume were found to be significant when assigned with random parameters. Existence of auxiliary lanes was significant in the random parameters model but insignificant in simple NB and multilevel models. Regarding the model performances of the three models, the results confirmed that by taking account of the hierarchical data structure and heterogeneity across observations, significant improvement in the model fit could be achieved. Comparing the DIC values of the models, the multi-level model showed better fit than NB model with DIC reduced by more than 70. By assigning random parameters to Loglength and Logvol, the multi-level model was further improved by another 49. Nevertheless, estimating variables at multi-levels and assigning variables with random parameters also caused increase ofthe effective number of variables incorporated in the models. Consequently, when modeling crash frequency with hierarchical structured data, multilevel andrandomparameters framework aremore suitable thanthe simple NB model but the tradeoff of model complexity should be considered at the same time.

6. Summary and conclusions

The traffic detection systems are the foundation of the Intelligent Transportation System (ITS). Development of traffic detection technology also brings new and more precise traffic data that benefits traffic safety analysis. Previous studies byAbdel-Aty et al.(2012) and Ahmed and Abdel-Aty (2012) have used the speed data generated from Automatic Vehicle Detection (AVI) systems for real-time crash prediction on the same road. Constrained by the availability of data, the speed data in these studies were processed at 1-min intervals and capped at the speed limits. In this study, unprocessed AVI data was introduced, which archives the original time stamps of the transponder reading and the speed is not capped. The number of vehicles equipped with tags passing an AVI detector can also be calculated as an indicator of traffic volume.

How well the unprocessed AVI data perform in traffic safety analysis has never been evaluated before. Comparisons between AADT and AVI traffic counts, speed data from processed AVI and unprocessed AVI data were conducted using multi-level crash frequency models on SR 408. The models were evaluated for crashes occurring on weekdays. With some issues of processed AVI speed data pointed out, the modeling results confirmed that it was more appropriate to use unprocessed AVI speed data. The strength and weakness of AADT and AVI traffic volume were listed and their performances in safety analysis were tested in the models. The results showed promising use of disaggregate volume as an alternative to aggregate volume indicators such as AADT. At the current stage, unprocessed AVI data are seldom archived by transportation authorities. However, the results from this study encourage the unprocessed AVI data to be stored and their use to be extended beyond ETC and travel time estimation.

When incorporating the roadway geometric information along with traffic data in crash frequency models, it is necessary to select the models based on the data structure. In the case of this study, the multi-level model could efficiently address the multi-level data structure. Furthermore, by allowing coefficients to vary across each observation, the random parameters model could increase model fitting in addition to multi-level NB model. Such results imply that multi-level and random parameters model could account for the complex data structure and unobserved heterogeneity among observations.

Higher volume, lower speed and larger variation of speed were identified as risk factors of crash frequency. For roadway geometric characteristics, the segment length and existence of auxiliary lanes were positively associated with crash frequency. Horizontal degree of curvature and inside shoulder width was significant with a negative sign, indicating that sharper curves and wider inside shoulder width reduced crash likelihood. Previous studies have found mixed effects of horizontal degree of curvature on crashes, which should be interpreted from both engineering effects and human behavior. For the expressway segment in this study, the sharpest degree of curvature is 5.25◦ per 100 feet which is not too sharp. Commuter traffic indicates that drivers are likely to be familiar with the roadway geometry and prepared for the curves. The effects of auxiliary lanes on mainline crash frequency were generally overlooked. However, relatively small distance between ramps on urban expressways makes segments with auxiliary lanes deserve careful safety investigation. Lane-changing and speed changes at these segments can greatly affect the probability of driving errors.

In light of opportunities to further improve safety on urban expressway, countermeasures should be taken from aspects of both the traffic and roadway geometric characteristics. SR 408 has Dynamic Message Signs (DMS) installed to inform travelers of the estimated time to a specific point. In addition to travel time estimation, the DMS could be used to display traffic warnings to alert drivers of traffic conditions at the downstream segment. On segments withauxiliary lanes,more lane-changing behavior and speed changes are expected. Close attention should be paid to the geometric design of the segments' auxiliary lanes, providing markings and signs to guide the drivers and forgive potential driving errors.

Acknowledgments

The authors wish to thank the Central Florida Expressway Authority (CFX) and FDOT for providing the data. This research was supported by the US Department of Transportation, Research and Innovative Technology Administration, Prime DFDA No. 20.701, Award No. DTRT13-G-UTC53.

References