- Email: [email protected]
Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities
j o u r n a l o f t r a f fi c a n d t r a n s p o r t a t i o n e n g i n e e r i n g ( e n g l i s h e d i t i o n ) x x x x ; x x x ( x x x ) : x x x
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.keaipublishing.com/jtte
Review Article
Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities Imalka C. Matarage*, Sunanda Dissanayake Department of Civil Engineering, Kansas State University, Manhattan, KS 66502, USA
highlights Calibration of freeway facility safety performance functions using Kansas data. Development of calibration functions for Kansas freeway facilities. Calibration functions fitted better over calibrated safety performance functions.
article info
abstract
Article history:
Crash prediction models are commonly used for network screening in highway safety
Received 11 February 2019
management process, where potential impacts of highway safety treatments are quanti-
Received in revised form
fied. The Highway Safety Manual (HSM) provides crash prediction models for various types
4 December 2019
of highway facilities that are often referred to as safety performance functions (SPFs).
Accepted 13 December 2019
Freeway facility SPFs in the HSM were developed using data gathered from the states of
Available online xxx
California, Maine, and Washington. When applying these HSM-default SPFs to a local jurisdiction, the HSM recommends calibration of HSM-default SPFs or development of
Keywords:
jurisdiction-specific SPFs to improve the accuracy of crash predictions. This study first
Transportation
calibrated the HSM-default freeway SPFs and for further accuracy and comparison pur-
Freeway segments
poses calibration functions were developed using Kansas freeway data. The performance
Speed-change lanes
of calibrated HSM-default SPFs was then compared with developed calibration functions
Crash prediction models
concerning the accuracy in crash prediction. Freeway facility calibration dataset included
Goodness-of-fit measures
521 freeway segments, 351 entrance-related speed-change lanes, and 366 exit-related
Calibration factor
speed-change lanes. Cumulative residual plots and several other goodness-of-fit measures were used to assess the quality of calibrated HSM-default SPFs and calibration functions. Calibration functions fitted better compared to calibrated HSM-default SPFs for Kansas freeway data. The methodology used in this study could be beneficial and practiced to any jurisdiction. Calibration functions could be used as an alternative to jurisdiction-specific SPFs or a replacement for HSM-default SPFs, which are frequently used in comparing
* Corresponding author. Tel.: þ1 785 340 5558. E-mail addresses: [email protected] (I.C. Matarage), [email protected] (S. Dissanayake). Peer review under responsibility of Periodical Offices of Chang'an University. https://doi.org/10.1016/j.jtte.2019.12.001 2095-7564/© 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
2
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
alternatives, in calculating economic benefits of project improvements, and in estimating economic effectiveness of crash reduction in highway safety-related decision making. © 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
1.
Introduction
Network screening is a process of identifying sites anticipated to benefit the most from cost-effective safety treatments. Empirical Bayes (EB) method is the most commonly used dependable approach in network screening process because it addresses the regression-to-mean (RTM) effect. The EB approach combines the predicted crash frequency with the observed crash frequency to estimate the expected crash frequency at a study site. Safety performance functions (SPFs), preferably calibrated to local conditions are used calculate the predicted crash frequency, which quantifies the probable safety effects of planning, design, operations, and maintenance judgments. The American Association of State Highway and Transportation Officials (AASHTO) issued the Highway Safety Manual (HSM) in 2010 as a result of extensive road safety research conducted over past few decades (AASHTO, 2010). Part C of the HSM provides SPFs for rural multilane highways, rural two-lane two-way roads, and urban and suburban arterials. The HSM supplement to the first edition published in 2014 provides SPFs for freeway and ramp facilities (AASHTO, 2014). When applying the HSM-default SPFs to a certain jurisdiction, the calibration of SPFs or the development of jurisdiction-specific SPFs is highly recommended to avoid biased crash predictions. As the HSM SPFs are already established, jurisdictions may calibrate the HSM-default SPFs and assess the quality of calibrated HSM-default SPFs prior to development of jurisdiction-specific SPFs (Srinivasan et al., 2013). The quality assessment of calibrated HSM-default SPFs captures inconsistencies of reported crashes among sites that may occur of calibration factor being a single multiplier (Lyon et al., 2016). This study used two techniques to evaluate the performance and quality of the calibration process. They are, the value of calibration factor and the goodness-of-fit tests such as cumulative residual (CURE) plots and coefficient of variation (CV). Calibrated SPF is acceptable if either an upper threshold of 5% or less of CURE plot fitted values (after applying the calibration factor) exceeding standard deviation (±2s) limits or the CV of the calibration factor is less than 0.15 (Hauer, 2015; Lyon et al., 2016). CURE plot or percent cure deviation is the most common and reliable goodness-of-fit measure that has been used in literature when assessing the performance of calibrated SPFs. A CURE plot graphically represents cumulative residuals against a variable of interest such as calibration factor, AADT, segment length, and median width arranged in ascending order. CURE plots provide further insight into whether the selected functional form is reasonable or not, while identifying possible concerns by providing a
visual depiction of goodness-of-fit over a range of variable of interest (Lyon et al., 2016). In general, if cumulative residuals oscillate around zero and do not exceed the two standard deviation limits, it is considered as a good CURE plot. Development of calibration functions is one solution that has been explored in literature to improve the fit to local data (Claros et al., 2018; Farid et al., 2018; Hauer, 2015; Srinivasan et al., 2016). This study demonstrates the HSM calibration procedure, the development of calibration functions, and the performance evaluation of calibrated HSM-default SPFs with calibration functions using data from freeway facilities in Kansas. At the time this study was conducted, limited research had conducted on calibration for freeway facilities succeeding the issue of the HSM supplement published in 2014. Since data systems are different from jurisdiction to jurisdiction, the HSM does provide any guidance on extensive data collection needed to perform the freeway facility calibration. Therefore, any jurisdiction could easily follow this study to perform the HSM calibration for freeway facilities with less effort. Freeway facilities for this study included freeway segments and speed-change lanes. A freeway segment is defined as a length of roadway consisting of “n” number of through lanes with a continuous cross section providing two directions of travel where travel lanes are physically separated by either distance or a barrier (AASHTO, 2014). A speed-change lane is defined as a section of roadway located between gore and taper points of a ramp's merge and diverge area (AASHTO, 2014). As identified in the HSM, there are two types of speedchange lanes: ramp entrance-related speed-change lanes (SCEN) and ramp exit-related speed-change lanes (SCEX).
2.
Literature review
This section provides a detailed literature review on the HSM freeway facility calibration prior to and after the issue of the HSM supplement. Maryland and Missouri were the first two states to calibrate HSM freeway and ramp SPFs to its local conditions subsequent to the HSM supplement. As the HSM supplement is relatively new, this study would be an additional guidance for future HSM calibration studies thereby stimulating the use of the HSM for highway safety-related decision making.
2.1.
HSM freeway facility calibration
Shin et al. (2016) carried out the latest comprehensive study on HSM freeway and ramp calibration using Maryland crash data from 2008 to 2010. This study included the calibration of freeway and ramp facilities such as freeway segments,
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
speed-change lanes, and crossroad ramp terminals. In this study, calibration factors were calculated using the Interactive Highway Safety Design Model (IHSDM) developed by the Federal Highway Administration (FHWA) (USDOT, 2019a). Results indicated the HSM methodology overpredicted both fatal and injury (FI) crashes and property damage only (PDO) crashes for all freeway and ramp facilities considered in this study. In addition, the Maryland study also estimated disaggregate calibration factors for all facilities by considering combinations of area type (urban and rural), cross section type (4, 6, 8, and 10 lanes), crash type (multiple-vehicle and single-vehicle), severity type (FI and PDO), and control type (signal-controlled and stopcontrolled). A study conducted by Sun et al. (2013) included the calibration of rural 4-lane freeways, urban 4-lane freeways, and urban 6-lane freeways using Missouri crash data from 2009 to 2011. However, this study followed the proposed freeway methodology in Appendix C of the HSM published in 2010 (AASHTO, 2010). Most required data to perform the calibration were collected using different data sources including state-maintained geometric database and Google street view photographs. Samples were randomly selected for the calibration from each district ensuring the geographic representativeness across the state. However, as some freeway types were limited to few districts, this random sampling method was not practicable for all freeway types. The values of estimated calibration factors for FI models were comparatively lower than PDO models for all freeway types considered in this study. Berry (2017) used the calibration methodology provided in Appendix B of the HSM supplement and estimated calibration factors for Missouri urban 6-lane freeway segments using recent crash data from 2012 to 2014. The results showed the HSM methodology underpredicted multiple-vehicle PDO crashes, and overpredicted all FI crashes and single-vehicle PDO only crashes in urban 6-lane freeway segments. Utilizing crash data from 2010 to 2012, Sun et al. (2016a) estimated calibration factors for Missouri speed-change lanes, ramp segments, and crossroad ramp terminals. In this study, calibration factors were calculated using the Enhanced Interchange Safety Analysis Tool (ISATe) (Bonneson et al., 2012). Identifying the accurate location of crashes occurred at interchange areas was a major challenge of this study. Consequently, Missouri conducted another study, in which 12,409 crashes were manually reviewed thoroughly to identify the exact location of freeway interchange-related crashes (Sun et al., 2016b). The study manually classified Missouri freeway and ramp facilities with respect to HSM definitions. For the calibration, sites were randomly selected while fulfilling the geographical representativeness across the state. The study managed to utilize at least 30 sites for the calibration of these facilities while satisfying the HSM minimum sample size of 30 sites. The recalibration of Missouri rural 4-lane freeway segments, urban 4-lane freeway segments, and urban 6-lane freeway segments was conducted Sun et al. (2018) using recent crash data from 2012 to 2014. At every possible occasion, the study used data from previous freeway
3
calibration studies conducted in Missouri. Furthermore, this study used the IHSDM tool to perform the recalibration (USDOT, 2019a). The new calibration factors for some facility types had minor changes from the previous calibration factors and the study further concluded that these changes may due to natural data variability, driver behavior changes, changes in crash reporting, and modifications in data collection methodology. Florida-specific SPFs for basic freeway segments and freeway interchange areas were developed by Lu et al. (2014) using the negative binomial (NB) regression and crash data from 2007 to 2010. Furthermore, the performance between calibrated SafetyAnalyst-default SPFs and Florida-specific SPFs was compared using goodness-of-fit measures and CURE plots. Results showed developed Florida-specific SPFs produced better-fitted models than calibrated SafetyAnalystdefault models. Srinivasan and Carter (2011) developed freeway SPFs for urban and rural freeways in North Carolina considering the influence of interchanges. Consequently, Smith et al. (2017) recalibrated the SPFs developed by Srinivasan and Carter (2011) using crash data from 2009 to 2015.
2.2.
Quality assessment of the calibration process
Srinivasan et al. (2016) estimated the calibration factor for total crashes (estimated calibration factor is 1.079) using crash, geometric, and traffic data from two-lane two-way roadways in Arizona. If the estimated calibration factor is very close to 1.000, it indicates that the data used in the study is very much closer to the data used to develop the original SPFs (Srinivasan et al., 2013). However, when CURE plots for fitted values for calibration factor, segment length, and AADT were created, a significant portion of the cumulative residuals were lying outside the two standard deviation limits indicating the first technique to evaluate the quality of the calibration process as discussed in the introduction section is not always precise. Furthermore, this study developed calibration functions in different forms to improve the fit to local data. Results indicated calibration functions fitted better to the data set used in this study. Calibration factors suggested in the HSM, calibration factors by ranges of variable of interest, calibration functions, and jurisdiction-specific SPFs were compared regarding the accuracy of crash prediction using 160 urban 4-lane freeway segments in Missouri (Claros et al., 2018). Claros et al. (2018) stated, “generally speaking, prediction accuracy increases from calibration factor, calibration factor by ranges of variable of interest, calibration function to jurisdictionspecific SPFs”. Results showed calibration factors by AADT ranges outperformed the HSM suggested calibration factors; however, calibration functions did not have any significant improvement in prediction accuracy compared to calibration factors by ranges of variable of interest. The performance between Florida-specific SPFs and calibrated SafetyAnalyst-default SPFs were compared by Vargas et al. (2019) in predicting crashes on rural and urban twolane and multi-lane highways in Florida using several goodness-of-fit measures. The main objective of this study was to discover the need for developing jurisdiction-specific
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
4
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
SPFs for these highway facilities. Results exposed Floridaspecific SPFs fitted better to local data compared to the calibrated SafetyAnalyst-default SPFs; however, calibrated SafetyAnalyst-default SPFs outperformed when calibrated to the most recent crash data.
suggested study period for calibration is a duration that is a multiple of 12 months to avoid seasonal effects (AASHTO, 2014). As the study period, a three-year period from 2013 to 2015 was considered for the calibration based on the availability of most recent data at the beginning of this study.
3.3.
3.
Data preparation
3.1.
Data sources
Most of the required geometric attributes, traffic attributes, and reported crashes for the freeway facility calibration were extracted from two state-maintained databases (KDOT, 2011). (1) The Control Section Analysis System (CANSYS) databaseeconsists of data on roadway classifications, geometrics and conditions from over 16,000 km of state roadways in Kansas. (2) The Kansas Crash Analysis and Reporting System (KCARS) databaseeincludes detailed information on all crashes reported by police in Kansas. In addition, ramp AADT values for the study period were obtained from Highway Performance Monitoring System (HPMS) shapefiles that are available on the Federal Highway Administration (FHWA) website (USDOT, 2018a). All states in the United States report AADTs of state roadways to HPMS each year.
3.2.
Data preparation and study period
Table 1 shows data needed for calibrating freeway segments and speed-change lanes together with sources of data extraction. A few required data elements that were absent in the three main data sources as discussed in Section 3.1 were collected using Google Earth (Google Earth, 2018). The HSM
Freeway segment database
The freeway segment database for the calibration was created by eliminating segments from the CANSYS database. The segment reduction procedure as illustrated in Table 2 was conducted because all I roadways and a portion of the US and K roadways satisfied the HSM freeway criteria. The “left side” and “right side” in Table 2 designates the two sides of the roadway, where the “left side” is the west-bound or south-bound while the “right side” is the east-bound or north-bound. The HSM recommends a freeway segment to be between 0.1 and 1.0 mile (0.16e1.60 km) in length for the calibration (AASHTO, 2014). In the case of segments longer than one-mile, the ET Geo Wizards Tool (Version 11.3) was used to create one-mile sections in ArcGIS (Spatial Techniques, 2019).
3.4.
Speed-change lane database
As compared to the freeway segment database, the development of speed-change lane database was more difficult because the CANSYS database did not generate a new homogeneous segment with a ramp being present in a segment. Table 3 provides actions directed to obtain the speed-change lane database from freeway segments that are connected to ramps, therefore, the Step 1 in Table 3 is same as the Step 4 in Table 2. In addition, ramp shapefiles were manually modified adding two fields named, “ramp side” and “EN/EX” because these files only consisted of AADT volumes of all ramps in Kansas. In “ramp side” field, left or right was recorded with respect to the side where the ramp was
Table 1 e Needed data elements in calibrating freeway facilities. Data element Area type (urban & rural) Number of through lanes Segment length Length of radii of horizontal curves Lane width Paved inside/outside shoulder width Median width Presence and length of rumble strips on inside/outside shoulders AADT volume of freeway AADT volume of ramp in speed-change lane Length of and offset to median barrier Length of and offset to outside barrier Clear zone width AADT volume of and distance to nearest upstream entrance ramp AADT volume of and distance to nearest downstream exit ramp Proportion of AADT that occurs during hours where lane volume exceeds 1000 veh/h/ln Presence and length of Type B weaving sections
Source of data extraction CANSYS CANSYS CANSYS CANSYS CANSYS CANSYS CANSYS CANSYS CANSYS HPMS GIS shapefiles CANSYS/Google Earth Google Earth Google Earth HPMS GIS shapefiles/GIS Measure Tool HPMS GIS shapefiles/GIS Measure Tool Calculated using the formula provided in Section 18.4.2 of the HSM No type B weaving sections present in selected segments
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
5
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
Table 2 e Development of the freeway segment database for the calibration. Step No.
1 2 3 4 5
Action taken
Number of segments
Extract fully access-controlled segments from CANSYS database Select freeway segments by HSM definition Divide into 1-mile (1.6 km) sections Select freeway segment connected to ramps Deduct the number of segments obtained in Step 4 from Step 3 (initial freeway segment database) Remove 2-lane, 5-lane and 7-lane segments Select segments with speed limit 65 mile/h (105 km/h) Select segments 0.1 mile (0.16 km) in length Select segments with matching mileposts in both sides of freeway (Final Freeway Segment Database)
5.1 5.2 5.3 5.4
Right side
Left side
Total
2700 1552 2484 1047 1433
2013 1189 2127 918 1204
4713 2741 4611 1965 2637
1417 1367 1131
1201 1174 995
2618 2541 2126 1133
Table 3 e Development of the speed-change lane database for the calibration. Step No.
1 2 3 4 5 6 7 8 9
Action taken
Number of segments
Select freeway segment connected to ramps Discard 2-lane, 5-lane, and 7-lane segments Select segments with speed limit 65 mile/h (105 km/h) Split the segment at gore points Split the segment at taper points and isolate speed-change lanes Select entrance-related speed-change lanes (manually completed) Select exit-related speed-change lanes (manually completed) Select entrance-related segments between 0.04 and 0.30 mile (0.06 e0.50 km) in length (Final EN Speed-Change Lane Database) Select exit-related segments between 0.02 and 0.30 mile (0.03e0.50 km) in length (Final EX Speed-Change Lane Database)
located on the freeway. In “EN/EX” filed, En or Ex was recorded, respectively, when the speed-change lane was connected to an entrance ramp or exit ramp.
3.5.
Site selection
The HSM recommendation for the calibration sample size is 30e50 sites with having 100 crashes per year. However, most recent literature has identified the HSM recommended sample size was not satisfactory to obtain an accurate calibration factor (Alluri et al., 2016; Bahar and Hauer, 2014; Banihashemi, 2012; Kim et al., 2015; Trieu et al., 2014). By following literature, this study calculated a reasonable sample considering 95% confidence level using Eq. (1) (Kim et al., 2015; Shin et al., 2014). 8 > > < n ¼ n0 N=½n0 þ ðN 1Þ 2 > > : n0 ¼ P ð1 PÞ z e
(1)
=
where n is the minimum sample size, N is the total population, Z is the area under normal curve to the preferred confidence level, e is the error margin, and P is the true population. For this study, a 5% margin of error and 50% of true population were considered. Table 4 provides calculated minimum sample sizes for freeway facilities considered in this study. The HSM freeway crash prediction models apply to rural freeways with four, six, and eight through lanes
Right Side
Left side
Total
1047 1030 920
918 909 833
1965 1939 1753
514 446 168 192 166
477 416 187 178 185
991 865 355 370 351
190
176
366
(R4F, R6F, and R8F) and urban freeways with four, six, eight, and ten through lanes (U4F, U6F, U8F, and U10F). Vast majority of freeways in Kansas are rural 4-lane freeways that account for over two-thirds of total freeway mileage within the state, whereas rural 8-lane and urban 10-lane freeways are not present within the state limits. In Table 4, “total population” indicates the total number of segments considered for calibration succeeding the segment reduction procedure in Tables 2 and 3. For the freeway segment calibration, a minimum sample size of 446 segments was required; however, this study employed 521 segments while fulfilling the HSM requirements. For the speed-change lane calibration, total population was used for both entrance- and exit-related speed-change lanes because even with estimated minimum sample sizes the HSM crash criteria was not met. Then, Hawth's Analysis Tool for ArcGIS (Version 3.27) was used to randomly select 521 freeway segments from the total population in ArcGIS (Bayer, 2004; ESRI, 2012). After gathering all required data for selected segments to conduct the calibration, ArcGIS software was used to merge three main sources (ESRI, 2012). Reported crashes were mapped in ArcGIS based on crash type, severity type, and crash year (ESRI, 2012). As shown in Fig. 1, the end goal was to obtain the number of crashes occurred within selected freeway segments and speed-change lanes during the study period.
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
6
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
Table 4 e Estimated minimum sample sizes for freeway facilities considered in this study. Freeway facility
Total Min No. of population sample segments used size (95% for the CI) calibration
Rural 4-lane freeways (R4F) Rural 6-lane freeways (R6F) Urban 4-lane freeways (U4F) Urban 6-lane freeways (U6F) Urban 8-lane freeways (U8F) Total freeway segments Speed-change lanes entering rural 4-lane freeway (R4SCEN) Speed-change lanes entering urban 4lane freeway (U4SCEN) Speed-change lanes entering urban 6lane freeway (U6SCEN) Speed-change lanes entering urban 8lane freeway (U8SCEN) Speed-change lanes exiting rural 4-lane freeway (R4SCEX) Speed-change lanes exiting urban 4-lane freeway (U4SCEX) Speed-change lanes exiting urban 6-lane freeway (U6SCEX) Speed-change lanes exiting urban 8-lane freeway (U8SCEX) Total entrance speedchange lanes (SCEN) Total exit speedchange lanes (SCEX)
study segment has 15 feet lanes, the SPF is multiplied by the CMF for lane width. Npredicted ¼ Nspf ðCMF1 CMF2 / CMFm ÞC
where Npredicted is the predicted average crash frequency, Nspf is the predicted average crash frequency determined from the SPF, CMFm is the crash modification factor, and C is the calibration factor. Eq. (3) shows the HSM estimation of the SPF for freeway facilities. This SPF is further divided in to a function of single-vehicle crashes and a function of multiple-vehicle crashes during the calibration.
896
270
338
18
18
18
178
122
142
35
35
20
4
4
3
1133
446
521
200
132
200
108
84
108
35
32
35
C¼
8
8
8
4.2.
215
138
215
114
99
114
31
29
31
6
6
6
351
184
351
366
187
366
4.
Methodology
4.1.
Calibration factors
Eq. (2) denotes the fundamental HSM crash predictive model. It consists of a SPF, a set of CMFs, and a calibration factor. SPFs in the HSM are developed for a group of base conditions that are unique to each facility type and crash type. If any segment consists of a feature that is different from given base conditions, relevant CMFs are then calculated and multiplied by the SPF. For example, 12 feet lane width is one of the base conditions for multiple-vehicle crashes and if a
(2)
L exp a0 þ b0 ln c0 AADTfs
(3)
where L is the effective length of freeway segment or length of speed-change lane, a'; b' are the regression coefficients (HSM Tables 18-5, 18-7, 18-9, 18-11), c' is the AADT scale coefficient (HSM Tables 18-5, 18-7, 18-9, 18-11), and AADTfs is the AADT volume of freeway segment. The calibration factor (C) is calculated by dividing the total observed crashed by total predicted crashes as denoted in Eq. (4). Obsereved crashes Predicted crashes
(4)
Calibration functions
The base calibration function presented in Eq. (5) is the power functional form, which is commonly used in road safety modeling (Claros et al., 2018; Hauer, 2015; Kononov et al., 2011; Srinivasan et al., 2016). In calibration context, it signifies the relationship between observed crashes and predicted crashes. When “b” is equal or closes to the value 1, “a” turns out to be the estimated value of calibration factor. Other than the base model, calibration functions could also be developed using other predictor variables such as segment length, AADT, and CMFs; however, this study only focused on the base calibration function. The most used ways of developing calibration functions are Ordinary Least Squares (OLS) method, Poisson (P) regression, and Negative Binomial (NB) regression. Amongst three methods mentioned above, P regression is the simplest method; however, the NB regression is often used in past studies due to its ability to account for over dispersion (Claros et al., 2018; Hauer, 2015; Srinivasan et al., 2016). Nobs ¼ aNpred b
(5)
where Nobs is the observed number of crashes, Npred is the predicted number of crashes using the HSM SPFs, a is the model coefficient multiplier, and b is the model coefficient exponent. This study developed calibration functions using the NB method (as discussed in Hauer (2015) and Srinivasan et al. (2016)) and the Calibrator tool. In fact, the calibrator tool provided similar results for the “a” and “b” parameters as the NB method. Eq. (6) represents the estimation of log-likelihood (LL) in NB method (Hauer, 2015). In order to estimate “a” and “b” parameters, the LL is maximized in the NB method.
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
7
Fig. 1 e Merging data sources in ArcGIS.
ln½Lðb0 ; b1 ; /; bÞ ¼
n h X
lnGðobsi þ bLi Þ lnGðbLi Þ þ bLi lnðbLi Þþ
obsi ln predi ðbLi þ obsi Þ ln bLi þ predi i¼1
Microsoft Excel datasheets were developed and used for the Kansas freeway facility calibration.
(6) where i indicates a study segment and Li is the length of study segment i. When the parameter estimates, b0 ; b1 ; /; b of the model are maximized, the sum of ln½Lðb0 ; b1 ; /; bÞ is maximized (Hauer, 2015). The dispersion parameter frequently referred as “k” is equal to the value of 1/ bLi . The dispersion parameters provided in the HSM are either a constant or a function of segment length for segments. Eq. (7) signifies the variance equation, which includes the dispersion parameter, k. V¼ Eþ
E2 bLi
(7)
where V is the estimated variance of mean crash rate, E is the estimated mean crash rate and 1/ bLi is the dispersion parameter, k.
4.3.
The calibrator
The Calibrator developed by FHWA is a spreadsheet-based tool, which could be used to calibrate SPFs and evaluate the performance of calibrated SPFs (USDOT, 2018b). Furthermore, latest version of the Calibrator tool can be used to develop calibration functions. The Calibrator tool determines how well the SPF fits to the input dataset by generating CURE plots and providing several other goodness-of-fit measures. In this study, the Calibrator tool was used to evaluate the performance of calibrated freeway SPFs. However, calibration
5.
Results
5.1. Estimated calibration factors and developed calibration functions Table 5 provides calibration factors and “a” and “b” parameters of calibration functions estimated for freeway facilities in Kansas. The estimated calibration factor greater than 1.000 signifies an underprediction, where Kansas experienced more crashes than the number of crashes predicted using the HSM methodology. On the contrary, the estimated calibration factor smaller than 1.000 signifies an overprediction, where Kansas experienced fewer crashes than the number of crashes predicted using the HSM methodology. The HSM methodology overpredicted both multiple-vehicle and single-vehicle FI crashes and underpredicted both multiple-vehicle and single-vehicle PDO crashes for freeway segments. The HSM methodology underpredicted both FI and PDO crashes for both entranceand exit-related speed-change lanes. In general, estimated values of calibration factors for FI crashes were much nearer to 1.000 compared to estimated values of calibration factors for PDO crashes. When estimated calibration factors are considerably far from value 1.000, a certain biasness exits in those estimated calibration factors. This makes a need to further evaluate the quality of calibrated SPFs as illustrated in previous studies (Hauer, 2015; Lyon et al., 2016; Srinivasan et al., 2013, 2016).
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
8
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
Table 5 e Developed calibration functions and estimated percent cure deviation for freeway facilities. Freeway facility type
R4F
U4F
All freeway (HSM criteria)
R4SC
U4SC
All speed-change lane (HSM criteria)
Crash type
MVFI SVFI MVPDO SVPDO MVFI SVFI MVPDO SVPDO MVFI SVFI MVPDO SVPDO ENFI ENPDO EXFI EXPDO ENFI ENPDO EXFI EXPDO ENFI ENPDO EXFI EXPDO
Observed crash
68 217 220 1069 83 150 310 662 219 441 746 2046 36 130 33 95 62 180 30 127 171 567 124 359
Predicted crash
Calibration factor (2013e2015)
72.88 280.51 99.92 609.69 89.63 123.46 138.22 313.48 230.13 470.95 376.33 1110.02 19.41 66.13 26.38 59.39 46.84 103.72 32.06 76.10 117.77 291.83 87.60 208.78
0.933 0.774 2.202 1.753 0.926 1.215 2.243 2.112 0.952 0.936 1.982 1.843 1.855 1.966 1.251 1.600 1.324 1.736 0.936 1.669 1.452 1.943 1.416 1.720
CV Calibration function
0.15 0.10 0.14 0.04 0.18 0.14 0.20 0.07 0.14 0.09 0.12 0.07 0.25 0.15 0.26 0.17 0.25 0.16 0.34 0.30 0.16 0.13 0.20 0.13
Cure deviation (%)
a
b
Calibration factor
Calibration function
1.31 0.76 2.24 2.06 0.92 1.20 2.38 2.98 0.96 0.95 2.08 2.23 0.52 1.44 2.06 1.37 1.24 1.79 0.98 1.62 1.39 1.95 1.70 1.72
1.31 0.76 1.10 0.78 0.94 0.50 0.54 0.63 1.06 0.76 0.90 0.80 0.44 0.70 1.25 0.87 0.90 0.78 1.03 0.88 0.91 0.99 1.20 0.99
9 8 11 60 1 27 7 79 7 49 14 80 29 1 8 0 2 16 6 1 16 6 18 1
9 2 9 6 1 5 7 1 6 1 4 2 1 0 0 0 2 6 6 1 5 6 0 0
Note: SV means single-vehicle, MV means multiple-vehicle, FI means fatal and injury, PDO means property damage only.
5.2. Performance evaluation between calibration functions and calibration factors The quality assessment of calibrated HSM-default SPFs and calibration functions were conducted for disaggregated SPFs using CURE plots. This assessment was only conducted for most common types of freeway sin Kansas, which included
more than 50 sample sites. It is known that smaller sample sizes may not provide accurate and reliable calibration factors (Alluri et al., 2016; Bahar and Hauer, 2014; Banihashemi, 2012; Kim et al., 2015; Trieu et al., 2014). Estimated percent cure deviation values and CV values for calibration factors and calibration functions are also presented in the Table 5. The Calibrator tool was used to estimate percent cure
Fig. 2 e Created cure plots for fitted values. (a) Calibration factor. (b) Calibration function (R4F SVPDO model).
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
R4F
U4F
All freeways (HSM criteria)
R4SC
U4SC
All speed-change lanes (HSM criteria)
Crash type
MVFI SVFI MVPDO SVPDO MVFI SVFI MVPDO SVPDO MVFI SVFI MVPDO SVPDO ENFI ENPDO EXFI EXPDO ENFI ENPDO EXFI EXPDO ENFI ENPDO EXFI EXPDO
Modified R2
AIC
BIC
k
MAD
Sum LL
Factor
Function
Factor
Function
Factor
Function
Factor
Function
Factor
Function
Factor
Function
0.59 0.36 0.36 0.54 0.46 0.00 0.24 0.38 0.75 0.36 0.43 0.58 0.08 0.16 0.55 0.38 0.30 0.68 0.18 0.40 0.65 0.69 0.27 0.47
0.77 0.34 0.40 0.55 0.48 0.00 0.54 0.44 0.73 0.35 0.46 0.58 0.16 0.19 0.59 0.38 0.31 0.71 0.18 0.38 0.70 0.69 0.27 0.47
283.24 567.54 270.09 669.78 201.76 256.34 221.32 898.39 504.60 889.90 394.98 2366.50 196.49 351.46 180.52 325.83 150.29 128.89 115.71 152.07 353.17 114.62 306.86 296.96
282.30 568.90 269.98 659.31 203.63 262.80 239.01 915.25 505.24 898.20 393.99 2341.39 198.07 351.63 182.06 327.48 152.14 127.86 117.7 153.57 354.64 114.56 309.90 297.01
287.06 572.72 273.91 655.49 204.72 262.76 233.10 909.34 508.85 894.16 383.74 2362.24 201.36 354.93 183.89 329.20 152.97 131.58 118.44 154.81 358.50 110.76 310.77 300.87
289.95 575.18 277.62 662.13 209.55 265.25 218.37 895.39 509.49 902.45 390.72 2333.13 203.09 358.05 188.80 334.22 157.5 133.22 123.17 159.04 357.03 110.70 313.80 300.91
0.52 0.43 0.62 0.21 0.52 0.71 1.87 0.35 0.48 0.46 1.08 0.27 0.43 0.49 0.15 0.40 1.23 0.14 1.91 0.58 0.73 0.28 1.36 0.63
0.29 0.43 0.59 0.19 0.52 0.58 1.72 0.30 0.48 0.45 1.07 0.25 0.37 0.48 0.14 0.39 1.23 0.12 1.90 0.58 0.69 0.28 1.29 0.63
0.30 0.68 0.69 1.75 0.58 1.04 2.09 2.49 0.45 0.81 1.25 2.10 0.30 0.70 0.25 0.56 0.69 1.10 0.41 1.01 0.54 1.12 0.46 0.90
0.28 0.67 0.67 1.73 0.57 0.98 2.01 2.46 0.44 0.81 1.24 2.09 0.29 0.70 0.25 0.55 0.63 1.09 0.41 1.01 0.52 1.12 0.45 0.90
140.62 283.45 134.05 330.66 99.88 130.40 111.66 450.20 251.62 448.10 195.00 1171.69 98.03 174.82 89.26 161.92 74.14 63.45 56.85 75.03 176.32 58.28 153.95 147.48
139.15 281.77 132.99 336.89 99.82 126.17 121.51 459.63 251.30 443.94 198.55 1184.43 96.25 173.73 89.03 161.74 74.07 61.93 56.85 74.78 175.59 58.31 152.43 147.50
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
9
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
Table 6 e Estimated goodness-of-fitness measures for calibration factors and calibration functions. Freeway faculty type
10
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
deviations and CV values and to create CURE plots (USDOT, 2018b). The calibration is successful when the percent cure deviation is less than 5% or the CV value is less than 0.15 (Lyon et al., 2016). Reviewing either CV values or percent cure deviations for calibration factor, it can be determined that the calibration process was satisfactory. However, most percent cure deviations for calibration factor were much greater than 5% representing biased predictions. Therefore, calibration functions were developed, and the accuracy in crash prediction was compared using CURE plots and several other goodness-of-fit measures. Fig. 2 represents two CURE plots created for fitted values for calibration factor and fitted values for calibration function using data from rural 4-lane freeways. Percent cure deviation indicates the percentage of cumulative residuals lying outside the two standard deviations (±s) of cumulative residuals. The x-axis and y-axis in Fig. 2 represent fitted values and cumulative residuals, respectively. Fitted values are calculated by multiplying the HSM predicted crashes with the estimated calibration factor. The residuals are the difference between observed crashes and predicted crashes. For this specific case, percent cure deviation was only 6% for the developed calibration function. However, the calibrated SPF had 60% of cumulative residuals lying outside the two standard deviations. Likewise, reported percent cure deviations for calibration functions were considerably lower than percent cure deviations for respective calibration factors for all freeway facilities indicating that calibration functions better fitted for Kansas freeway facility data than calibrated HSM-default SPFs. Table 6 provides estimated other goodness-of-fit measures for calibration factor and calibration function by each freeway model. Estimated goodness-of-fit measures include modified R2, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), dispersion parameter (k), and Mean Absolute Deviation (MAD). In addition, the sum of log-likelihood is also presented for both calibration factors and calibration functions. When considering goodness-of-fit measures, smaller values are preferred for MAD, AIC, BIC, and k and larger values are preferred for modified R2. When determining the combined performance, the preferred smallest or largest value of MAD, AIC, BIC, k, and modified R2 for was ranked number 1 to n, where 1 represents the best method and n represents the number of alternative methods. Further, the lowest sum of numeric rankings of all measures was considered as the preferred method following Lyon et al. (2016). However, the decisions are still needed to be made depending on the overall performance of goodness-of-fit measures together with preferred values for percent cure deviation or CV value. Combined results from Tables 5 and 6 indicated calibration functions provided better fitted models to Kansas freeway facility data compared to calibrated HSMdefault SPFs because only a small percentage of cumulative residuals were lying outside the two standard deviation limits and other goodness-of-fit measures such as modified R2, AIC, BIC, MAD, and k even provided a higher ranking for calibration functions, respectively.
6.
Discussion
Calibration of HSM-default SPFs or development jurisdictionspecific SPFs are highly recommended for local jurisdictions to make effective highway safety-related decisions. Furthermore, it is extremely critical to assess the safety effectiveness of an applied new countermeasure to distinguish whether the new countermeasure has helped in reducing crashes (Galgamuwa et al., 2019). In addition, jurisdictions are required to perform the HSM analysis for safety-related road designs such as alignment, shoulder type, etc. (Sun et al., 2018). Reducing major risk factors on highway planning, design, operations, and maintenance decisions may save many valuable lives and several hundred million dollars associated with direct and indirect costs. The importance of having calibrated SPFs or calibration functions for a certain jurisdiction in evaluating safety effectiveness is well explained in a benefit cost analysis conducted by Hachey et al. (2019). Hachey et al. (2019) compared costs and benefits of a new safety countermeasure with the existing condition in view of safety, travel time, travel time reliability, vehicle operating costs, and externalities. The expected average crash frequency was calculated for the existing condition considering weighted average of observed crash frequency and predicted crash frequency. The predicted crash frequency is generally calculated using calibrated SPFs, jurisdiction-specific SPFs, or calibration functions. Then, high-quality CMFs from the CMF clearing house representing safety effects of new countermeasures were extracted and multiplied by the estimated expected crash frequency (USDOT, 2019b). Benefits generated by applying a new safety countermeasure are the change in safety performance, where the safety performance is the estimated long-term average crash frequency and severity. Further, results showed that economical savings associated with reduction of the crash frequency and severity are huge compared to other benefits considered in this study. Accordingly, the calibrated HSM-default SPFs and calibration functions developed in this study could easily be applied or replaced with existing uncalibrated SPFs available in safety management software such as Safety Analyst, IHSDM, or ISATe for more accurate crash predictions in Kansas (Bonneson et al., 2012; Harwood et al., 2010; USDOT, 2019a). As of now, limited research has been performed regarding the HSM calibration procedure for freeway facilities following the issue of the HSM supplement in 2014. The HSM does not deliver methods to collect data to accomplish calibrations as the data reporting systems vary from state to state. Hence, any other jurisdiction could simply practice data collection techniques and evaluation methodologies used in this study.
7.
Conclusions
This study first calibrated the HSM-default freeway facility SPFs to Kansas conditions and further assessed the quality of the calibration process. For this calibration study, 521 freeway
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
segments, 351 entrance-related speed-change lanes, and 366 exit-related speed-change lanes were used. In the case of freeway segments, the HSM methodology overpredicted FI crashes and underpredicted PDO crashes in Kansas. Estimated calibration factors for speed-change lanes indicated the HSM methodology consistently underpredicted both FI and PDO crashes in Kansas. The quality of calibrated HSM-default freeway SPFs was satisfactory considering either the CV value or percent cure deviation. However, percent cure deviations for majority of freeway models were greater than the accepted minimum of 5%. Therefore, for further accuracy and comparison purposes, calibration functions were developed, and the performance of calibrated HSM-default SPFs and calibration functions was compared using numerous goodness-of-fit measures such as percent cure deviation, modified R2, AIC, BIC, MAD and k. The combined results of performance measures showed calibration functions fitted better to Kansas freeway data compared to calibrated HSM-default SPFs mainly due to reported lower percent cure deviation values as shown in Table 5. This study recommends the application of estimated calibration factors and developed calibration functions for all freeway facilities considered for accurate freeway safetyrelated decision making in Kansas. Considering that calibration functions provided a decent reliability, chances are that calibration functions provide more accurate crash predictions. In addition, the use of disaggregate calibration functions and calibration factors are suggested to predict crashes more precisely by each freeway type or speed-change lane type. All crash-related studies experience issues of miscoding, misreporting, incompleteness in reported crash data. Since the value of calibration factor wholly depends up on the number of reported crashes, a certain possibility exists in resulting vague calibration factors. In addition, since few geometric data elements required for the calibration were gathered using Google Earth, therefore, the possibility exits of obtaining inexact geometries.
Conflict of interest The authors do not have any conflict of interest with other entities or researchers.
Acknowledgments This work was ostensibly supported by the Kansas Department of Transportation (KDOT) under the K-TRAN program. Authors are grateful to Mr. Benjamin Ware and Ms. Carla Anderson for providing great assistance as project monitors of this study. In addition, authors would like to acknowledge the support given by Mr. Steven Buckley throughout the study. Authors are thankful to Ms. Elsit Mandal from KDOT for providing data needs for this study. Authors extend their sincere gratitude to Mr. Fouad Alangurli, the undergraduate research assistant for assisting during the data collection process.
11
references
American Association of State Highway and Transportation Officials (AASHTO), 2010. Highway Safety Manual, first ed. AASHTO, Washington DC. American Association of State Highway and Transportation Officials (AASHTO), 2014. Highway Safety Manual Supplement, first ed. AASHTO, Washington DC. Alluri, P., Saha, D., Gan, A., 2016. Minimum sample sizes for estimating reliable highway safety manual (HSM) calibration factors. Journal of Transportation Safety & Security 8 (1), 56e74. Bahar, G., Hauer, E., 2014. User's Guide to Develop Highway Safety Manual Safety Performance Function Calibration Factors. HR 20-7(332). National Cooperative Highway Research Program, Transportation Research Board, Washington DC. Banihashemi, M., 2012. Sensitivity analysis of data set sizes for highway safety manual calibration factors. Transportation Research Record 2279, 75e81. Bayer, H.L., 2004. Hawth's Analysis Tools for ArcGIS. Available at: http://www.spatialecology.com/htools/overview.php (Accessed 15 August 2017). Berry, J.A., 2017. Safety Evaluation of Roundabouts at Freeway Ramp Terminals and HSM Calibration (master's thesis). University of Kansas, Kansas. Bonneson, J.A., Geedipally, S., Pratt, M.P., 2012. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. National Cooperative Highway Research Program Transportation Research Board of the National Academies, Washington DC. Claros, B., Sun, C., Edara, P., 2018. HSM calibration factor, calibration function, or jurisdiction-specific safety modelea comparative analysis. Journal of Transportation Safety & Security, https://doi.org/10.1080/19439962.2018.1477896. ESRI, 2012. ArcGIS Desktop: Release 10.1. Environmental Systems Research Institute, Redlands. Farid, A., Abdel-Aty, M., Lee, J., 2018. A new approach for calibrating safety performance functions. Accident Analysis & Prevention 119, 188e194. Galgamuwa, U., Vahl, C.I., Dissanayake, S., 2019. Role of driver behaviors and environmental characteristics in evaluating safety effectiveness of roadway countermeasures: a novel approach of estimating crash modification factors. Journal of Transportation Safety & Security, https://doi.org/10.1080/ 19439962.2018.1545714. Google Earth, 2018. Google Earth Download. Available at: http:// www.google.com/earth/download/ge/, (Accessed 22 September 2017). Hachey, A., Lawrence, M.F., Gross, F., et al., 2019. Evaluating performance of safety countermeasures: applied benefit cost analysis. In: The 98th Annual Meeting of the Transportation Research Board, Washington DC, 2019. Harwood, D.W., Torbic, D.J., Richard, K.R., et al., 2010. Safety Analysis: Software Tools for Safety Management of Specific Highway Sites. FHWA-HRT-10-063. U.S. Department of Transportation, Washington DC. Hauer, E., 2015. The Art of Regression Modeling in Road Safety 38. Springer, New York. KDOT, 2011. Kansas Data Support-the Data Team. Available at: http://www.ksdot.org/burTrafficSaf/reports/ ksshspdatasupport.pdf (Accessed 17 July 2017). Kim, J., Anderson, M., Gholston, S., 2015. Modeling safety performance functions for Alabama's urban and suburban arterials. International Journal of Traffic and Transportation Engineering 4 (3), 84e93. Kononov, J., Lyon, C., Allery, B.K., 2011. Relation of flow, speed, and density of urban freeways to functional form of a safety
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
12
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
performance function. Transportation Research Record 2236, 11e19. Lu, J., Haleem, K., Gan, A., et al., 2014. Safety performance functions for Florida's freeways. In: The T&DI Congress 2014: Planes, Trains, and Automobiles, Florida, 2014. Lyon, C., Persaud, B., Gross, F., 2016. The Calibrator: an SPF Calibration and Assessment Tool User Guide. FHWA-SA-17016. FHWA, Washington DC. Shin, H., Lee, Y.J., Dadvar, S., 2014. The Development of Local Calibration Factors for Implementing the Highway Safety Manual in Maryland. MD-14-SP209B4J. Maryland State Highway Administration, Baltimore. Shin, H., Lee, Y.J., Dadvar, S., et al., 2016. The Development of Local Calibration FactorsePhase II: Maryland Freeways and Ramps. MD-16-SHA-MSU-4-6. Maryland State Highway Administration, Baltimore. Smith, S., Carter, D., Srinivasan, R., 2017. Updated and Regional Calibration Factors for Highway Safety Manual Crash Prediction Models. FHWA/NC/2016-09. FHWA, Washington DC. Spatial Techniques, 2019. ET GeoWizards for ArcGIS. Available at: https://www.ianko.com/ETGeoWizards.html (Accessed 22 September 2017). Srinivasan, R., Carter, D., 2011. Development of Safety Performance Functions for North Carolina. FHWA/NC/201009. FHWA, Washington DC. Srinivasan, R., Carter, D., Bauer, K., 2013. Safety Performance Function Decision Guide: SPF Calibration vs SPF Development. FHWA-SA-14-004. FHWA, Washington DC. Srinivasan, R., Colety, M., Bahar, G., et al., 2016. Estimation of calibration functions for predicting crashes on rural twolane roads in Arizona. Transportation Research Record 2583, 17e24. Sun, C., Edara, P., Brown, H., et al., 2013. Calibration of the Highway Safety Manual for Missouri. Cmr14-007. Missouri Department of Transportation, Mid-America Transportation Center, Missouri. Sun, C., Edara, P., Brown, H., et al., 2016a. Highway Safety Manual Applied in Missouri e Freeway/Software. Cmr16-009. Missouri Department of Transportation, Mid-America Transportation Center, Missouri. Sun, C., Edara, P., Brown, H., et al., 2016b. Crash Location Correction for Freeway Interchange Modeling. Cmr16-010. Missouri Department of Transportation, Mid-America Transportation Center, Missouri. Sun, C., Edara, P., Brown, H., et al., 2018. Missouri Highway Safety Manual Recalibration. Cmr18-001. Missouri Department of Transportation, Mid-America Transportation Center, Missouri. Trieu, V., Park, S., McFadden, J., 2014. Use of Monte Carlo simulation for a sensitivity analysis of highway safety manual calibration factors. Transportation Research Record 2435, 1e10.
USDOT, 2018a. HPMS Public Release of Geospatial Data in Shapefile Format. Available at: https://www.fhwa.dot.gov/ policyinformation/hpms/shapefiles.cfm (Accessed 20 June 2018). USDOT, 2018b. Roadway Safety Data Program. Available at: https://safety.fhwa.dot.gov/rsdp/toolbox-content.aspx? toolid¼150 (Accessed 20 June 2018). USDOT, 2019a. Interactive Highway Safety Design Model (IHSDM): Overview Available at: https://highways.dot.gov/safety/ interactive-highway-safety-design-model/interactivehighway-safety-design-model-ihsdm (Accessed 15 July 2019). USDOT, 2019b. Crash Modification Factors Clearinghouse. Available at: https://safety.fhwa.dot.gov/tools/crf/resources/ (Accessed 15 July 2019). Vargas, H., Raihan, A.P., Alluri, P., et al., 2019. Jurisdiction-specific versus SafetyAnalyst-default safety performance functions: a case study on two-lane and multi-lane arterials. In: The 98th Annual Meeting of the Transportation Research Board, Washington DC, 2019.
Imalka C. Matarage, B.Sc. Eng. (Hons), M.Eng, is a PhD candidate in the Department of Civil Engineering at Kansas State University. Her dissertation research focusses on calibration of the Highway Safety Manual freeway and ramp crash prediction models to Kansas conditions. Her research interests include studies on highway safety, crash data analysis, traffic flow modeling and simulation, and design and analysis of roundabouts. She earned her bachelor's degree in civil and infrastructure engineering and master's degree in transportation engineering from Asian Institute of Technology, Thailand.
Sunanda Dissanayake, PhD, P.E., F. ASCE, is a professor of civil engineering and associate dean of Graduate School at Kansas State University. Her research focuses on studies related to solving applied and practical problems related to transportation engineering, with emphasis on traffic operations and safety of the highway mode. She has authored and co-authored more than 50 journal papers and presented more than 165 papers at national, international, and regional conferences, most of which are proceedings papers. She is a member of two journal editorial boards, a member of two TRB technical committees, and the chair of the Transportation Safety Committee of ASCE/T&DI.
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.keaipublishing.com/jtte
Review Article
Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities Imalka C. Matarage*, Sunanda Dissanayake Department of Civil Engineering, Kansas State University, Manhattan, KS 66502, USA
highlights Calibration of freeway facility safety performance functions using Kansas data. Development of calibration functions for Kansas freeway facilities. Calibration functions fitted better over calibrated safety performance functions.
article info
abstract
Article history:
Crash prediction models are commonly used for network screening in highway safety
Received 11 February 2019
management process, where potential impacts of highway safety treatments are quanti-
Received in revised form
fied. The Highway Safety Manual (HSM) provides crash prediction models for various types
4 December 2019
of highway facilities that are often referred to as safety performance functions (SPFs).
Accepted 13 December 2019
Freeway facility SPFs in the HSM were developed using data gathered from the states of
Available online xxx
California, Maine, and Washington. When applying these HSM-default SPFs to a local jurisdiction, the HSM recommends calibration of HSM-default SPFs or development of
Keywords:
jurisdiction-specific SPFs to improve the accuracy of crash predictions. This study first
Transportation
calibrated the HSM-default freeway SPFs and for further accuracy and comparison pur-
Freeway segments
poses calibration functions were developed using Kansas freeway data. The performance
Speed-change lanes
of calibrated HSM-default SPFs was then compared with developed calibration functions
Crash prediction models
concerning the accuracy in crash prediction. Freeway facility calibration dataset included
Goodness-of-fit measures
521 freeway segments, 351 entrance-related speed-change lanes, and 366 exit-related
Calibration factor
speed-change lanes. Cumulative residual plots and several other goodness-of-fit measures were used to assess the quality of calibrated HSM-default SPFs and calibration functions. Calibration functions fitted better compared to calibrated HSM-default SPFs for Kansas freeway data. The methodology used in this study could be beneficial and practiced to any jurisdiction. Calibration functions could be used as an alternative to jurisdiction-specific SPFs or a replacement for HSM-default SPFs, which are frequently used in comparing
* Corresponding author. Tel.: þ1 785 340 5558. E-mail addresses: [email protected] (I.C. Matarage), [email protected] (S. Dissanayake). Peer review under responsibility of Periodical Offices of Chang'an University. https://doi.org/10.1016/j.jtte.2019.12.001 2095-7564/© 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
2
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
alternatives, in calculating economic benefits of project improvements, and in estimating economic effectiveness of crash reduction in highway safety-related decision making. © 2019 Periodical Offices of Chang'an University. Publishing services by Elsevier B.V. on behalf of Owner. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
1.
Introduction
Network screening is a process of identifying sites anticipated to benefit the most from cost-effective safety treatments. Empirical Bayes (EB) method is the most commonly used dependable approach in network screening process because it addresses the regression-to-mean (RTM) effect. The EB approach combines the predicted crash frequency with the observed crash frequency to estimate the expected crash frequency at a study site. Safety performance functions (SPFs), preferably calibrated to local conditions are used calculate the predicted crash frequency, which quantifies the probable safety effects of planning, design, operations, and maintenance judgments. The American Association of State Highway and Transportation Officials (AASHTO) issued the Highway Safety Manual (HSM) in 2010 as a result of extensive road safety research conducted over past few decades (AASHTO, 2010). Part C of the HSM provides SPFs for rural multilane highways, rural two-lane two-way roads, and urban and suburban arterials. The HSM supplement to the first edition published in 2014 provides SPFs for freeway and ramp facilities (AASHTO, 2014). When applying the HSM-default SPFs to a certain jurisdiction, the calibration of SPFs or the development of jurisdiction-specific SPFs is highly recommended to avoid biased crash predictions. As the HSM SPFs are already established, jurisdictions may calibrate the HSM-default SPFs and assess the quality of calibrated HSM-default SPFs prior to development of jurisdiction-specific SPFs (Srinivasan et al., 2013). The quality assessment of calibrated HSM-default SPFs captures inconsistencies of reported crashes among sites that may occur of calibration factor being a single multiplier (Lyon et al., 2016). This study used two techniques to evaluate the performance and quality of the calibration process. They are, the value of calibration factor and the goodness-of-fit tests such as cumulative residual (CURE) plots and coefficient of variation (CV). Calibrated SPF is acceptable if either an upper threshold of 5% or less of CURE plot fitted values (after applying the calibration factor) exceeding standard deviation (±2s) limits or the CV of the calibration factor is less than 0.15 (Hauer, 2015; Lyon et al., 2016). CURE plot or percent cure deviation is the most common and reliable goodness-of-fit measure that has been used in literature when assessing the performance of calibrated SPFs. A CURE plot graphically represents cumulative residuals against a variable of interest such as calibration factor, AADT, segment length, and median width arranged in ascending order. CURE plots provide further insight into whether the selected functional form is reasonable or not, while identifying possible concerns by providing a
visual depiction of goodness-of-fit over a range of variable of interest (Lyon et al., 2016). In general, if cumulative residuals oscillate around zero and do not exceed the two standard deviation limits, it is considered as a good CURE plot. Development of calibration functions is one solution that has been explored in literature to improve the fit to local data (Claros et al., 2018; Farid et al., 2018; Hauer, 2015; Srinivasan et al., 2016). This study demonstrates the HSM calibration procedure, the development of calibration functions, and the performance evaluation of calibrated HSM-default SPFs with calibration functions using data from freeway facilities in Kansas. At the time this study was conducted, limited research had conducted on calibration for freeway facilities succeeding the issue of the HSM supplement published in 2014. Since data systems are different from jurisdiction to jurisdiction, the HSM does provide any guidance on extensive data collection needed to perform the freeway facility calibration. Therefore, any jurisdiction could easily follow this study to perform the HSM calibration for freeway facilities with less effort. Freeway facilities for this study included freeway segments and speed-change lanes. A freeway segment is defined as a length of roadway consisting of “n” number of through lanes with a continuous cross section providing two directions of travel where travel lanes are physically separated by either distance or a barrier (AASHTO, 2014). A speed-change lane is defined as a section of roadway located between gore and taper points of a ramp's merge and diverge area (AASHTO, 2014). As identified in the HSM, there are two types of speedchange lanes: ramp entrance-related speed-change lanes (SCEN) and ramp exit-related speed-change lanes (SCEX).
2.
Literature review
This section provides a detailed literature review on the HSM freeway facility calibration prior to and after the issue of the HSM supplement. Maryland and Missouri were the first two states to calibrate HSM freeway and ramp SPFs to its local conditions subsequent to the HSM supplement. As the HSM supplement is relatively new, this study would be an additional guidance for future HSM calibration studies thereby stimulating the use of the HSM for highway safety-related decision making.
2.1.
HSM freeway facility calibration
Shin et al. (2016) carried out the latest comprehensive study on HSM freeway and ramp calibration using Maryland crash data from 2008 to 2010. This study included the calibration of freeway and ramp facilities such as freeway segments,
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
speed-change lanes, and crossroad ramp terminals. In this study, calibration factors were calculated using the Interactive Highway Safety Design Model (IHSDM) developed by the Federal Highway Administration (FHWA) (USDOT, 2019a). Results indicated the HSM methodology overpredicted both fatal and injury (FI) crashes and property damage only (PDO) crashes for all freeway and ramp facilities considered in this study. In addition, the Maryland study also estimated disaggregate calibration factors for all facilities by considering combinations of area type (urban and rural), cross section type (4, 6, 8, and 10 lanes), crash type (multiple-vehicle and single-vehicle), severity type (FI and PDO), and control type (signal-controlled and stopcontrolled). A study conducted by Sun et al. (2013) included the calibration of rural 4-lane freeways, urban 4-lane freeways, and urban 6-lane freeways using Missouri crash data from 2009 to 2011. However, this study followed the proposed freeway methodology in Appendix C of the HSM published in 2010 (AASHTO, 2010). Most required data to perform the calibration were collected using different data sources including state-maintained geometric database and Google street view photographs. Samples were randomly selected for the calibration from each district ensuring the geographic representativeness across the state. However, as some freeway types were limited to few districts, this random sampling method was not practicable for all freeway types. The values of estimated calibration factors for FI models were comparatively lower than PDO models for all freeway types considered in this study. Berry (2017) used the calibration methodology provided in Appendix B of the HSM supplement and estimated calibration factors for Missouri urban 6-lane freeway segments using recent crash data from 2012 to 2014. The results showed the HSM methodology underpredicted multiple-vehicle PDO crashes, and overpredicted all FI crashes and single-vehicle PDO only crashes in urban 6-lane freeway segments. Utilizing crash data from 2010 to 2012, Sun et al. (2016a) estimated calibration factors for Missouri speed-change lanes, ramp segments, and crossroad ramp terminals. In this study, calibration factors were calculated using the Enhanced Interchange Safety Analysis Tool (ISATe) (Bonneson et al., 2012). Identifying the accurate location of crashes occurred at interchange areas was a major challenge of this study. Consequently, Missouri conducted another study, in which 12,409 crashes were manually reviewed thoroughly to identify the exact location of freeway interchange-related crashes (Sun et al., 2016b). The study manually classified Missouri freeway and ramp facilities with respect to HSM definitions. For the calibration, sites were randomly selected while fulfilling the geographical representativeness across the state. The study managed to utilize at least 30 sites for the calibration of these facilities while satisfying the HSM minimum sample size of 30 sites. The recalibration of Missouri rural 4-lane freeway segments, urban 4-lane freeway segments, and urban 6-lane freeway segments was conducted Sun et al. (2018) using recent crash data from 2012 to 2014. At every possible occasion, the study used data from previous freeway
3
calibration studies conducted in Missouri. Furthermore, this study used the IHSDM tool to perform the recalibration (USDOT, 2019a). The new calibration factors for some facility types had minor changes from the previous calibration factors and the study further concluded that these changes may due to natural data variability, driver behavior changes, changes in crash reporting, and modifications in data collection methodology. Florida-specific SPFs for basic freeway segments and freeway interchange areas were developed by Lu et al. (2014) using the negative binomial (NB) regression and crash data from 2007 to 2010. Furthermore, the performance between calibrated SafetyAnalyst-default SPFs and Florida-specific SPFs was compared using goodness-of-fit measures and CURE plots. Results showed developed Florida-specific SPFs produced better-fitted models than calibrated SafetyAnalystdefault models. Srinivasan and Carter (2011) developed freeway SPFs for urban and rural freeways in North Carolina considering the influence of interchanges. Consequently, Smith et al. (2017) recalibrated the SPFs developed by Srinivasan and Carter (2011) using crash data from 2009 to 2015.
2.2.
Quality assessment of the calibration process
Srinivasan et al. (2016) estimated the calibration factor for total crashes (estimated calibration factor is 1.079) using crash, geometric, and traffic data from two-lane two-way roadways in Arizona. If the estimated calibration factor is very close to 1.000, it indicates that the data used in the study is very much closer to the data used to develop the original SPFs (Srinivasan et al., 2013). However, when CURE plots for fitted values for calibration factor, segment length, and AADT were created, a significant portion of the cumulative residuals were lying outside the two standard deviation limits indicating the first technique to evaluate the quality of the calibration process as discussed in the introduction section is not always precise. Furthermore, this study developed calibration functions in different forms to improve the fit to local data. Results indicated calibration functions fitted better to the data set used in this study. Calibration factors suggested in the HSM, calibration factors by ranges of variable of interest, calibration functions, and jurisdiction-specific SPFs were compared regarding the accuracy of crash prediction using 160 urban 4-lane freeway segments in Missouri (Claros et al., 2018). Claros et al. (2018) stated, “generally speaking, prediction accuracy increases from calibration factor, calibration factor by ranges of variable of interest, calibration function to jurisdictionspecific SPFs”. Results showed calibration factors by AADT ranges outperformed the HSM suggested calibration factors; however, calibration functions did not have any significant improvement in prediction accuracy compared to calibration factors by ranges of variable of interest. The performance between Florida-specific SPFs and calibrated SafetyAnalyst-default SPFs were compared by Vargas et al. (2019) in predicting crashes on rural and urban twolane and multi-lane highways in Florida using several goodness-of-fit measures. The main objective of this study was to discover the need for developing jurisdiction-specific
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
4
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
SPFs for these highway facilities. Results exposed Floridaspecific SPFs fitted better to local data compared to the calibrated SafetyAnalyst-default SPFs; however, calibrated SafetyAnalyst-default SPFs outperformed when calibrated to the most recent crash data.
suggested study period for calibration is a duration that is a multiple of 12 months to avoid seasonal effects (AASHTO, 2014). As the study period, a three-year period from 2013 to 2015 was considered for the calibration based on the availability of most recent data at the beginning of this study.
3.3.
3.
Data preparation
3.1.
Data sources
Most of the required geometric attributes, traffic attributes, and reported crashes for the freeway facility calibration were extracted from two state-maintained databases (KDOT, 2011). (1) The Control Section Analysis System (CANSYS) databaseeconsists of data on roadway classifications, geometrics and conditions from over 16,000 km of state roadways in Kansas. (2) The Kansas Crash Analysis and Reporting System (KCARS) databaseeincludes detailed information on all crashes reported by police in Kansas. In addition, ramp AADT values for the study period were obtained from Highway Performance Monitoring System (HPMS) shapefiles that are available on the Federal Highway Administration (FHWA) website (USDOT, 2018a). All states in the United States report AADTs of state roadways to HPMS each year.
3.2.
Data preparation and study period
Table 1 shows data needed for calibrating freeway segments and speed-change lanes together with sources of data extraction. A few required data elements that were absent in the three main data sources as discussed in Section 3.1 were collected using Google Earth (Google Earth, 2018). The HSM
Freeway segment database
The freeway segment database for the calibration was created by eliminating segments from the CANSYS database. The segment reduction procedure as illustrated in Table 2 was conducted because all I roadways and a portion of the US and K roadways satisfied the HSM freeway criteria. The “left side” and “right side” in Table 2 designates the two sides of the roadway, where the “left side” is the west-bound or south-bound while the “right side” is the east-bound or north-bound. The HSM recommends a freeway segment to be between 0.1 and 1.0 mile (0.16e1.60 km) in length for the calibration (AASHTO, 2014). In the case of segments longer than one-mile, the ET Geo Wizards Tool (Version 11.3) was used to create one-mile sections in ArcGIS (Spatial Techniques, 2019).
3.4.
Speed-change lane database
As compared to the freeway segment database, the development of speed-change lane database was more difficult because the CANSYS database did not generate a new homogeneous segment with a ramp being present in a segment. Table 3 provides actions directed to obtain the speed-change lane database from freeway segments that are connected to ramps, therefore, the Step 1 in Table 3 is same as the Step 4 in Table 2. In addition, ramp shapefiles were manually modified adding two fields named, “ramp side” and “EN/EX” because these files only consisted of AADT volumes of all ramps in Kansas. In “ramp side” field, left or right was recorded with respect to the side where the ramp was
Table 1 e Needed data elements in calibrating freeway facilities. Data element Area type (urban & rural) Number of through lanes Segment length Length of radii of horizontal curves Lane width Paved inside/outside shoulder width Median width Presence and length of rumble strips on inside/outside shoulders AADT volume of freeway AADT volume of ramp in speed-change lane Length of and offset to median barrier Length of and offset to outside barrier Clear zone width AADT volume of and distance to nearest upstream entrance ramp AADT volume of and distance to nearest downstream exit ramp Proportion of AADT that occurs during hours where lane volume exceeds 1000 veh/h/ln Presence and length of Type B weaving sections
Source of data extraction CANSYS CANSYS CANSYS CANSYS CANSYS CANSYS CANSYS CANSYS CANSYS HPMS GIS shapefiles CANSYS/Google Earth Google Earth Google Earth HPMS GIS shapefiles/GIS Measure Tool HPMS GIS shapefiles/GIS Measure Tool Calculated using the formula provided in Section 18.4.2 of the HSM No type B weaving sections present in selected segments
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
5
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
Table 2 e Development of the freeway segment database for the calibration. Step No.
1 2 3 4 5
Action taken
Number of segments
Extract fully access-controlled segments from CANSYS database Select freeway segments by HSM definition Divide into 1-mile (1.6 km) sections Select freeway segment connected to ramps Deduct the number of segments obtained in Step 4 from Step 3 (initial freeway segment database) Remove 2-lane, 5-lane and 7-lane segments Select segments with speed limit 65 mile/h (105 km/h) Select segments 0.1 mile (0.16 km) in length Select segments with matching mileposts in both sides of freeway (Final Freeway Segment Database)
5.1 5.2 5.3 5.4
Right side
Left side
Total
2700 1552 2484 1047 1433
2013 1189 2127 918 1204
4713 2741 4611 1965 2637
1417 1367 1131
1201 1174 995
2618 2541 2126 1133
Table 3 e Development of the speed-change lane database for the calibration. Step No.
1 2 3 4 5 6 7 8 9
Action taken
Number of segments
Select freeway segment connected to ramps Discard 2-lane, 5-lane, and 7-lane segments Select segments with speed limit 65 mile/h (105 km/h) Split the segment at gore points Split the segment at taper points and isolate speed-change lanes Select entrance-related speed-change lanes (manually completed) Select exit-related speed-change lanes (manually completed) Select entrance-related segments between 0.04 and 0.30 mile (0.06 e0.50 km) in length (Final EN Speed-Change Lane Database) Select exit-related segments between 0.02 and 0.30 mile (0.03e0.50 km) in length (Final EX Speed-Change Lane Database)
located on the freeway. In “EN/EX” filed, En or Ex was recorded, respectively, when the speed-change lane was connected to an entrance ramp or exit ramp.
3.5.
Site selection
The HSM recommendation for the calibration sample size is 30e50 sites with having 100 crashes per year. However, most recent literature has identified the HSM recommended sample size was not satisfactory to obtain an accurate calibration factor (Alluri et al., 2016; Bahar and Hauer, 2014; Banihashemi, 2012; Kim et al., 2015; Trieu et al., 2014). By following literature, this study calculated a reasonable sample considering 95% confidence level using Eq. (1) (Kim et al., 2015; Shin et al., 2014). 8 > > < n ¼ n0 N=½n0 þ ðN 1Þ 2 > > : n0 ¼ P ð1 PÞ z e
(1)
=
where n is the minimum sample size, N is the total population, Z is the area under normal curve to the preferred confidence level, e is the error margin, and P is the true population. For this study, a 5% margin of error and 50% of true population were considered. Table 4 provides calculated minimum sample sizes for freeway facilities considered in this study. The HSM freeway crash prediction models apply to rural freeways with four, six, and eight through lanes
Right Side
Left side
Total
1047 1030 920
918 909 833
1965 1939 1753
514 446 168 192 166
477 416 187 178 185
991 865 355 370 351
190
176
366
(R4F, R6F, and R8F) and urban freeways with four, six, eight, and ten through lanes (U4F, U6F, U8F, and U10F). Vast majority of freeways in Kansas are rural 4-lane freeways that account for over two-thirds of total freeway mileage within the state, whereas rural 8-lane and urban 10-lane freeways are not present within the state limits. In Table 4, “total population” indicates the total number of segments considered for calibration succeeding the segment reduction procedure in Tables 2 and 3. For the freeway segment calibration, a minimum sample size of 446 segments was required; however, this study employed 521 segments while fulfilling the HSM requirements. For the speed-change lane calibration, total population was used for both entrance- and exit-related speed-change lanes because even with estimated minimum sample sizes the HSM crash criteria was not met. Then, Hawth's Analysis Tool for ArcGIS (Version 3.27) was used to randomly select 521 freeway segments from the total population in ArcGIS (Bayer, 2004; ESRI, 2012). After gathering all required data for selected segments to conduct the calibration, ArcGIS software was used to merge three main sources (ESRI, 2012). Reported crashes were mapped in ArcGIS based on crash type, severity type, and crash year (ESRI, 2012). As shown in Fig. 1, the end goal was to obtain the number of crashes occurred within selected freeway segments and speed-change lanes during the study period.
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
6
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
Table 4 e Estimated minimum sample sizes for freeway facilities considered in this study. Freeway facility
Total Min No. of population sample segments used size (95% for the CI) calibration
Rural 4-lane freeways (R4F) Rural 6-lane freeways (R6F) Urban 4-lane freeways (U4F) Urban 6-lane freeways (U6F) Urban 8-lane freeways (U8F) Total freeway segments Speed-change lanes entering rural 4-lane freeway (R4SCEN) Speed-change lanes entering urban 4lane freeway (U4SCEN) Speed-change lanes entering urban 6lane freeway (U6SCEN) Speed-change lanes entering urban 8lane freeway (U8SCEN) Speed-change lanes exiting rural 4-lane freeway (R4SCEX) Speed-change lanes exiting urban 4-lane freeway (U4SCEX) Speed-change lanes exiting urban 6-lane freeway (U6SCEX) Speed-change lanes exiting urban 8-lane freeway (U8SCEX) Total entrance speedchange lanes (SCEN) Total exit speedchange lanes (SCEX)
study segment has 15 feet lanes, the SPF is multiplied by the CMF for lane width. Npredicted ¼ Nspf ðCMF1 CMF2 / CMFm ÞC
where Npredicted is the predicted average crash frequency, Nspf is the predicted average crash frequency determined from the SPF, CMFm is the crash modification factor, and C is the calibration factor. Eq. (3) shows the HSM estimation of the SPF for freeway facilities. This SPF is further divided in to a function of single-vehicle crashes and a function of multiple-vehicle crashes during the calibration.
896
270
338
18
18
18
178
122
142
35
35
20
4
4
3
1133
446
521
200
132
200
108
84
108
35
32
35
C¼
8
8
8
4.2.
215
138
215
114
99
114
31
29
31
6
6
6
351
184
351
366
187
366
4.
Methodology
4.1.
Calibration factors
Eq. (2) denotes the fundamental HSM crash predictive model. It consists of a SPF, a set of CMFs, and a calibration factor. SPFs in the HSM are developed for a group of base conditions that are unique to each facility type and crash type. If any segment consists of a feature that is different from given base conditions, relevant CMFs are then calculated and multiplied by the SPF. For example, 12 feet lane width is one of the base conditions for multiple-vehicle crashes and if a
(2)
L exp a0 þ b0 ln c0 AADTfs
(3)
where L is the effective length of freeway segment or length of speed-change lane, a'; b' are the regression coefficients (HSM Tables 18-5, 18-7, 18-9, 18-11), c' is the AADT scale coefficient (HSM Tables 18-5, 18-7, 18-9, 18-11), and AADTfs is the AADT volume of freeway segment. The calibration factor (C) is calculated by dividing the total observed crashed by total predicted crashes as denoted in Eq. (4). Obsereved crashes Predicted crashes
(4)
Calibration functions
The base calibration function presented in Eq. (5) is the power functional form, which is commonly used in road safety modeling (Claros et al., 2018; Hauer, 2015; Kononov et al., 2011; Srinivasan et al., 2016). In calibration context, it signifies the relationship between observed crashes and predicted crashes. When “b” is equal or closes to the value 1, “a” turns out to be the estimated value of calibration factor. Other than the base model, calibration functions could also be developed using other predictor variables such as segment length, AADT, and CMFs; however, this study only focused on the base calibration function. The most used ways of developing calibration functions are Ordinary Least Squares (OLS) method, Poisson (P) regression, and Negative Binomial (NB) regression. Amongst three methods mentioned above, P regression is the simplest method; however, the NB regression is often used in past studies due to its ability to account for over dispersion (Claros et al., 2018; Hauer, 2015; Srinivasan et al., 2016). Nobs ¼ aNpred b
(5)
where Nobs is the observed number of crashes, Npred is the predicted number of crashes using the HSM SPFs, a is the model coefficient multiplier, and b is the model coefficient exponent. This study developed calibration functions using the NB method (as discussed in Hauer (2015) and Srinivasan et al. (2016)) and the Calibrator tool. In fact, the calibrator tool provided similar results for the “a” and “b” parameters as the NB method. Eq. (6) represents the estimation of log-likelihood (LL) in NB method (Hauer, 2015). In order to estimate “a” and “b” parameters, the LL is maximized in the NB method.
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
7
Fig. 1 e Merging data sources in ArcGIS.
ln½Lðb0 ; b1 ; /; bÞ ¼
n h X
lnGðobsi þ bLi Þ lnGðbLi Þ þ bLi lnðbLi Þþ
obsi ln predi ðbLi þ obsi Þ ln bLi þ predi i¼1
Microsoft Excel datasheets were developed and used for the Kansas freeway facility calibration.
(6) where i indicates a study segment and Li is the length of study segment i. When the parameter estimates, b0 ; b1 ; /; b of the model are maximized, the sum of ln½Lðb0 ; b1 ; /; bÞ is maximized (Hauer, 2015). The dispersion parameter frequently referred as “k” is equal to the value of 1/ bLi . The dispersion parameters provided in the HSM are either a constant or a function of segment length for segments. Eq. (7) signifies the variance equation, which includes the dispersion parameter, k. V¼ Eþ
E2 bLi
(7)
where V is the estimated variance of mean crash rate, E is the estimated mean crash rate and 1/ bLi is the dispersion parameter, k.
4.3.
The calibrator
The Calibrator developed by FHWA is a spreadsheet-based tool, which could be used to calibrate SPFs and evaluate the performance of calibrated SPFs (USDOT, 2018b). Furthermore, latest version of the Calibrator tool can be used to develop calibration functions. The Calibrator tool determines how well the SPF fits to the input dataset by generating CURE plots and providing several other goodness-of-fit measures. In this study, the Calibrator tool was used to evaluate the performance of calibrated freeway SPFs. However, calibration
5.
Results
5.1. Estimated calibration factors and developed calibration functions Table 5 provides calibration factors and “a” and “b” parameters of calibration functions estimated for freeway facilities in Kansas. The estimated calibration factor greater than 1.000 signifies an underprediction, where Kansas experienced more crashes than the number of crashes predicted using the HSM methodology. On the contrary, the estimated calibration factor smaller than 1.000 signifies an overprediction, where Kansas experienced fewer crashes than the number of crashes predicted using the HSM methodology. The HSM methodology overpredicted both multiple-vehicle and single-vehicle FI crashes and underpredicted both multiple-vehicle and single-vehicle PDO crashes for freeway segments. The HSM methodology underpredicted both FI and PDO crashes for both entranceand exit-related speed-change lanes. In general, estimated values of calibration factors for FI crashes were much nearer to 1.000 compared to estimated values of calibration factors for PDO crashes. When estimated calibration factors are considerably far from value 1.000, a certain biasness exits in those estimated calibration factors. This makes a need to further evaluate the quality of calibrated SPFs as illustrated in previous studies (Hauer, 2015; Lyon et al., 2016; Srinivasan et al., 2013, 2016).
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
8
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
Table 5 e Developed calibration functions and estimated percent cure deviation for freeway facilities. Freeway facility type
R4F
U4F
All freeway (HSM criteria)
R4SC
U4SC
All speed-change lane (HSM criteria)
Crash type
MVFI SVFI MVPDO SVPDO MVFI SVFI MVPDO SVPDO MVFI SVFI MVPDO SVPDO ENFI ENPDO EXFI EXPDO ENFI ENPDO EXFI EXPDO ENFI ENPDO EXFI EXPDO
Observed crash
68 217 220 1069 83 150 310 662 219 441 746 2046 36 130 33 95 62 180 30 127 171 567 124 359
Predicted crash
Calibration factor (2013e2015)
72.88 280.51 99.92 609.69 89.63 123.46 138.22 313.48 230.13 470.95 376.33 1110.02 19.41 66.13 26.38 59.39 46.84 103.72 32.06 76.10 117.77 291.83 87.60 208.78
0.933 0.774 2.202 1.753 0.926 1.215 2.243 2.112 0.952 0.936 1.982 1.843 1.855 1.966 1.251 1.600 1.324 1.736 0.936 1.669 1.452 1.943 1.416 1.720
CV Calibration function
0.15 0.10 0.14 0.04 0.18 0.14 0.20 0.07 0.14 0.09 0.12 0.07 0.25 0.15 0.26 0.17 0.25 0.16 0.34 0.30 0.16 0.13 0.20 0.13
Cure deviation (%)
a
b
Calibration factor
Calibration function
1.31 0.76 2.24 2.06 0.92 1.20 2.38 2.98 0.96 0.95 2.08 2.23 0.52 1.44 2.06 1.37 1.24 1.79 0.98 1.62 1.39 1.95 1.70 1.72
1.31 0.76 1.10 0.78 0.94 0.50 0.54 0.63 1.06 0.76 0.90 0.80 0.44 0.70 1.25 0.87 0.90 0.78 1.03 0.88 0.91 0.99 1.20 0.99
9 8 11 60 1 27 7 79 7 49 14 80 29 1 8 0 2 16 6 1 16 6 18 1
9 2 9 6 1 5 7 1 6 1 4 2 1 0 0 0 2 6 6 1 5 6 0 0
Note: SV means single-vehicle, MV means multiple-vehicle, FI means fatal and injury, PDO means property damage only.
5.2. Performance evaluation between calibration functions and calibration factors The quality assessment of calibrated HSM-default SPFs and calibration functions were conducted for disaggregated SPFs using CURE plots. This assessment was only conducted for most common types of freeway sin Kansas, which included
more than 50 sample sites. It is known that smaller sample sizes may not provide accurate and reliable calibration factors (Alluri et al., 2016; Bahar and Hauer, 2014; Banihashemi, 2012; Kim et al., 2015; Trieu et al., 2014). Estimated percent cure deviation values and CV values for calibration factors and calibration functions are also presented in the Table 5. The Calibrator tool was used to estimate percent cure
Fig. 2 e Created cure plots for fitted values. (a) Calibration factor. (b) Calibration function (R4F SVPDO model).
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
R4F
U4F
All freeways (HSM criteria)
R4SC
U4SC
All speed-change lanes (HSM criteria)
Crash type
MVFI SVFI MVPDO SVPDO MVFI SVFI MVPDO SVPDO MVFI SVFI MVPDO SVPDO ENFI ENPDO EXFI EXPDO ENFI ENPDO EXFI EXPDO ENFI ENPDO EXFI EXPDO
Modified R2
AIC
BIC
k
MAD
Sum LL
Factor
Function
Factor
Function
Factor
Function
Factor
Function
Factor
Function
Factor
Function
0.59 0.36 0.36 0.54 0.46 0.00 0.24 0.38 0.75 0.36 0.43 0.58 0.08 0.16 0.55 0.38 0.30 0.68 0.18 0.40 0.65 0.69 0.27 0.47
0.77 0.34 0.40 0.55 0.48 0.00 0.54 0.44 0.73 0.35 0.46 0.58 0.16 0.19 0.59 0.38 0.31 0.71 0.18 0.38 0.70 0.69 0.27 0.47
283.24 567.54 270.09 669.78 201.76 256.34 221.32 898.39 504.60 889.90 394.98 2366.50 196.49 351.46 180.52 325.83 150.29 128.89 115.71 152.07 353.17 114.62 306.86 296.96
282.30 568.90 269.98 659.31 203.63 262.80 239.01 915.25 505.24 898.20 393.99 2341.39 198.07 351.63 182.06 327.48 152.14 127.86 117.7 153.57 354.64 114.56 309.90 297.01
287.06 572.72 273.91 655.49 204.72 262.76 233.10 909.34 508.85 894.16 383.74 2362.24 201.36 354.93 183.89 329.20 152.97 131.58 118.44 154.81 358.50 110.76 310.77 300.87
289.95 575.18 277.62 662.13 209.55 265.25 218.37 895.39 509.49 902.45 390.72 2333.13 203.09 358.05 188.80 334.22 157.5 133.22 123.17 159.04 357.03 110.70 313.80 300.91
0.52 0.43 0.62 0.21 0.52 0.71 1.87 0.35 0.48 0.46 1.08 0.27 0.43 0.49 0.15 0.40 1.23 0.14 1.91 0.58 0.73 0.28 1.36 0.63
0.29 0.43 0.59 0.19 0.52 0.58 1.72 0.30 0.48 0.45 1.07 0.25 0.37 0.48 0.14 0.39 1.23 0.12 1.90 0.58 0.69 0.28 1.29 0.63
0.30 0.68 0.69 1.75 0.58 1.04 2.09 2.49 0.45 0.81 1.25 2.10 0.30 0.70 0.25 0.56 0.69 1.10 0.41 1.01 0.54 1.12 0.46 0.90
0.28 0.67 0.67 1.73 0.57 0.98 2.01 2.46 0.44 0.81 1.24 2.09 0.29 0.70 0.25 0.55 0.63 1.09 0.41 1.01 0.52 1.12 0.45 0.90
140.62 283.45 134.05 330.66 99.88 130.40 111.66 450.20 251.62 448.10 195.00 1171.69 98.03 174.82 89.26 161.92 74.14 63.45 56.85 75.03 176.32 58.28 153.95 147.48
139.15 281.77 132.99 336.89 99.82 126.17 121.51 459.63 251.30 443.94 198.55 1184.43 96.25 173.73 89.03 161.74 74.07 61.93 56.85 74.78 175.59 58.31 152.43 147.50
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
9
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
Table 6 e Estimated goodness-of-fitness measures for calibration factors and calibration functions. Freeway faculty type
10
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
deviations and CV values and to create CURE plots (USDOT, 2018b). The calibration is successful when the percent cure deviation is less than 5% or the CV value is less than 0.15 (Lyon et al., 2016). Reviewing either CV values or percent cure deviations for calibration factor, it can be determined that the calibration process was satisfactory. However, most percent cure deviations for calibration factor were much greater than 5% representing biased predictions. Therefore, calibration functions were developed, and the accuracy in crash prediction was compared using CURE plots and several other goodness-of-fit measures. Fig. 2 represents two CURE plots created for fitted values for calibration factor and fitted values for calibration function using data from rural 4-lane freeways. Percent cure deviation indicates the percentage of cumulative residuals lying outside the two standard deviations (±s) of cumulative residuals. The x-axis and y-axis in Fig. 2 represent fitted values and cumulative residuals, respectively. Fitted values are calculated by multiplying the HSM predicted crashes with the estimated calibration factor. The residuals are the difference between observed crashes and predicted crashes. For this specific case, percent cure deviation was only 6% for the developed calibration function. However, the calibrated SPF had 60% of cumulative residuals lying outside the two standard deviations. Likewise, reported percent cure deviations for calibration functions were considerably lower than percent cure deviations for respective calibration factors for all freeway facilities indicating that calibration functions better fitted for Kansas freeway facility data than calibrated HSM-default SPFs. Table 6 provides estimated other goodness-of-fit measures for calibration factor and calibration function by each freeway model. Estimated goodness-of-fit measures include modified R2, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), dispersion parameter (k), and Mean Absolute Deviation (MAD). In addition, the sum of log-likelihood is also presented for both calibration factors and calibration functions. When considering goodness-of-fit measures, smaller values are preferred for MAD, AIC, BIC, and k and larger values are preferred for modified R2. When determining the combined performance, the preferred smallest or largest value of MAD, AIC, BIC, k, and modified R2 for was ranked number 1 to n, where 1 represents the best method and n represents the number of alternative methods. Further, the lowest sum of numeric rankings of all measures was considered as the preferred method following Lyon et al. (2016). However, the decisions are still needed to be made depending on the overall performance of goodness-of-fit measures together with preferred values for percent cure deviation or CV value. Combined results from Tables 5 and 6 indicated calibration functions provided better fitted models to Kansas freeway facility data compared to calibrated HSMdefault SPFs because only a small percentage of cumulative residuals were lying outside the two standard deviation limits and other goodness-of-fit measures such as modified R2, AIC, BIC, MAD, and k even provided a higher ranking for calibration functions, respectively.
6.
Discussion
Calibration of HSM-default SPFs or development jurisdictionspecific SPFs are highly recommended for local jurisdictions to make effective highway safety-related decisions. Furthermore, it is extremely critical to assess the safety effectiveness of an applied new countermeasure to distinguish whether the new countermeasure has helped in reducing crashes (Galgamuwa et al., 2019). In addition, jurisdictions are required to perform the HSM analysis for safety-related road designs such as alignment, shoulder type, etc. (Sun et al., 2018). Reducing major risk factors on highway planning, design, operations, and maintenance decisions may save many valuable lives and several hundred million dollars associated with direct and indirect costs. The importance of having calibrated SPFs or calibration functions for a certain jurisdiction in evaluating safety effectiveness is well explained in a benefit cost analysis conducted by Hachey et al. (2019). Hachey et al. (2019) compared costs and benefits of a new safety countermeasure with the existing condition in view of safety, travel time, travel time reliability, vehicle operating costs, and externalities. The expected average crash frequency was calculated for the existing condition considering weighted average of observed crash frequency and predicted crash frequency. The predicted crash frequency is generally calculated using calibrated SPFs, jurisdiction-specific SPFs, or calibration functions. Then, high-quality CMFs from the CMF clearing house representing safety effects of new countermeasures were extracted and multiplied by the estimated expected crash frequency (USDOT, 2019b). Benefits generated by applying a new safety countermeasure are the change in safety performance, where the safety performance is the estimated long-term average crash frequency and severity. Further, results showed that economical savings associated with reduction of the crash frequency and severity are huge compared to other benefits considered in this study. Accordingly, the calibrated HSM-default SPFs and calibration functions developed in this study could easily be applied or replaced with existing uncalibrated SPFs available in safety management software such as Safety Analyst, IHSDM, or ISATe for more accurate crash predictions in Kansas (Bonneson et al., 2012; Harwood et al., 2010; USDOT, 2019a). As of now, limited research has been performed regarding the HSM calibration procedure for freeway facilities following the issue of the HSM supplement in 2014. The HSM does not deliver methods to collect data to accomplish calibrations as the data reporting systems vary from state to state. Hence, any other jurisdiction could simply practice data collection techniques and evaluation methodologies used in this study.
7.
Conclusions
This study first calibrated the HSM-default freeway facility SPFs to Kansas conditions and further assessed the quality of the calibration process. For this calibration study, 521 freeway
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
segments, 351 entrance-related speed-change lanes, and 366 exit-related speed-change lanes were used. In the case of freeway segments, the HSM methodology overpredicted FI crashes and underpredicted PDO crashes in Kansas. Estimated calibration factors for speed-change lanes indicated the HSM methodology consistently underpredicted both FI and PDO crashes in Kansas. The quality of calibrated HSM-default freeway SPFs was satisfactory considering either the CV value or percent cure deviation. However, percent cure deviations for majority of freeway models were greater than the accepted minimum of 5%. Therefore, for further accuracy and comparison purposes, calibration functions were developed, and the performance of calibrated HSM-default SPFs and calibration functions was compared using numerous goodness-of-fit measures such as percent cure deviation, modified R2, AIC, BIC, MAD and k. The combined results of performance measures showed calibration functions fitted better to Kansas freeway data compared to calibrated HSM-default SPFs mainly due to reported lower percent cure deviation values as shown in Table 5. This study recommends the application of estimated calibration factors and developed calibration functions for all freeway facilities considered for accurate freeway safetyrelated decision making in Kansas. Considering that calibration functions provided a decent reliability, chances are that calibration functions provide more accurate crash predictions. In addition, the use of disaggregate calibration functions and calibration factors are suggested to predict crashes more precisely by each freeway type or speed-change lane type. All crash-related studies experience issues of miscoding, misreporting, incompleteness in reported crash data. Since the value of calibration factor wholly depends up on the number of reported crashes, a certain possibility exists in resulting vague calibration factors. In addition, since few geometric data elements required for the calibration were gathered using Google Earth, therefore, the possibility exits of obtaining inexact geometries.
Conflict of interest The authors do not have any conflict of interest with other entities or researchers.
Acknowledgments This work was ostensibly supported by the Kansas Department of Transportation (KDOT) under the K-TRAN program. Authors are grateful to Mr. Benjamin Ware and Ms. Carla Anderson for providing great assistance as project monitors of this study. In addition, authors would like to acknowledge the support given by Mr. Steven Buckley throughout the study. Authors are thankful to Ms. Elsit Mandal from KDOT for providing data needs for this study. Authors extend their sincere gratitude to Mr. Fouad Alangurli, the undergraduate research assistant for assisting during the data collection process.
11
references
American Association of State Highway and Transportation Officials (AASHTO), 2010. Highway Safety Manual, first ed. AASHTO, Washington DC. American Association of State Highway and Transportation Officials (AASHTO), 2014. Highway Safety Manual Supplement, first ed. AASHTO, Washington DC. Alluri, P., Saha, D., Gan, A., 2016. Minimum sample sizes for estimating reliable highway safety manual (HSM) calibration factors. Journal of Transportation Safety & Security 8 (1), 56e74. Bahar, G., Hauer, E., 2014. User's Guide to Develop Highway Safety Manual Safety Performance Function Calibration Factors. HR 20-7(332). National Cooperative Highway Research Program, Transportation Research Board, Washington DC. Banihashemi, M., 2012. Sensitivity analysis of data set sizes for highway safety manual calibration factors. Transportation Research Record 2279, 75e81. Bayer, H.L., 2004. Hawth's Analysis Tools for ArcGIS. Available at: http://www.spatialecology.com/htools/overview.php (Accessed 15 August 2017). Berry, J.A., 2017. Safety Evaluation of Roundabouts at Freeway Ramp Terminals and HSM Calibration (master's thesis). University of Kansas, Kansas. Bonneson, J.A., Geedipally, S., Pratt, M.P., 2012. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. National Cooperative Highway Research Program Transportation Research Board of the National Academies, Washington DC. Claros, B., Sun, C., Edara, P., 2018. HSM calibration factor, calibration function, or jurisdiction-specific safety modelea comparative analysis. Journal of Transportation Safety & Security, https://doi.org/10.1080/19439962.2018.1477896. ESRI, 2012. ArcGIS Desktop: Release 10.1. Environmental Systems Research Institute, Redlands. Farid, A., Abdel-Aty, M., Lee, J., 2018. A new approach for calibrating safety performance functions. Accident Analysis & Prevention 119, 188e194. Galgamuwa, U., Vahl, C.I., Dissanayake, S., 2019. Role of driver behaviors and environmental characteristics in evaluating safety effectiveness of roadway countermeasures: a novel approach of estimating crash modification factors. Journal of Transportation Safety & Security, https://doi.org/10.1080/ 19439962.2018.1545714. Google Earth, 2018. Google Earth Download. Available at: http:// www.google.com/earth/download/ge/, (Accessed 22 September 2017). Hachey, A., Lawrence, M.F., Gross, F., et al., 2019. Evaluating performance of safety countermeasures: applied benefit cost analysis. In: The 98th Annual Meeting of the Transportation Research Board, Washington DC, 2019. Harwood, D.W., Torbic, D.J., Richard, K.R., et al., 2010. Safety Analysis: Software Tools for Safety Management of Specific Highway Sites. FHWA-HRT-10-063. U.S. Department of Transportation, Washington DC. Hauer, E., 2015. The Art of Regression Modeling in Road Safety 38. Springer, New York. KDOT, 2011. Kansas Data Support-the Data Team. Available at: http://www.ksdot.org/burTrafficSaf/reports/ ksshspdatasupport.pdf (Accessed 17 July 2017). Kim, J., Anderson, M., Gholston, S., 2015. Modeling safety performance functions for Alabama's urban and suburban arterials. International Journal of Traffic and Transportation Engineering 4 (3), 84e93. Kononov, J., Lyon, C., Allery, B.K., 2011. Relation of flow, speed, and density of urban freeways to functional form of a safety
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001
12
J. Traffic Transp. Eng. (Engl. Ed.) xxxx; xxx (xxx): xxx
performance function. Transportation Research Record 2236, 11e19. Lu, J., Haleem, K., Gan, A., et al., 2014. Safety performance functions for Florida's freeways. In: The T&DI Congress 2014: Planes, Trains, and Automobiles, Florida, 2014. Lyon, C., Persaud, B., Gross, F., 2016. The Calibrator: an SPF Calibration and Assessment Tool User Guide. FHWA-SA-17016. FHWA, Washington DC. Shin, H., Lee, Y.J., Dadvar, S., 2014. The Development of Local Calibration Factors for Implementing the Highway Safety Manual in Maryland. MD-14-SP209B4J. Maryland State Highway Administration, Baltimore. Shin, H., Lee, Y.J., Dadvar, S., et al., 2016. The Development of Local Calibration FactorsePhase II: Maryland Freeways and Ramps. MD-16-SHA-MSU-4-6. Maryland State Highway Administration, Baltimore. Smith, S., Carter, D., Srinivasan, R., 2017. Updated and Regional Calibration Factors for Highway Safety Manual Crash Prediction Models. FHWA/NC/2016-09. FHWA, Washington DC. Spatial Techniques, 2019. ET GeoWizards for ArcGIS. Available at: https://www.ianko.com/ETGeoWizards.html (Accessed 22 September 2017). Srinivasan, R., Carter, D., 2011. Development of Safety Performance Functions for North Carolina. FHWA/NC/201009. FHWA, Washington DC. Srinivasan, R., Carter, D., Bauer, K., 2013. Safety Performance Function Decision Guide: SPF Calibration vs SPF Development. FHWA-SA-14-004. FHWA, Washington DC. Srinivasan, R., Colety, M., Bahar, G., et al., 2016. Estimation of calibration functions for predicting crashes on rural twolane roads in Arizona. Transportation Research Record 2583, 17e24. Sun, C., Edara, P., Brown, H., et al., 2013. Calibration of the Highway Safety Manual for Missouri. Cmr14-007. Missouri Department of Transportation, Mid-America Transportation Center, Missouri. Sun, C., Edara, P., Brown, H., et al., 2016a. Highway Safety Manual Applied in Missouri e Freeway/Software. Cmr16-009. Missouri Department of Transportation, Mid-America Transportation Center, Missouri. Sun, C., Edara, P., Brown, H., et al., 2016b. Crash Location Correction for Freeway Interchange Modeling. Cmr16-010. Missouri Department of Transportation, Mid-America Transportation Center, Missouri. Sun, C., Edara, P., Brown, H., et al., 2018. Missouri Highway Safety Manual Recalibration. Cmr18-001. Missouri Department of Transportation, Mid-America Transportation Center, Missouri. Trieu, V., Park, S., McFadden, J., 2014. Use of Monte Carlo simulation for a sensitivity analysis of highway safety manual calibration factors. Transportation Research Record 2435, 1e10.
USDOT, 2018a. HPMS Public Release of Geospatial Data in Shapefile Format. Available at: https://www.fhwa.dot.gov/ policyinformation/hpms/shapefiles.cfm (Accessed 20 June 2018). USDOT, 2018b. Roadway Safety Data Program. Available at: https://safety.fhwa.dot.gov/rsdp/toolbox-content.aspx? toolid¼150 (Accessed 20 June 2018). USDOT, 2019a. Interactive Highway Safety Design Model (IHSDM): Overview Available at: https://highways.dot.gov/safety/ interactive-highway-safety-design-model/interactivehighway-safety-design-model-ihsdm (Accessed 15 July 2019). USDOT, 2019b. Crash Modification Factors Clearinghouse. Available at: https://safety.fhwa.dot.gov/tools/crf/resources/ (Accessed 15 July 2019). Vargas, H., Raihan, A.P., Alluri, P., et al., 2019. Jurisdiction-specific versus SafetyAnalyst-default safety performance functions: a case study on two-lane and multi-lane arterials. In: The 98th Annual Meeting of the Transportation Research Board, Washington DC, 2019.
Imalka C. Matarage, B.Sc. Eng. (Hons), M.Eng, is a PhD candidate in the Department of Civil Engineering at Kansas State University. Her dissertation research focusses on calibration of the Highway Safety Manual freeway and ramp crash prediction models to Kansas conditions. Her research interests include studies on highway safety, crash data analysis, traffic flow modeling and simulation, and design and analysis of roundabouts. She earned her bachelor's degree in civil and infrastructure engineering and master's degree in transportation engineering from Asian Institute of Technology, Thailand.
Sunanda Dissanayake, PhD, P.E., F. ASCE, is a professor of civil engineering and associate dean of Graduate School at Kansas State University. Her research focuses on studies related to solving applied and practical problems related to transportation engineering, with emphasis on traffic operations and safety of the highway mode. She has authored and co-authored more than 50 journal papers and presented more than 165 papers at national, international, and regional conferences, most of which are proceedings papers. She is a member of two journal editorial boards, a member of two TRB technical committees, and the chair of the Transportation Safety Committee of ASCE/T&DI.
Please cite this article as: Matarage, I.C., Dissanayake, S., Quality assessment between calibrated highway safety manual safety performance functions and calibration functions for predicting crashes on freeway facilities, Journal of Traffic and Transportation Engineering (English Edition), https://doi.org/10.1016/j.jtte.2019.12.001