development of accident prediction models for rural highway intersections_oh

Transportation Research Record: Journal of the Transportation Research Board,No. 1897, TRB, National Research Council, Washington, D.C., 2004, pp. 1827.

18

A study was done to develop macrolevel crash prediction models that canbe used to understand and identify effective countermeasures for improv-ing signalized highway intersections and multilane stop-controlled high-way intersections in rural areas. Poisson and negative binomial regressionmodels were fit to intersection crash data from Georgia, California, andMichigan. To assess the suitability of the models, several goodness-of-fitmeasures were computed. The statistical models were then used to shedlight on the relationships between crash occurrence and traffic and geo-metric features of the rural signalized intersections. The results revealedthat traffic flow variables significantly affected the overall safety perfor-mance of the intersections regardless of intersection type and that the geo-metric features of intersections varied across intersection type and alsoinfluenced crash type.

Transportation is vital to both economic success and quality of lifein urban and rural areas. However, the rapid growth of city popula-tions and corresponding vehicle miles of travel, commerce, andtransportation infrastructure has generated such negative effects ascongestion, deterioration of air quality, noise, and motor vehiclecrashes. According to NHTSA, there were 6,322,795 traffic crashesin 2001 (1). A fatal crash occurred every 13 min on average. Thesestatistics emphasize why traffic safety remains a major concern of thetraveling public and why traffic safety improvements are needed.

To improve traffic safety, each element of the roadway trans-portation system should be examined. Representing conflict pointsin the road network, intersections have received and should continueto receive considerable attention, since intersections continue to rep-resent crash-prone locations on a transportation network. Whenapproaching intersections, drivers are confronted with a complexdriving task that includes observing and responding to traffic controldevices, reacting to these devices by stopping, reducing speed, orproceeding without delay, executing turns, observing and reacting topedestrians and bicyclists, and avoiding conflicts with other vehicles.Adding further complexity are drivers that disobey traffic controldevices, most notably significant red-light-running violations in manystates. The complex vehicle movements at intersections lead to traf-fic conflicts. A subset of conflicts lead to crashes. Thus, intersectionsafety is a high priority in local, regional, and state traffic agenciesand among transportation researchers and academicians.

Considerable research has concentrated on identifying the safetyeffects of accident countermeasures. Inconsistency of findings across

studies, however, presents difficulties in understanding and esti-mating the safety effects of countermeasures. Furthermore, littleresearch has been done to identify and understand factors that con-tribute to accidents on multilane stop-controlled and signalizedhighway intersections in rural areas. Several accident predictionmodels (24) have provided limited knowledge on the safety effectsof traffic flow and geometric designrelated countermeasures forrural multilane stop-controlled and signalized intersections. Thesecrash prediction models, furthermore, may be inaccurate acrossjurisdictions because the estimation data were limited in number ofexplanatory variables, geographical diversity of the intersections,and overall sample size.

This research presents the estimation results of statistical crashprediction models based on larger sample sizes, greater geographi-cal diversity, and a larger set of explanatory variables than in previ-ous research efforts. Statistical models are discussed for the followingthree intersection types in rural areas:

Three-legged intersections with major-road four-lane andminor-leg two-lane stop-controlled intersections, Four-legged intersections with major-road four-lane and

minor-leg two-lane stop-controlled intersections, and Signalized intersections with both major- and minor-road two-

lane intersections.

The accident prediction models were calibrated for total accidentsand injury (fatal and nonfatal injury) accidents within 250 ft of theintersection center and were used to identify traffic flow and designcountermeasure safety effects for these rural intersections.

DATA DESCRIPTION

The data for the study were based on a total of 136 three-legged and124 four-legged stop-controlled multilane and 100 four-legged sig-nalized highway intersections in rural areas. The data used for modelcalibration were obtained from two sources. The calibration data wereobtained from the California and Michigan Highway Safety Informa-tion System. The crash and other data were available from 1993 to1998. The second source of data was the state of Georgia. Four datasources were used to study Georgia intersections: crash files, roadwaycharacteristic (RC) files, aerial photographs, and geographic infor-mation system (GIS) maps. Crash and RC files were available for1996 and 1997. RC files provided detailed information on road char-acteristics. Digital orthophotography quarter-quadrangles (DOQQs)aerial photos were used from 1994 and 2000 to extract informationabout intersection angle and degree of horizontal curvature of selectedintersections by overlapping with GIS roadmaps. Table 1 summarizesthe sources of data used for the models.

Development of Accident PredictionModels for Rural Highway Intersections

Jutaek Oh, Simon Washington, and Keechoo Choi

J. Oh, Korea Transportation Institute, Ilsan 411-701, Republic of Korea. S. Wash-ington, Department of Civil Engineering, University of Arizona, Tucson, AZ 85721-0072. K. Choi, Department of Transportation Engineering, Ajou University, Suwon442-749, Republic of Korea.

Oh, Washington, and Choi 19

Number of SitesNumber of

Total/Injury Accidents

State Years of

Data 3-

Legged 4-

Legged Signalized 3-

Legged 4-

Legged Signalized California 1991-1998 60 54 18 427/196 478/268 507/200Michigan 1993-1997 24 18 31 248/63 277/92 1262/159Georgia 1996-1997 52 52 51 124/56 222/104 489/118

TABLE 1 Data Sources

On the basis of underlying theories of crash causation and toestablish a suitable statistical model that enabled the examination ofpossible relationships among accident frequencies, geometric, andtraffic characteristics of intersections, 53 possible explanatory vari-ables were considered. Traffic volumes, including left-, right-, andU-turn volumes, were estimated from annual average daily traffic(AADT). Geometric elements included vertical and horizontalcurves, sight distances, hazard ratings around the intersection, ter-rain, presence of exclusive left- and right-turn lanes, lane and shoul-der widths, median types and widths, driveway intensity, and signalcontrol types. Driving characteristics, such as peak period left-turn,right-turn, and through traffic percentages and peak period truckpercentages, were also included.

Table 2 describes the variables available in the analysis, theirunits, and the abbreviation used in model estimation results. Tables3, 4, and 5 give the summary statistics of the variables discussed inthis paper. Summary statistics of all variables considered for modelingare available elsewhere (5).

MODEL CALIBRATION METHODS

This section briefly presents the statistical methods used for cali-brating the crash prediction models. The basic statistical backgroundand general model forms of Poisson and negative binomial regres-sion models are provided. Additional information on count modelsis available elsewhere (6 ).

Poisson Model

Since the occurrences of accidents at intersections are relatively rarediscrete events, the Poisson model is a natural choice. On the assump-tion that the number of accidents, Yi, follows a Poisson distribution, thegeneral form of the expected number of accidents occurring at the ithintersection with m intersection parameters, Xi1, Xi2, Xi3, . . . , Xim, is

where j are estimated regression coefficients.In the case of a Poisson regression model, the model coefficients

are estimated by using the maximum likelihood method (7 ). Thelikelihood function for the Poisson regression model is given by

The maximum possible value of the likelihood function for agiven data set occurs if the model fits the data exactly. This occursif i is replaced by yi, as shown in the likelihood equation

L f Y X XYi ii

ni

Yi

ii

n i

( ) = ( ) = ( )[ ] ( )[ ]= =

1 1

, exp ,!

exp expY X X X X Xi m m j jj

m

= + + + +( ) =

=

0 0 1 1 2 20

L

In practice, crashes do not fit a Poisson process exactly because(a) the exact relationships between explanatory variables and crashesare unknown and approximated, (b) crashes are stochastic, (c) someinsignificant but real explanatory variables may be omitted, and(d ) some significant explanatory variables may be omitted (but it ishoped not). For these reasons, a maximum value of the likelihoodfunction is sought.

Negative Binomial Model

The negative binomial distribution can be used to relax the limita-tion of the Poisson distribution requirement that the mean equals thevariance of the distribution. In Poisson regression models used formodeling crash occurrence, if the variance of the data exceeds theestimated mean of the data, then the data are said to be overdispersed.Overdispersion occurs in practice because the crash means varyacross segments (road, intersections, ramps, etc.) as a consequenceof unobserved heterogeneity. In these cases, the negative binomialprovides an appealing alternative for dealing with overdispersionin crash data. Similar to the Poisson model, the negative binomialregression model relates the expected number of accidents occur-ring at the ith element with q explanatory variables, Xi1, Xi2, . . . , Xiq,as follows:

However, the negative binomial regression model results in aquadratic term added to the variance repressing overdispersion. Thenegative binomial model takes the form

where K is the overdispersion parameter and the variance is givenby

As a result, the negative binomial regression model accommo-dates extra-Poisson variation because of unobserved heterogeneity.If overdispersion, K, equals 0, the negative binomial model reducesto the Poisson model. The larger the value of K, the more variabil-ity there is in the data beyond that associated with the mean i. Forthe Poisson model, the coefficients j are estimated by maximizingthe log-likelihood loge L(). For the negative binomial distribu-tion, the estimated coefficient vector and yi, along with an estimateK for K, are obtained by maximizing loge L(, K ):

Var y E y KE yi i i( ) = [ ] + [ ]2

P y y Ky Ki

i

i

y

y K

i

i( ) = + ( )

( ) +( ) +1

1 1!

! !

Function i i i q iqX X X( ) = + + + +0 1 1 2 2 L

( )

= +( ) =loge i i ii

L y X 0

20 Transportation Research Record 1897

Variable Abbreviation Variable Description

AADT1 Annual average daily traffic on major road (vehicles per day) AADT2 Annual average daily traffic on minor road (vehicles per day) COMDRWY1 Commercial driveways on major road within 250 feet of the

intersection center HAU Intersection angle variable defined where the angle between the

major and minor roads is measured from the far side of the minor road:

3-Legged Intersections angle-90 if minor road is to the right of the major road in the

increasing direction 90-angle if minor road is to the left of the major road in the

increasing direction 4-Legged Intersections

(right angle - left angle)/2 HAZRAT1 Roadside hazard rating on major road within 250 feet of the

intersection (from 1, least hazardous case, to 7, most hazardous case) HI Sum of degree of curve in degrees per hundred feet of each horizontal

curve on major road any portion of which is within 250 feet of the intersection center divided by the number of such curves

HEI1 Sum of degree of curve in degrees per hundred feet of each horizontal curve on major road within 800 feet of the intersection center divided by the number of such curves

HEI2 Sum of degree of curve in degrees per hundred feet of each horizontal curve on minor road within 800 feet of the intersection center divided by the number of such curves

HEICOM (1 / 2) (HEI1 + HEI2) LIGHT Light at intersection (0 = no, 1 = yes) MEDTYPE Median type on major road (0 = no median, 1 = painted, 2 = curbed, 3

= others) MEDWDTH1 Median width on major road (feet) PKLEFT Left-turn percentage during the peak hour (%) PKLEFT1 Left-turn percentage on major road during the peak hour (%) PKLEFT2 Left-turn percentage on minor road during the peak hour (%) PKTHRU2 Through percentage on minor road during the peak hour (%) PKTRUCK Truck percentage passing through the intersection during the peak

hour (%) PKTURN Peak turning percentage (%) SDR2 Right-side sight distance on minor road (feet) SPD1 The average posted speed on major road in vicinity of the intersection

(mph) SPD2 The average posted speed on minor road in vicinity of the intersection

(mph) VEI1 Sum of absolute change of grade in percent per hundred feet for each

curve on major road any portion of which is within 800 feet of the intersection center, divided by the number of such curves

VEI2 Sum of absolute change of grade in percent per hundred feet for each curve on minor road any portion of which is within 800 feet of the intersection center, divided by the number of such curves

VEICOM (1 / 2) (VEI1 + VEI2)

TABLE 2 Analysis Variables

Model Validation Methods

Note that only through the assessment of several goodness-of-fit cri-teria can an objective statement be made about the performance of

log ,

log log log

log log !

e

e jjy

e i i e i

i i i

i

L K

K Ky y

yK

K y

i

( ) =+( )( ) +( ) +

+ +( ) ( )

=

1 1

1 1

0

a particular model or set of models. The goodness-of-fit measuresused in this research are Pearson product-moment correlation co-efficients, mean prediction bias (MPB), mean absolute deviation(MAD), and overdispersion.

Pearson Product-Moment Correlation Coefficients

The Pearson product-moment correlation coefficient, usually denotedr, is an example of a correlation coefficient. It is a measure of thelinear association between two variables Y1 and Y2 that have beenmeasured on interval or ratio scales and is given by

Variables Frequency Mean Median Minimum MaximumTOTAL accidents per year 136 1.35 0.80 0.00 10.60INJURY accidents per year 136 0.55 0.33 0.00 4.00AADT1 136 13011 12100 2360 33333AADT2 136 709 430 15 9490MEDTYPE on major road No median Painted Curbed Other

136 69(50.7%) 45(33.1%) 14(10.3%)

8(5.9%) MEDWIDTH1 136 12.6 6 63HAU 136 1.3 0

0-65 90

HAZRAT1 1 2 3 4 5 6 7

136 16(11.8%) 58(42.6%) 26(19.1%) 25(18.4%)

8(5.9%) 2(1.5%) 1(0.7%)

COMDRWY1 136 1.5 0 0 14SPD1 136 52.5 55 30 65LIGHT 0 1

136 97(71.3%) 39(28.7%)

HEI1 136 2.01 0.73 0 26.63VEI1 136 0.9 0.6 0.0 6.7PKTRUCK 84 9.15 7.79 1.18 28.16PKTURN 84 6.68 4.28 0.27 53.09PKLEFT 84 3.28 2.16 0.13 25.97PKLEFT2 84 55.31 60.29 0.00 100.00SDR2 136 1428 1555 80 2000

TABLE 3 Summary Statistics for Three-Legged Stop-Controlled Multilane Intersections

Variables Frequency Mean Median Minimum MaximumTOTAL accidents per year 124 2.0 1.4 0.0 10.8INJURY accidents per year 124 0.9 0.5 0.0 5.7AADT1 124 12881 11496 3150 73799AADT2 124 621 430 21 2990MEDTYPE on major road 0: No median 1: Painted 2: Curbed 3: Other

124 70(56.5%) 27(21.8%) 22(17.7%) 5(4.0%)

MEDWDTH1 124 16.1 6.5 0 60HAZRAT1 1 2 3 4 5 6

124 24(19.4%) 43(34.7%) 32(25.8%) 21(16.9%) 2(1.6%) 2(1.6%)

COMDRWY1 124 0.6 0 0 12LIGHT 124 0 1

87(70.2%) 37(29.8%)

VEI1 124 0.87 0.35 0.00 12.50HEI 124 3.28 0.60 0.00 233.33HAU 124 1.5 0 -50 55SPD1 124 55.6 55 25 65SPD2 124 34.7 35 25 55PKTRUCK 72 10.95 8.36 1.75 37.25PKTURN 72 9.47 6.56 0.00 48.52PKLEFT 72 4.80 3.08 0.00 25.26PKTHRU2 72 15.69 10.82 0.00 68.09PKLEFT2 72 38.89 36.66 0.00 100.00SDR2 124 1329 1354 215 2000

TABLE 4 Summary Statistics for Four-Legged Stop-Controlled Multilane Intersections

where Y is the mean of the Yi observations.

MPB

The MPB statistic provides a measure of the magnitude and directionof the average model bias compared to validation data. The smallerthe average prediction bias the better the model is for predictingobserved data:

where n is the validation data sample size and Y is the fitted value Y.

MAD

MAD provides a measure of the average misprediction of themodel. It differs from MPB in that positive and negative predic-tion errors will not cancel each other. A value close to zero sug-gests that on average the model predicts observed data well. It isgiven by

MPB =

( )=

Y Yn

i ii

n

1

rY Y Y Y

Y Y Y Yi i

i i

121 1 2 2

1 12

2 22 1 2=

( )

( )

( )

( )[ ]


Overdispersion (K)

Overdispersion in a Poisson model causes underestimation of thevariance of the model coefficients. This results in overstating thesignificance of the coefficients. The deviance of the model contain-ing all the parameters (including the intercept) divided by its degreesof freedom, n-p, provides a test for over- or underdispersion and ameasure of fit of the model. Evidence of underdispersion or over-dispersion indicates inadequate fit of the Poisson model. For thePoisson regression model, the model deviance is as follows:

MODEL CALIBRATION AND INTERPRETATION

The crash prediction models were estimated by using LIMDEPeconometric software. The models include many theoretically appeal-ing variables to explain as much variation in crash occurrence as pos-sible, given knowledge of crash causation and the available set of

DEV . . logX X X Y Y Yp i ei

ni

ii i

i

n

0 1 11 1

2, , . ,

= =

( ) = ( )

MAD =

=

Y Yn

i ii

n

1

Variables Frequency Mean Median Minimum MaximumTOTAL accidents per year 100 5.9 5.3 0.0 26.5INJURY accidents per year 100 1.8 1.5 0.0 6.5AADT1 100 9126 8700 430 25132AADT2 100 3544 3100 420 12478MEDTYPE on major road 0:No median 1:Painted 2:Other

100 87(87%) 12(12%) 1(1%)

MEDWDTH1 100 1.3 0 0 13HAZRAT1 1 2 3 4 5 6 7

100 12(12%) 29(29%) 27(27%) 16(16%) 13(13%) 3(3%) 0(0%)

COMDRWY1 100 2.64 2 0 11LIGHT 0 1

100 29(29%) 71(715)

SDR1 51 822 798 103 2000VEI1 100 1.45 1.19 0.00 11.97HEI 100 3.95 0.61 0.00 94.87HEICOM 100 2.56 0.58 0.00 32.54HAU 100 0.07 0.00 -45.00 40.00SPD1 100 45.2 45 25 65SPD2 100 40.9 40 20 55PKTRUK 49 8.96 7.71 2.69 45.43PKTURN 49 35.64 34.48 7.07 72.66PKTHRU2 49 43.90 41.99 8.45 84.09PKLEFT 49 18.17 17.97 4.20 37.07PKLEFT2 49 28.21 24.88 2.59 75.73

TABLE 5 Summary Statistics for Signalized Intersections

potential explanatory variables. The best models discussed in the fol-lowing section were selected by comparing several candidate models.When all candidate models were compared, the goodness-of-fit mea-sures discussed previously were used, in addition to inspection andtheoretical appeal of model coefficients and their associated statisticalsignificance. A detailed discussion of these comparison and selectionactivities was provided by Washington et al. (5).

During model selection an alpha (probability of a Type I error)equal to 0.10 was used. Model results are presented in Tables 6 and 7.The model findings agree with results of previous studies and alsoshed new light on the effect of countermeasures on intersectionsafety. The following sections describe the implications of themodeling results for each of the explanatory variables.

Traffic Flow and Safety

In agreement with numerous studies, traffic volumes are the moststable and reliable predictor of crash occurrence at intersections.Results showed that crash frequency increased with higher log(AADT) on major and minor roads for the three intersection and twoaccident types investigated. Coefficients relating crash frequenciesto the major-road AADT ranged between 0.5 and 0.9 and reflect thenonlinear relationship between traffic volume and crashes with thelog transformation. The estimated coefficients are between 0.2 and


0.3 for minor-road AADT, reflecting the relative influence of majorand minor-road AADT on crashes at intersections. The resultsreveal that the turning volume percentages are significant for three-legged, or T, intersections for injury crashes.

Driveways and Safety

The number of commercial driveways on the major within 250 ft ofthe intersection is associated with higher crash frequencies for three-legged stop-controlled multilane intersections and signalized inter-sections. To interpret the safety effect of commercial drivewaydensity, it is important to understand what types of accidents occurat commercial driveways. Numerous research studies have beenconducted into the nature of traffic accidents that occur near drive-ways. Although the results of previous studies vary considerably(24), a common conclusion is that entering and exiting turningvehicles are involved in most driveway-related crashes. Thus, it isthe presence of additional conflict points near intersections that isassociated with crashes. The modeling results revealed that three-legged stop-controlled multilane intersections and signalized inter-sections had significant commercial driveway effects, whereasfour-legged stop-controlled multilane intersections did not. A pos-sible reason for the difference is the high correlation between peakturning movements and commercial driveway density. For four-

Variables

3-legged Intersection

(s.e., p-value)


(s.e., p-value)

Signalized Intersection

(s.e., p-value)

Intercept -10.1914

(1.5232,0.0000)-7.4713

(1.8930,0.0001)-5.1527

(1.8653,0.0057)

LOG of AADT1 0.8877

(0.1666,0.0000)0.7350

(0.1849,0.0001)0.4499

(0.1968,0.0223)

LOG of AADT2 0.3228

(0.0585,0.0000)0.2390

(0.0926,0.0099)0.2699

(0.0767,0.0004)

COMDRWY1 0.0681

(0.0281,0.0154)0.0539

(0.0304,0.0757)

VEI1 0.1081

(0.0556,0.0519)

HAU 0.0101

(0.0059,0.0861)

MEDWDTH1 -0.0106

(0.0060,0.0760)

MEDTYPE1 -0.3209

(0.1771,0.0700)

SDR2 -0.0003

(0.0001,0.0403)

PKTRUCK -0.0479

(0.0110,0.0000)

PKLEFT 0.0229

(0.0118,0.0525)

SPD1 0.0177

(0.0090,0.0482)

HEICOM -0.0288

(0.0153,0.0597)

LIGHT -0.2938

(0.1837,0.1098)

Overdispersion, K 0.4229

(0.1064,0.0001)0.4001

(0.0958,0.0000)0.4019

(0.0765,0.0000)Pearson product-moment correlation coefficients 0.70 0.77 0.77

MPB/year 0.09 0.12 -0.02MAD/year 0.84 1.16 2.90

TABLE 6 Parameter Estimates for Total Accident Main Models

legged stop-controlled multilane intersections and signalized inter-sections, correlations between peak turning movements and com-mercial driveway density were statistically significant, whereas therewas no significant correlation for three-legged stop-controlled multi-lane intersections. This indicates that peak turning movements havegreater explanatory power than commercial driveway density for four-legged stop-controlled multilane intersections, and vice versa forsignalized intersections. Another possible reason is the observednegative correlation between driveway density and channelizationat intersections. Compared to three-legged stop-controlled multilaneintersections (64% of the sites had left-turn lanes onto a major road),four-legged stop-controlled multilane intersections (77% of the siteshad left-turn lanes onto a major road) were relatively well channel-ized, which suggests that high access management decreases poten-tial conflict points near intersections, which in turn decreases left-turncrash frequencies. Since access management involves managingtraffic movements into and out of commercial driveways, these find-ings support the notion that effective access management can improvesafety near intersections.

Presence of Trucks and Safety

The modeling results suggest that the influence of truck volume per-centages on safety is different for stop-controlled intersections and


signalized intersections. For three- and four-legged stop-controlledmultilane intersections, higher peak truck percentages are associatedwith lower frequency of crashes, and the opposite is true for signal-ized intersections. A possible explanation for this lies in the operationof stop-controlled versus signalized intersections. At stop-controlledintersections, trucks enter an intersection while vehicles on alterna-tive approaches wait until the intersection is clear before proceeding.Truck drivers are spared gap-acceptance maneuvers at stop-controlledintersections and simply wait their turn. At signalized intersections,truck drivers are routinely forced to determine an acceptable timegap in traffic to execute turns, which results in potential conflictswith oncoming traffic. In addition, commercial trucks can take longerto execute a maneuver (e.g., a left turn) than the clearance time pro-vided by yellow and all-red phases, which results in potential conflictswith perpendicular traffic.

For both three- and four-legged stop-controlled intersections,the injury accident models included the peak truck percentagevariable, whereas the variable was significant only in the total acci-dent model for four-legged stop-controlled intersections. Peak truckpercentage is negatively correlated with traffic flow on three- andfour-legged stop-controlled multilane intersections, suggesting per-haps that truck drivers in general seek rural routes with low trafficvolumes on average.

Finally, the model coefficient of the peak truck percentage vari-able for the total accident model is lower than the same coefficient

Variables


(s.e., p-value)


(s.e., p-value)

Signalized Intersection

(s.e., p-value)

Intercept -10.6443

(2.0474,0.0000)-7.3927

(2.1279,0.0005)-9.0707

(1.9064,0.0000)

LOG of AADT1 0.8498

(0.2097,0.0001)0.5008

(0.2186,0.0220)0.6697

(0.1899,0.0004)

LOG of AADT2 0.2188

(0.0949,0.0212)0.3027

(0.1341,0.0240)0.2509

(0.0929,0.0069)

COMDRWY1 0.0627

(0.0353,0.0756)

HAZRAT1 0.1889

(0.0923,0.0407)

HAU 0.0163

(0.0053,0.0021)

PKTRUCK -0.0253

(0.0135,0.0605)-0.0520

(0.0127,0.0000)

PKTURN 0.0254

(0.0135,0.0592)

PKLEFT1 0.0523

(0.0128,0.0000)

SPD1 0.0397

(0.0093,0.0000)

SPD2 0.0289

(0.0145,0.0465)

HEI2 -0.0284

(0.0126,0.0244)

LIGHT -0.3985

(0.1702,0.0192)

Overdispersion, K 0.5102

(0.1426,0.0003)0.4671

(0.1296,0.0003)0.2360

(0.0958,0.0138)Pearson product-

moment correlation coefficients 0.71 0.68

MPB/year 0.05 0.00

MAD/year

0.66

-0.05

0.43 0.65 0.98

TABLE 7 Parameter Estimates for Injury Accident Main Models

for the injury accident model. These findings agree with results ofresearch by Vogt and Bared (3) and Miaou et al. (8), who found thathigher percentages of truck traffic are associated with fewer truckcrashes and fewer crashes on rural roads. However, this finding doesnot apply for signalized intersections. Relating to the earlier discus-sion about truck maneuvers, about 40% of the total maneuvers at signalized intersections were turning movements, compared toabout 6% and 10%, respectively, for three- and four-legged stop-controlled multilane intersections.

Vertical Curves and Safety

Researchers have examined the effect of vertical curves on safetybut did not establish a clear relationship between vertical curves andaccident frequency (Hauer, unpublished draft, 2001). In addition,significant safety effects of vertical curves on total crashes wereestablished only at three-legged stop-controlled multilane ruralintersections. A possible explanation is that vertical curves at ruralhighway intersections in the data set consist of minor initial grades,and adequate sight distance to the intersections is provided. Aninteresting observation is the correlations among the roadside haz-ard rating, posted speed, and vertical curvature on major road. Forfour-legged stop-controlled multilane intersections and signalizedintersections, vertical curves are significantly negatively correlatedwith sight distance and posted speed limit. Because the models forthese intersection types include these variables, sight distance andposted speed limit appear to have greater explanatory power forcrash frequency than vertical curves for four-legged stop-controlledmultilane intersections and signalized intersections. In short, theeffect of vertical curvature may be accounted for in these modelsindirectly.

Intersection Angle and Safety

Inspection of the final negative binomial regression models re-veals that an intersection angle that departs from a 90 angle is, inaccord with expectation, detrimental to safety at three-legged stop-controlled multilane intersections. Engineering judgment suggeststhat sight-distance restrictions, difficulty in maneuvers, and incon-sistency with driver expectation because of skew angles lead toreduced safety. However, skew angle was not found to be a signif-icant factor at four-legged stop-controlled multilane intersectionsand signalized intersections. A possible explanation is that trafficmaneuvers at four-legged stop-controlled intersections are morecomplex than at three-legged intersections, and drivers are morecautious. Another likely explanation is that skew angles are, onaverage, more severe at three-legged intersections and are morelikely to affect safety adversely.

Finally, for signalized intersections, intersection angle has a rel-atively smaller effect on safety than for stop-controlled intersectionsbecause the traffic signal manages conflicting vehicles and hencedrivers are provided greater traffic control.

Horizontal Curves and Safety

Numerous studies have examined the relationship between hori-zontal curves and safety (Hauer, unpublished draft, 2001). Unlike


crashes on roadway segments, intersection crashes are defined asthose crashes occurring within 250 ft of an intersection center.This relatively small crash region suggests that safety effects ofhorizontal curves differ from those for roadway segments becausemost crashes at intersections occur from turning or stoppingmaneuvers. The analysis presented here revealed that for three-and four-legged stop-controlled multilane highway intersections,a horizontal curve is not a significant contributor to the number ofobserved accidents. Similar to that for vertical curves, this findingmay be an indication that horizontal curves at existing rural high-way intersections are constrained to be mild in that they possesssmall central angles, large radii, and little to no superelevation, andin general they do not represent significant safety problems.According to the summary statistics for three- and four-leggedintersections, the average horizontal curves of major roads are 2(2,870 ft for radius) and 3.3 (1,740 ft for radius) per 100 ft,respectively. These statistics indicate that horizontal curves atmost of the three- and four-legged intersections examined in thisresearch are larger than the minimum horizontal curve radiusguidelines provided by AASHTO (9). At signalized intersections,horizontal curves have positive safety effects for both total andinjury crashes. It is hypothesized that on average, drivers reducespeeds when encountering sharp horizontal curves near intersections,and driver attentiveness is relatively high.

Speed and Safety

Although the role of speed in crashes is a primary concern insafety, the effect of average speed on safety is murky. Numerousstudies have demonstrated positive and negative safety effects ofspeed (1012). Some studies indicate that fast speeds are not haz-ardous and perhaps are safer because turning or lane-changingmaneuvers occur more frequently when the average speed of traf-fic is lower. Other studies revealed that higher speeds considerablyincrease crash involvement because speeding reduces the distancein which drivers can react and avoid crashes and lengthens stop-ping distances, which in turn increases both the likelihood of crash-ing and the severity of crashes. The findings in this research suggestthat the safety effects of speed are different across intersection andaccident types.

For both three- and four-legged stop-controlled multilane inter-sections, the frequency of total accidents is not consistently relatedto speed. This is probably because turning maneuvers at stop-controlled intersections are controlled by a stop sign, so that a driveron a minor road must stop or at least reduce vehicle speed beforeentering the intersection, which indicates that the driver may havetime to avoid possible conflicts with oncoming traffic on a majorroad. When three- and four-legged intersections are compared, higherspeed increases injury accidents only at four-legged stop-controlledintersections, presumably because of increased turning maneuversat four-legged stop-controlled intersections. For four-legged stop-controlled intersections, turning activities are one of the factors thatincrease accidents, and these intersections experienced about twicethe proportion of turning movements as three-legged intersectionson average. For signalized intersections, the research revealed neg-ative safety effects of speed for both total and injury crash frequen-cies. For both intersection types, the speed of the oncoming vehiclesmay be a factor in crashes because higher speeds of oncoming traf-fic make it more difficult for other vehicle drivers to judge the

amount of time and distance required to safely negotiate an inter-section. The inconsistency of the effect of speed across crash andintersection type is also related to the incongruence between postedand actual speeds and the importance of variance in speeds in crashoccurrence.

Medians and Safety

The analysis suggests that painted medians are associated with lowerfrequencies of accidents for three-legged intersections and totalcrashes. Similarly, median widths are negatively related to crash fre-quencies for three-legged stop-controlled intersections. No safetyeffects were observed for curbed medians for all intersection andaccident types. Curbed medians have a trade-off safety effect: plac-ing a curb in the median will largely reduce cross-median accidentsbut may increase sideswipe crashes and crashes that result from vehi-cles being deflected back into the traffic stream. Hence, the net effectof placing a curb in the median is unclear for rural highway intersec-tions. The effect of medians in this research is unclear and is proba-bly the consequence of inconsistencies in median treatment acrossstatesfor example, medians installed in response to crash histories,access management policies, or traffic volumes.

Turning Maneuvers and Safety

Turning maneuvers have been shown to have significant effects onintersection safety because turning vehicles result in conflicts withoncoming traffic, and vehicles slowing to turn cause conflicts withfollowing vehicles. This analysis supports that turning maneuverssignificantly affect safety at three- and four-legged stop-controlledmultilane intersections. For three-legged intersections, vehicle turn-ing percentage was significant for injury accidents, and left-turningmaneuvers were significant contributors for both total and injuryaccidentswith increased percentages associated with increasedcrash frequencies. However, turning maneuvers did not reveal sig-nificant safety effects for signalized intersections. These findings areconsistent with engineering expectationsuperior control of left-turn movements is often part of the justification for signalization ofintersections.

Sight Distance and Safety

It is generally believed that intersection sight distance is one of theimportant safety factors at intersections. This study revealed thatsafety effects of sight distance varied across intersection types. Forfour-legged stop-controlled multilane intersections, sight distancewas a significant effect, whereas no significant effects were revealedfor three-legged multilane intersections and signalized intersections.For three-legged intersections, sight distance shows only minor pos-itive safety effects, which are also insignificant. At signalized inter-sections, traffic is controlled by signals such that sight distanceshould be less of a concern than at stop-controlled intersections.When left and right sight distances were compared, right sight dis-tance revealed itself as a more important safety consideration thanother sight distances (longitudinal and left sight distance) at stop-controlled multilane intersections. This is explained by observing thatright sight distance influences potential crashes between left-turningvehicles and through vehicles entering from the rightconflictingvehicles that must be observed across the median. In other words,


left turns are more protracted intersection movements than rightturns, and left-turn movements require right sight distance, whereasright turns require left sight distance.

Lighting and Safety

This research found a positive relationship between the presence ofintersection lighting and safety for signalized rural intersections, inagreement with previous research findings. At signalized intersec-tions, the absence of lighting contributes significantly to the fre-quency of both total and injury crashes. However, for three- andfour-legged stop-controlled multilane intersections, no significantsafety effects of lighting were observed. For three- and four-leggedstop-controlled intersections, fewer than 30% had installed lighting,which may suggest that lighting was installed because of high acci-dent conditions. If this is true, the presence of lighting may be associ-ated with higher numbers of crashes after the installation of lighting.This phenomenon could explain the positive correlation signsbetween crashes and lighting and also the positive correlationsbetween lighting and commercial driveways and turning move-ments, which also were associated with the frequency of crashes atstop-controlled intersections.

CONCLUSIONS

The difficulties and challenges faced during the model developmentactivities in this study were related primarily to the data, the collec-tion of variables available for analysis, and the intended end use ofthe crash prediction models. These included the following:

Interactions among variables that contribute to accident expe-rience, most notably the interactions between geometric variablesand AADT, had to be carefully considered in model estimation. The need to forecast crashes across states posed significant

difficulties. Hence, interstate versus intrastate variability in crashoccurrences leads to inconsistencies in countermeasure effectsacross states. Observational data also limit the amount of variation in inde-

pendent variables observed. The lack of sufficient variation in somevariables of interest made it difficult at times to estimate their effectswith the highest reliability, resulting in the possibility that someimportant effects were omitted from the models. Resource and data reliability restrictions prohibited assembly

of a data set that was sufficiently large, was randomly selected,and contained all the pertinent variables that contribute to accidentexperience. Incongruencies between data sets across states and across peri-

ods required the assembly of unique sets of data to support each ofthe three intersection models.

Despite these challenges, it was possible to develop the accidentprediction models for the three types of rural intersection. Aftercareful assessment of the modeling results, and a detailed look ataspects of the intersection crash prediction models, the followinggeneral conclusions regarding model calibration were drawn.

Traffic flows were the most reliable explanatory factor in acci-dent occurrence. This indicates that obtaining reliable AADT esti-mates is very important for improving or estimating crash predictionmodels. However, the collection and reporting of reliable AADTs

is practically difficult, largely because of the limited number of per-manent traffic flow count stations and limits in the frequency andduration of counts (e.g., frequency of once yearly and duration of24 h). Most of the state AADT data used in this research were esti-mated AADTs. That is, all three states used in this research col-lected short-term traffic counts (for example, for a 48-h period) formany of their highway segments and adjusted the traffic flow forday of week and seasonality to derive AADT estimates. Hence, itcan be assumed that the use of such estimated AADTs may causesome bias in model estimation for safety. Furthermore, the AADTestimates used in this research are from highway segments nearestthe intersection, not necessarily at the intersection. Unlike crashmodels for highway segments, the crash prediction models forintersections use only 250 ft for the crash location such that trafficflows affecting intersection accidents may be different from thosefor the highway segments. Furthermore, measurement errors inturning maneuver counts also inhibit the ability to estimate reliablemodels. The conclusion arising from these observations is thatimprovements in intersection traffic volume counts, including turn-ing movement counts, will yield commensurate improvements incrash models estimated by using these data.

To test for individual state effects, state indicator variables weretested, and no significant effects were retained in the final models.However, several preliminary candidate models included the stateindicator variable for the Michigan data for total accidents at four-legged intersections and for injury accidents at signalized intersec-tions. [More detailed discussions about these results are availableelsewhere (5).] That state indicator variables can reveal themselvesas significant explains why many existing fully parameterized mod-els (models with many explanatory variables) are not transferableacross jurisdictions and illustrates that high intercorrelation of explana-tory variables with traffic volumes may render isolation of the safetyeffects of individual variables difficult at best, leading to inconsis-tent predictions. Therefore, one cannot realistically expect that mod-els with many variables will predict crashes equally well acrossstates. These state effects arise because states, and jurisdictions withinstates, apply safety countermeasures in different ways. Some inter-sections receive countermeasures because of political pressures,some because volume warrants are met, some because crash war-rants are met, and some because safety audits support their applica-tion. These differences in countermeasure application result ininconsistent magnitudes and directions of effects in crash models,as revealed by the effect of the lighting variable in this researcheffort. Caution should be exercised, therefore, in generalizing toobroadly the results of models estimated by using data of this nature.

It is recommended that national standards for estimating andreporting crash, traffic flow, and geometric variable information atintersections be established. There are no national standards for themeasurement and reporting of these variables, and reporting prac-tices vary across states and jurisdictions. Furthermore, the variablesmeasured across states and jurisdictions are inconsistent andupdated too infrequently to be wholly reliable for crash prediction.In this research effort, considerable time was spent assembling datafrom each state, and difficulties were encountered in trying to obtainmissing information (such as peak turning percentage movementsin Georgia and minor-road geometric information in California andMichigan) required for model development. Hence, developing anational standard for measurement and reporting of the variables


will yield major improvements in the ability to estimate models fornational applications.

Finally, the study results developed strong support for the inter-active highway safety design model (IHSDM) approach: use of basemodels with accident modification factors. Support for the approachincluded inconsistency of geometric explanatory variables acrossstates, strong interstate crash variability, and the dominance of AADTas the prime explanatory factor in crash occurrence. After detailedexamination of the data obtained across several states and periods,it became apparent that the most defensible approach for forecast-ing crashes, given current data availability, is the approach pro-posed by IHSDM. As a corollary, statistical models that rely on anexpanded set of predictor variables are not reliable across states andshould be applied with caution.

ACKNOWLEDGMENTS

The authors acknowledge FHWA sponsorship of the core work thatled to the paper. The authors thank B. N. Persaud and Craig Lyonfor their support and contributions during the course of the study andtheir parallel efforts and thank Joe Bared of FHWA, Andrew Vogtof Pragmatics, Inc., Yusuf Mohamedshah and Forrest Council of theLandis Corporation, and the Georgia Department of Transportationfor their assistance in acquiring data needed for this study.

REFERENCES

1. Traffic Safety Facts. NHTSA, U.S. Department of Transportation, 2001.2. Vogt, A. Crash Models for Rural Intersections: Four-Lane by Two-

Lane Stop-Controlled and Two-Lane by Two-Lane Signalized. FHWA-RD-99-128. FHWA, U.S. Department of Transportation, 1999.

3. Vogt, A., and J. Bared. Accident Prediction Models for Two-Lane RuralRoads: Segments and Intersections. FHWA-RD-98-133. FHWA, U.S.Department of Transportation, 1998.

4. Harwood, D. W., F. M. Council, E. Hauer, W. E. Hughes, and A. Vogt.Prediction of the Expected Safety Performance of Rural Two-LaneHighways. FHWA-RD-99-207. FHWA, U.S. Department of Trans-portation, 2000.

5. Washington, S., B. Persaud, J. Oh., and C. Lyon. Validation and Recal-ibration of Accident Prediction Models for Rural Intersections. FHWA,U.S. Department of Transportation, 2003.

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7. Neter, J., M. H. Kutner, C. J. Nachtsheim, and W. Wasserman. AppliedLinear Statistical Models, 4th ed., McGrawHill, New York, 1996.

8. Miaou, S. P., P. S. Hu, T. Wright, S. C. Davis, and A. K. Rathi. Devel-opment of Relationship Between Truck Accidents and GeometricDesign. FHWA-RD-91-124. FHWA, U.S. Department of Transporta-tion, 1993.

9. A Policy on Geometric Design of Highways and Streets, 4th ed.,AASHTO, Washington, D.C., 2001.

10. Parker, M. R. Effects of Lowering and Raising Speed Limits on SelectedRoadway Sections. FHWA-RD-92-084. FHWA, U.S. Department ofTransportation, 1997.

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12. Shinar, D. Speed and Crashes: A Controversial Topic and an ElusiveRelationship. Traffic Engineering, Vol. 41, 1999, pp. 5255.

Publication of this paper sponsored by Safety Data, Analysis and EvaluationCommittee.

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