Factors Affecting Crash Severity on Gravel Roads

Abstract

This study focused on the characteristics of crashes reported on gravel roads, with the objective of identifying factors affecting severity of crashes on such roads. Crash data from Kansas over a 10 year period was used in the analysis. Logistic regression models were developed to estimate the probability of having a crash of different level of severity for a given set of explanatory variables. The regression modeling considered 29 candidate variables related to driver, road, environment, and collision type, which have been recorded by the police. It was found that multiple factors were very significant in these models, such as safety equipment usage, driver ejection, alcohol involvement, speed limit, and some driver-related factors. Existence of these factors was very likely to result in high-severity crashes on gravel roads, compared to the circumstances without them. The magnitude of such contributing effects was also estimated by computing the conditional odds ratios for individual predictors.

Full text

Journal of Transportation Safety & Security, 1:254–267, 2009
Copyright © Taylor & Francis Group, LLC and The University of Tennessee
ISSN: 1943-9962 print / 1943-9970 online
DOI: 10.1080/19439960903381669
Factors Affecting Crash Severity on Gravel Roads
LITAO LIU AND SUNANDA DISSANAYAKE
Department of Civil Engineering, Kansas State University,
Manhattan, Kansas, USA
This study focused on the characteristics of crashes reported on gravel roads, with
the objective of identifying factors affecting severity of crashes on such roads. Crash
data from Kansas over a 10 year period was used in the analysis. Logistic regression
models were developed to estimate the probability of having a crash of different level of
severity for a given set of explanatory variables. The regression modeling considered 29
candidate variables related to driver, road, environment, and collision type, which have
been recorded by the police. It was found that multiple factors were very significant
in these models, such as safety equipment usage, driver ejection, alcohol involvement,
speed limit, and some driver-related factors. Existence of these factors was very likely to
result in high-severity crashes on gravel roads, compared to the circumstances without
them. The magnitude of such contributing effects was also estimated by computing the
conditional odds ratios for individual predictors.
Keywords gravel roads, crash severity, regression models, low volume roads
1. Introduction
In 2006, 20,734 fatal crashes were reported on rural highways in the United States, which
accounted for 53.7% of total fatal crashes that year. In the state of Kansas, 330 fatal crashes
were recorded on rural highways, consisting of 77.3% of total fatal crashes in 2006 (U.S.
Department of Transportation [USDOT], 2008). Gravel roads occupy a large proportion of
the rural road network, especially in relatively rural states. Based on 2005 year data, gravel
roads accounted for about 78.5% of total rural road mileage in Kansas (USDOT, 2006).
Based on the total number of fatal crashes on gravel roads, Kansas ranked fourth highest
among the 50 states in 2006, only behind Nebraska, Iowa, and Missouri (USDOT, 2008).
During recent years, the total annual number of crashes on Kansas gravel roads has been
fluctuating around 3,500 (Kansas Department of Transportation, 2006). Figure 1 shows the
percent of injury crashes in total crash occurrences on Kansas gravel roads from 1996 to
2005. The percentage of fatal and disabled crashes remained relatively constant, whereas
the percentages of nonincapacitating and possible injury crashes appear to have increased
from 2003.
The equivalent economic loss due to gravel road crashes is significantly high, which is
estimated to be more than $200 million every year in Kansas alone. Although total fatalities
Address correspondence to Sunanda Dissanayake, PhD, PE, Associate Professor, Department of
Civil Engineering, 2118 Fiedler Hall, Kansas State University, Manhattan, KS 66506-5000. E-mail:
sunanda@ksu.edu
254
Downloaded by [Texas A&M University Libraries] at 22:38 13 April 2013

Crash Severity on Gravel Roads 255
Figure 1. Percent of injury crashes based on severity in Kansas 1996–2005. Source: Kansas Accident
Recording System (2007).
due to crashes on gravel roads have been decreasing from 1996 to 2005, because the unit
costs for each fatality and injury increase with time, the annual equivalent economic cost
never dropped below $200 million from 2000 to 2005, as shown in Table 1. Estimated costs
nearly equaled 4,660 times the median household income of $42,920 in Kansas in 2005
(U.S. Census Bureau, 2006). With the high percentage of gravel roads in the total network
and huge amount of economic loss due to gravel road crashes, there is an imperative need
to provide insight into the potential effects of various factors that might contribute to the
occurrences of crashes so that appropriate countermeasures can be implemented to save
economic losses to society.
Based on an extensive literature review, no documented previous efforts could be found
to have been carried out on this topic. Many of the previous studies focused on interstate
highway and high-volume road crashes, and some of them studied crashes related to a
Table 1
Equivalent economic loss due to gravel road crashes in Kansas
Economic Loss Due to Gravel Road Crashes by Severity
(Million Dollars)
Non- Possible
Year Fatal Disabled incapacitating Injury PDO Total
2000 165 37 37 16 7 262
2001 153 37 35 18 7 250
2002 158 36 38 16 7 255
2003 142 36 36 16 8 238
2004 115 28 35 15 7 200
2005 122 38 36 15 6 217
PDO =property damage only.
Downloaded by [Texas A&M University Libraries] at 22:38 13 April 2013

256 Liu and Dissanayake
specific aspect, such as two-vehicle crashes, vehicle-animal crashes, and so on. As part of
a comprehensive research project that looked into safety and operational issues on gravel
roads, this article specifically focuses on gravel road crash data that have been extracted
from a statewide crash database in Kansas.
2. Objectives
The primary objective of this research is to study the characteristics of gravel road crashes
and to identify the factors that have important effects toward the severity of crashes on
gravel roads. Based on the findings in the current study, it is possible to understand to what
extent the change of a single factor will influence the probability of observing a crash at a
given level of severity. The current study also expects to gain preliminary perspectives that
will provide a basic understanding of gravel road crashes for subsequent researches.
3. Literature Review
In most of the crash modeling studies, logistic regression or relevant statistical methods,
such as log-linear regression, were commonly carried out and successfully studied the
association between a set of contributory variables and crash severity. Contributory factors
toward crashes are usually categorized into four aspects based on their association with
driver, road, environment, and vehicle. Crashes could also be classified in order from less
severe to more severe, that is, from property damage only (PDO) to fatal crashes, based
on the personal injuries that were involved. The nature of crashes and related contributory
factors makes logit models more convenient to interpret their relationships.
Gates, Noyce, and Stine (2005) developed logistic regression models to analyze the
characteristics of run-off-road crashes that occurred on the approach or departure to highway
bridges in Minnesota over a 15-year period. Zhang and Ivan (2005) applied negative
binomial generalized linear models to evaluate the effects of roadway geometric features
on the incidence of head-on crashes on two-lane rural roads in Connecticut. Krull, Khattak,
and Council (2000) established logistic regression models of fatal and incapacitating injuries
versus other injuries and noninjuries for 3-year rollover crash data in Michigan and Illinois.
Ratnayake (2004) applied ordered probit modeling approach to identify critical factors
contributing toward higher crash severity in rural and urban highway crashes. Abdel-Aty
and Abdelwahab (2004) calibrated a nested logit model to estimate the probabilities of
rear-end crashes as a function of driver’s age, gender, vehicle type, vehicle maneuver,
light conditions, driver’s visibility, and speed. Shanker, Mannering, and Barfield (1996)
estimated a nested logit model to study the effects of environmental conditions, highway
design, accident type, driver characteristics, and vehicle on accident severity. Mercier,
Shelley, Rimkus, and Mercier (1997) used ordinal logistic regression to assess the influence
of driver age and gender on the severity of crashes suffered in head-on automobile collisions
on rural highways.
Zegeer, Stewart, Council, and Newman (1994) studied the relationship between ac-
cidents and roadway width on 4,100 miles of two-lane low-volume roads in seven states
including Alabama, Michigan, Montana, North Carolina, Utah, Washington, and West Vir-
ginia in 2004. Their study found that unpaved roads had higher accident and injury rates
than paved roads and that unpaved roads with average daily traffic (ADT) higher than 250
vehicles per day had significantly higher accident rates than paved roads. It was also found
that accident rates increased as road widths of unpaved roads increased, which was opposite
Downloaded by [Texas A&M University Libraries] at 22:38 13 April 2013

Crash Severity on Gravel Roads 257
of what was found on paved roads. The situation was explained by saying that drivers might
have reduced their speeds on very narrow unpaved roads, thereby decreasing accident rates.
Another study by Calvert and Wilson (1999) found injury crash rates on selected Wyoming
unpaved road sections were more than 5 times higher than the rate for all roads within the
state.
Dhungana and Qu (2005) conducted a crash study on the probabilistic linkage of crash,
emergency medical services, and hospital data for 1999 and 2000 in Nebraska by using
the Crash Outcome Data Evaluation System (CODES). Based on speed limit, roads were
categorized into three groups: <50, 50, and >50 mph. It was found that gravel surface
was an additional risk factor and contributed to unexpectedly high severity of crashes on
50 mph roads. This study suggested that additional training be given to student drivers and
level of law enforcement be increased on gravel roads.
Wade, Hammond, and Kim (2004) conducted an accident analysis on very low-volume
roads in 10 counties in Minnesota. Their study concluded that, in addition to improper
driving, many other factors were related to accidents on low-volume roads. Stamatiadis,
Jones, and Hall (1999) analyzed 1993 to 1995 crash data on low-volume rural roads
in Kentucky and North Carolina using the quasi-induced exposure method instead of
conventional vehicle miles traveled. This study found low-volume roads presented similar
crash trends as other types of roads. It was also found that gender and age of driver had
effects on crash propensities on low-volume roads. Drivers of older vehicles were found
more likely to have serious injuries than drivers of new vehicles. Drivers were also found to
be exposed to different crash propensities based on the types of vehicles they were driving.
4. Crash Data
A Microsoft Access-based database, Kansas Accident Recording System (KARS), was used
to obtain 10 year crash data from 1996 to 2005 as reported by police officers in Kansas. A
preliminary screening was conducted to select crashes that occurred on gravel road surfaces
and related information. Based on the field On Road Surface Type, gravel road crashes
were separated from the raw database and rebuilt into a new data set, which contained
details of driver, vehicle, roadway, and environment at the time of crash occurrences. One
of the five levels of severity has been assigned to each crash based on the existence of
injuries at a certain level. For instance, if at least one fatality has been caused due to a
crash, it is then identified as a fatal crash, and when there is no fatality but at least one
incapacitating injury, it is classified as an incapacitating crash (also known as a disabled
crash). A crash without resulting in any injuries is called PDO crash.
Crash data involving more than two vehicles were not considered in the current study,
due to their very small number of observations and unique nature from others. Some records
with missing fields, abnormal input, or unknown factors were also discarded. The final data
set had 18,635 records, of which 265 were fatal crashes, 697 incapacitating crashes, 3,304
nonincapacitating crashes, 2,075 possible injury crashes, and 12,294 PDO crashes. The
sample size of this data set is relatively large and therefore sufficient in avoiding possible
biases that are usually caused by a limited number of observations. Characteristics of the
screened crash data set are shown in Table 2.
Pedestrian-involved crashes are only about 0.2% of total crashes on gravel roads. How-
ever, pedestrian involvement is still considered in the current study because a preliminary
questionnaire survey showed that rural residents, especially those who live along gravel
roads, are very concerned about pedestrian safety issues on gravel roads. It is important
to look into the effects of pedestrian involvement on possible injuries due to automobile
crashes. Weather and light conditions were considered as environmental factors. More than
Downloaded by [Texas A&M University Libraries] at 22:38 13 April 2013

Table 2
Characteristics of gravel road crashes in Kansas 1996–2005
Crash Severity
Factors Fatal Incapacitating Nonincapacitating Possible PDO Total Percent
Environment
Good weather 252 658 3,038 1,891 11,003 16,842 90.4
Adverse weather 13 39 266 184 1,291 1,793 9.6
Dark/unlit 97 251 1,267 663 5,014 7,292 39.1
Day/light 168 446 2,037 1,412 7,280 11,343 60.9
Road
Off roadway 60 115 612 310 1,281 2,378 12.8
Ruts 5 30 135 81 250 501 2.7
Slippery 26 82 460 327 2,498 3,393 18.2
Straight and level 166 356 1,744 1,108 7,171 10,545 56.6
Curve/grade 99 341 1,560 967 5,123 8,090 43.4
Driver
Alcohol involved 81 147 467 176 546 1,417 7.6
Old driver involved 44 67 288 215 1,451 2,065 11.1
Young driver involved 132 405 2,082 1,280 5,988 9,887 53.1
Male driver involved 168 411 1,865 1,029 7,535 11,008 59.1
Safety equipment not used 36 224 1,761 1,367 10,168 13,556 72.7
Driver ejected 142 145 190 37 22 536 2.9
Failed to yield right-of-way 46 95 262 178 766 1,347 7.2
Disregarded traffic control devices 17 36 110 58 191 412 2.2
Exceeded speed limit 15 49 153 80 206 503 2.7
Too fast for conditions 116 331 1,567 864 2,965 5,843 31.4
Inattention 133 317 1,408 908 3,700 6,466 34.7
Avoidance/evasive action 13 33 310 193 752 1,301 7.0
Crash type
Pedestrian involved 1 3 20 12 2 38 0.2
Two-vehicle 79 188 539 390 2,509 3,705 19.9
Overturned 97 170 916 546 1,404 3,133 16.8
Vehicle-animal 1 7 44 48 3,450 3,550 19.1
Vehicle-fixed-object 86 318 1,717 1,050 4,431 7,602 40.8
Head-on 8 38 81 36 159 322 1.7
Rear-end 4 14 62 62 353 495 2.7
Angle-side 49 120 328 240 1,245 1,982 10.6
Sidewipe 1 4 37 42 417 501 2.7
Back-into 0 0 3 4 292 299 1.6
PDO =property damage only.
258
Downloaded by [Texas A&M University Libraries] at 22:38 13 April 2013

Crash Severity on Gravel Roads 259
Table 3
Descriptions of four response variables for modeling
Response
Model Variable Description
1FATAL =1 if the observation is a fatal crash, =0 otherwise (i.e.,
incapacitating, nonincapacitating, possible, or PDO)
2 INCAP =1 if the observation is a disabled crash, =0 otherwise
(i.e., fatal, nonincapacitating, possible, or PDO)
3 NON INCAP =1 if the observation is a nonincapacitating crash, =0
otherwise (i.e., fatal, incapacitating, possible, or PDO)
4 POSSIBLE =1 if the observation is a possible injury crash, =0
otherwise (i.e. fatal, incapacitating, nonincapacitating, or
PDO)
PDO =Property Damage Only.
90% of total crashes occurred under normal weather conditions, and 60.9% occurred during
daytime or with adequate light.
A number of driver-related factors were considered in the data set, such as alcohol
involvement, age, gender, safety equipment use, driving behaviors, speed, and so on. Com-
pared to old drivers (≥65 years), young drivers (≤25 years) were involved in gravel road
crashes at a much higher percentage. Crashes involving male drivers totaled 59.1%. It was
also noticed that 72.7% of the crashes involved nonuse of safety equipment (i.e., seat belt).
Although only 2.7% of crashes were attributed to exceeding the speed limit, there were
31.4% of crashes that involved driving too fast for existing conditions. Inattention when
driving was also a significant factor by possibly contributing to 34.7% of total crashes. It
should be noted that a single crash might be contributed to by multiple potential factors,
thus the sum of percentages does not equal 100%.
Based on Table 2, it was found that gravel roads had more single-vehicle crashes
than two-vehicle crashes, which accounted for about 80% of the total. Vehicle-fixed-
object crashes totaled 40.8% of the total, which is a significant percentage compared to
other crash types. The fixed objects very likely to be hit were identified as ditches, trees,
fences/gates, utility devices, and embankments. Animal-vehicle and overturned crashes
were also commonly observed crash types on gravel roads.
5. Variables for Severity Modeling
A total of 29 variables were initially considered as important contributory factors affecting
the severity of gravel road crashes. Selection of these variables from the database was
subjected to the availability of data in the data set. As many variables as possible were
included to develop a systematic evaluation of the characteristics of gravel road crashes.
Crash severity was treated as the response variable. Because there are five categories for
crash severity, four response variables were treated, as shown in Table 3. All four response
variables are binary variables. For instance, the response FAT A L takes value of “1” if that
crash is a fatal crash, otherwise it takes “0.”
The selected candidate explanatory variables and related information are shown in
Table 4. Of all 29 variables, only speed limit is a continuous variable. All other variables
Downloaded by [Texas A&M University Libraries] at 22:38 13 April 2013

Table 4
Selected candidate explanatory variables for modeling
Variable MSD Description
TWO VEH CR 0.199 0.399 =1 if two vehicles were involved, =0 otherwise
PED INVL 0.002 0.045 =1 if pedestrian was involved, =0 otherwise
ALCOHOL 0.076 0.265 =1 if there was alcohol involvement, =0 otherwise
ON RDW 0.872 0.334 =1 if the crash occurred on a roadway, =0 otherwise
SPEED LIMIT 50.381 9.633 Speed limit in mi/h
LIGHT CON 0.391 0.488 =1 if the crash occurred in dark or unlit condition, =0 otherwise
WTH CON 0.904 0.295 =1 if there was no adverse weather condition, =0 otherwise
SLP RD SURF 0.182 0.386 =1 if road surface was slippery, =0 otherwise
RD CHAR 0.566 0.496 =1 if the road was straight and level, =0 otherwise
OVERTURNED 0.168 0.374 =1 if it was an overturned crash, =0 otherwise
VEH ANM 0.191 0.393 =1 if the vehicle collided with an animal, =0 otherwise
VEH FXD OBJ 0.408 0.491 =1 if the vehicle collided with a fixed object, =0 otherwise
HDON 0.017 0.130 =1 if it was a head-on crash, =0 otherwise
REAR END 0.027 0.161 =1 if it was a rear-end crash, =0 otherwise
ANGLE SIDE 0.106 0.308 =1 if it was an angle-side crash, =0 otherwise
SIDEWIPE 0.027 0.162 =1 if it was a side-wipe crash, =0 otherwise
BACK INTO 0.016 0.126 =1 if it was a backed-into crash, =0 otherwise
DR OLD 0.111 0.314 =1 if one involved driver was older than 65, =0 otherwise
DR YOUNG 0.531 0.499 =1 if one involved driver was younger than 25, =0 otherwise
DR GENDER 0.591 0.492 =1 if at least one male driver was involved, =0 otherwise
SAFE EQMT USE 0.273 0.445 =1 if one driver did not use safety equipment, =0 otherwise
DR EJECT 0.029 0.167 =1 if one driver was ejected or partially ejected, =0 otherwise
DR FAI L ROW 0.072 0.259 =1 if the driver failed to yield right-of-way, =0 otherwise
DR DISR TCD 0.022 0.147 =1 if due to disregarding traffic signs, signals, =0 otherwise
DR EXCD SL 0.027 0.162 =1 if the driver exceeded posted speed limit, =0 otherwise
DR TOO FAST 0 .314 0.464 =1 if the driver drove too fast for conditions, =0 otherwise
DR INATTN 0.347 0.476 =1 if the crash was due to driver’s inattention, =0 otherwise
DR AV / E V ACT 0.070 0.255 =1 if the driver took avoidance or evasive action, =0 otherwise
RD RUT 0.027 0.162 =1 if the roadway had ruts, holes or bumps, =0 otherwise
Note: 1 mi/h =1.61 km/h.
260
Downloaded by [Texas A&M University Libraries] at 22:38 13 April 2013

Crash Severity on Gravel Roads 261
are dummy variables that have only two values, 0 or 1 in this case. For example, if a
crash involves at least one driver under the influence of alcohol, the variable ALCOHOL
is assigned “1” as its value, otherwise “0” is assigned to this variable. The means for
all variables except speed limit are actually related to the fraction of crashes related to
corresponding variables.
6. Method
For a binary response variable y, let it have value “1” for success and value “0” for
failure. If the probability for observing a “success” of the response variable yis denoted
by P(Y=1|X)=π(x) for a given set of k covariates (i.e., X=x1,x
2,···,x
k), it is the
parameter for the binomial distribution and has a logit form as shown in Equation 1 (Agresti,
2007):
π(X)=eα+k
i=1βiXi
1+eα+k
i=1βiXi
(1)
And the multiple logistic regression model can be written in the following form:
log it[π(x)] =log π(x)
1−π(x)=α+
k

i=1
βiXi(2)
Where,
α=the intercept, and
{βi}=regression coefficients for covariates X.
The parameter βirefers to the effect of xion the log odds that Y=1, controlling the
other xs. For example, exp(βi) is the multiplicative effect on the odds of a one-unit increase
in xiat fixed levels of the other xs (Agresti, 2007).
The regression coefficients are estimated using the maximum likelihood method, which
maximizes the log-likelihood function as follows to obtain the best-fitted model:
log L=
n

i=1
yiπ(Xi)
1−π(Xi)+
n

i=1
[1 −π(Xi)] (3)
Where,
L=the likelihood of observing the outcome for all the observations, and
yi=outcome of the ith observation and nis the total number of observations.
The coefficient of determination, R2, is proposed by Cox and Snell (1989) to assess the
effectiveness of the fitted multiple logistic model, which is estimated using the following
equation:
R2=1−L(0)
L(ˆ
θ)2
n
(4)
Where,
L(0) =the likelihood of the intercept-only model,
L(ˆ
θ)=the likelihood of the specified model, and
n=the sample size.
Downloaded by [Texas A&M University Libraries] at 22:38 13 April 2013

262 Liu and Dissanayake
The quantity R2achieves a maximum of less than one for discrete models, where the
maximum is given by
R2
max =1−{L(0)}2
n(5)
To solve this problem, Nagelkerke (1991) proposed the following adjusted coefficient,
which can achieve a maximum value of one:
˜
R2=R2
R2
max
(6)
In SAS output, R2is labeled as “R-Square” and ˜
R2is labeled as “Max-rescaled R-Square”
(SAS Version 9.1). To fit data with the best model, the stepwise selection method is used
to select those most important terms in the final model. Stepwise selection always checks
the significance of the variables in the existing model before it adds another variable into
the model.
Goodness-of-fit test of logistic models uses three criteria to compare different models
for the same data (SAS Version 9.1):
•−2 log likelihood criterion (2LLC)
•Akaike Information Criterion (AIC)
•Schwarz Criterion (SC).
In the first criterion, the 2LLC is computed using the following formula:
−2Log L=−2
j
wjfj{rjlog(ˆπj)+(nj−rj)log(1 −ˆπj)}(7)
Where,
wj,fj=the weight and frequency values of the jth observation,
rj=the number of events,
nj=the number of observations, and
ˆπj=the estimated event probability.
Under the null hypothesis that all explanatory effects in the model are zero, the 2LLC
has a chi-squared distribution.
The AIC statistic is computed as follows:
AIC =−2LogL +2p(8)
The SC statistic is computed by:
SC =−2Log L +plog ⎛
⎝
j
fj⎞
⎠(9)
In Equations 8 and 9, pis the number of parameters in the model. The lower the three
statistics, the more desirably the model fits the data.
In addition to the three statistics just mentioned, the Hosmer–Lemeshow test (HL test)
is also able to test the goodness-of-fit for binary response models (SAS Version 9.1). The
HL statistic is obtained by calculating the Pearson chi-square statistic from the 2 ×gtable
Downloaded by [Texas A&M University Libraries] at 22:38 13 April 2013

Crash Severity on Gravel Roads 263
of observed and expected frequencies, where gis the number of groups. The statistic is
written as Equation 10:
X2
HL =
g

i=1
(Oi−Ni¯πi)2
Ni¯πi(1 −¯πi)(10)
Where,
Ni=the total frequency of subjects in the ith group,
Oi=the total frequency of event outcomes in the ith group, and
¯πi=the average estimated probability of an event outcome for the ith group.
The HL statistic is then compared to a chi-square distribution with (g−n) degrees of
freedom, where the value of nhas a default value of 2 in SAS. Large values of X2
HL together
with small pvalues indicate a lack of fit of the model.
7. Model Estimates
As some of the explanatory variables may not be significant in predicting severity of gravel
road crashes, variable selection was carried out to choose the most important variables for
a given significance level. In the current study, the significance level was set at 0.10. The
stepwise method was used for variable selection, as it is more powerful than forward and
backward methods, and widely used in previous studies. The stepwise method is somewhat
similar to the forward method except that effects already in the model do not necessarily
remain. Explanatory variables are entered into and removed from the model in such a way
that each forward selection step may be followed by one or more backward elimination
steps. The stepwise selection process terminates if no further variables can be added to
the model or if the variable just entered into the model is the only variable removed in the
subsequent backward elimination (SAS Version 9.1). The estimated coefficients and related
statistics are presented in Table 5.
The estimated R2value for the fatal crash model is 0.36, higher than the R2values of the
other three models. The fatal crash model has the smallest number of significant predictors
in the final model, compared to the other three models. Therefore, fatal crashes have a much
simpler prediction equation with fewer variables, whereas a higher percentage of variety
to be well predicted than the other three levels of crash severity. In addition, less severe
crashes, such as nonincapacitating and possible injury crashes, are likely to involve more
contributory factors and be more complicated to be predicted, which is represented by the
lower estimated R2values.
The measures for goodness-of-fit criteria are also shown in Table 5. Two numbers
(measure with intercept only/measure with intercept and covariates) are shown for each
cell of the three criteria. The differences between the two numbers for all four models are
fairly large, indicating good fits of the estimated models. The HL tests were also carried
out and gave pvalues higher than 0.05 for all four models, which indicates that the models
fit the crash data adequately.
8. Discussion of Results
As described in Equations 1 and 2, the logit form of estimated injury crash risks has a
linear relationship with explanatory variables that are in the final logistic model. Accord-
ingly, those predictors with positive coefficients cause an increasing tendency to result in
Downloaded by [Texas A&M University Libraries] at 22:38 13 April 2013

Table 5
Estimated parameters of the logistic regression models
Fatal Incapacitating Nonincapacitating Possible
Variabl e
Estimated
Parameter Odds Ratio
Estimated
Parameter Odds Ratio
Estimated
Parameter Odds Ratio
Estimated
Parameter Odds Ratio
INTERCEPT −6.762 — −4.216 0.015 −1.309 0.27 0.02 1.02
TWO VEH ——————0.289 1.336
PED INVL — — — — 1.28 3.596 2.533 12.597
ALCOHOL 0.469 1.598 0.336 1.402 0.289 1.335 0.153 1.165
SPEED LIMIT 0.038 1.039 0.026 1.024 0.019 1.019 0.017 1.017
LIGHT CON ——————−0.086 0.918
SLP RD SURF — — −0.204 0.816 −0.208 0.812 −0.174 0.84
OVERTURNED — — — — 0.408 1.504 0.748 2.114
VEH ANM −1.435 0.238 −1.19 0.304 −1.107 0.331 −0.701 0.496
VEH FXD OBJ −0.201 0.818 — — 0.262 1.30.551 1.735
HDON — — 0.558 1.747 0.382 1.465 — —
SIDEWIPE −1.019 0.361 −0.989 0.407 −0.485 0.616 −0.312 0.732
BACK INTO — — — — −1.288 0.276 −1.271 0.281
DR OLD 0.29 1.336 — — 0.084 1.087 0.132 1.141
DR YOUNG −0.186 0.83 — — 0.059 1.061 0.06 1.062
DR GENDER — — — — −0.135 0.873 −0.289 0.749
SAFE EQMT USE 0.85 2.34 0.608 1.836 0.467 1.595 0.356 1.427
DR EJECT 1.419 4.133 0.992 2.695 0.93 2.534 0.808 2.243
DR FAIL ROW 0.379 1.461 0.403 1.497 0.263 1.30.207 1.23
DR EXCD SL — — 0.279 1.321 0.185 1.203 0.237 1.267
DR TOO FAST — — 0.193 1.213 0.21.222 0.146 1.157
DR INATTN 0.144 1.155—— ——0.097 1.102
RD RUT — — — — 0.275 1.316 0.273 1.314
AIC 2782.3/1845.4 5929.9/4848.1 17030.7/14133.4 11867.5/10174.5
SC 2790.2/1947.3 5937.8/4941.9 17038.5/14304.5 11875.1/10341.2
2LLC 2780.3/1819.4 5927.9/4824.1 17028.7/14089.4 11865.5/10130.5
HL statistic 0.5202 0.1189 0.053 0.9403
R20.36 0.21 0.25 0.20
AIC =Akaike Information Criterion; SC =Schwarz Criterion; 2LLC =−2 log likelihood criterion; HL statistic =Hosmer–Lemeshow statistic; — =
corresponding variable is not significant.
264
Downloaded by [Texas A&M University Libraries] at 22:38 13 April 2013

Crash Severity on Gravel Roads 265
injury crashes at the corresponding severity. In the same way, negative coefficients indicate
decreasing tendency for those significant predictors. Table 5 also shows the estimated odds
ratios based on the estimated coefficients for every significant predictor in all the four
models. These odds ratios reflect the magnitude of the effect of these predictors on injury
crash risks. Taking variable ALCOHOL in the fatal model as an example, the estimated odds
ratio is 1.598, which indicates that, compared to no alcohol involvement, the probability
of a crash tending to be a fatal crash is about 60% times higher when alcohol is involved,
assuming all other factors remain the same.
Altogether, 11 explanatory variables are significant for the fatal crash model, and 7
of them are driver-related factors, including alcohol involvement, age, safety equipment
use, driver ejection, failure to yield right-of-way, and inattention to driving. All these
seven driver-related factors, except DR YOUNG have positive coefficients, indicating the
probability of a gravel road crash to be a fatal one is likely to increase when one or more
of these factors are involved. It is significant that the ejection of the driver tends to cause
the probability of a fatal crash to be more than 3 times higher. Similarly, nonuse of safety
equipment causes this probability to be 134% times higher. When a driver fails to yield
right-of-way or drives inattentively, the probability of suffering a fatal crash tends to be
46% and15.5% times higher, respectively. Three crash types, vehicle with animal, vehicle
with fixed object, and sidewipe, are less likely to be a fatal crash on gravel roads when
other situations are the same. Young driver involved crashes are also 17% less likely to be
fatal crashes compared to crashes without young driver involved.
Speed limit is a surrogate measure of actual vehicular speed at the time of crash,
because actual vehicular speed is unavailable in the crash database. It is hard to say all
traffic followed the speed limits on gravel roads, whereas it is appropriate to assume that
the majority of traffic followed speed limits at reasonable levels. And, this assumption seems
to be verified by the modeling results. Speed limit is significant not only in the estimated
fatal crash model, but also in all the other three injury severity models. All the coefficients
were estimated to be positive in the models, so it can be concluded that gravel roads with
higher speed limits are very likely to observe higher propensity of injury crashes at all
four severity levels. The estimated odds ratio for speed limit are the increasing tendency
of the probability of having an injury crash corresponding to every one-unit increase of
speed limit, that is, 1 mph in this case. It is necessary to transform this tendency to a value
corresponding to a 5 mph increment, because speed limits are always set at a multiple of 5
mph interval, such as from 35 mph to 40 mph or from 35 to 45 mph. This transform can be
easily achieved by using the following equation (Dissanayake & Liu, 2008):
θ =(θ5−1) ×100%
Where, θis the estimated odds ratio.
The estimated effects for every 5 mph increment of speed limit on increasing the
probability of suffering injury crash risks on gravel roads are as follows:
•increase fatal injury risk by 21%
•increase incapacitating injury risk by 12.6%
•increase nonincapacitating injury risk by 10%
•increase possible injury risk by 8.8%.
This finding shows that the speed limit on gravel roads is a critically important factor
in reducing severity of crashes. In addition to speed limit, alcohol involvement, safety
equipment usage, driver ejection, and failure to yield right-of-way are also significant in the
Downloaded by [Texas A&M University Libraries] at 22:38 13 April 2013

266 Liu and Dissanayake
other three models with positive coefficients. Safety equipment usage and driver ejection
have very significant odds ratios in these models, that is, the estimated odds ratio for nonuse
of safety equipment is 1.427, and 2.243 for driver ejection, indicating very significant effects
of these two factors on injury crash risks. Alcohol involvement is estimated to increase
incapacitating crash risk by 40.2%, increase nonincapacitating crash risk by 33.5%, and
increase possible injury risk by 16.5%. For a driver failing to yield right-of-way, the risk
of suffering an incapacitating crash tends to be 50% higher, 30% higher for suffering a
nonincapacitating crash, and 23% higher for suffering a possible injury crash.
For a crash that has involved old or young drivers or pedestrians, or that occurs on a
gravel road with ruts, the probability of being a nonincapacitating or possible injury crash
is going to be higher. Motorists driving too fast for conditions or exceeding speed limits
are more likely to suffer nonfatal crashes when other conditions are kept unchanged. As
previously discussed, the magnitude of these effects could be explained by the odds ratios.
In addition, some factors are also found to be likely to decrease injury crash risks,
such as slippery road surface, collision with animal, sidewipe collision of vehicles, back-
into collision, and male-driver involvement. This situation might be explained by drivers
tending to be more cautious when driving on slippery road surfaces. Sidewipe and back-into
collision types seem safer than overturned and head-on collisions. Although found to be
less likely to result in a fatal crash, vehicle collisions with fixed objects are more likely to
suffer nonincapacitating or possible injuries.
9. Conclusions
With the logistic regression method, the models that can adequately estimate crash risks
on gravel roads for a given set of contributory factors were developed for different crash
severities. Factors related to the nature of driver, roadway, and environment were considered
in the current study to identify which of them are affecting the severity of crashes on gravel
roads, which are local roads.
This analysis was carried out as a part of a study that evaluated the speed limit–related
issues on gravel roads (Dissanayake & Liu, 2008). The findings confirmed that the speed
limit is a major determinant in the severity outcome of crashes on gravel roads. In addition,
the results of modeling indicate that other factors contributing to a higher probability of
more severe crashes on gravel roads include lack of safety equipment usage, driver ejection,
alcohol involvement, failing to yield right-of-way, inattention while driving, driving too
fast or exceeding speed limit, older driver, and ruts/potholes on surfaces. Overturned, head-
on, and collision with fixed object crashes are dangerous types of collisions that very
likely increase the probability of having more severe crashes. Findings shed some light
on understanding the safety experience on this less studied type of roadway facility that is
important for states with higher percentage of rural roadways.
Acknowledgments
The authors would like to acknowledge the Kansas Department of Transportation for
providing funding to carry out this research.
Downloaded by [Texas A&M University Libraries] at 22:38 13 April 2013

Crash Severity on Gravel Roads 267
References
Abdel-Aty, M., & Abdelwahab, H. (2004). Modeling rear-end collisions including the role of driver’s
visibility and light truck vehicles using nested logit structure. Accident Analysis and Prevention,
36(3), 447–456.
Agresti, A. (2007). An introduction to categorical data analysis (2nd ed.). New York: John Wiley
and Sons, Inc.
Calvert, E. C., & Wilson, E. M. (1999). Incremental safety improvement for unpaved rural roads.
Transportation Research Record 1652 (Vol. 1, pp. 118–125). Washington, DC: Transportation
of Research Board, National Academy of Sciences.
Cox, D. R., & Snell, E. J. (1989). Analysis of Binary Data (2nd ed). London: Chapman and Hall.
Dhungana, P., & Qu, M. (2005). The risks of driving on roadways with 50 miles per hour posted
speed limit. Journal of Safety Research-Traffic Records Forum Proceedings,36, 501–504.
Dissanayake, S., & Liu, L. (2008). Speed limit related issues on Kansas gravel roads (K-TRAN:
KSU-06-5). Topeka: Kansas Department of Transportation.
Gates, T. J., Noyce, D. A., & Stine, P. H. (2005). The safety and cost-effectiveness of approach
guardrail for bridges on low volume roads. Proceedings of the 85th Annual Meeting of the
Transportation Research Board [CD-ROM]. Washington, DC: National Academy of Sciences.
Kansas Department of Transportation. (2006). Kansas Accident Reporting System database. Topeka,
KS: Kansas Department of Transportation.
Krull, K. A., Khattak, A. J., & Council, F. M. (2000). Injury effects of rollovers and events sequence
in single-vehicle crashes. Transportation Research Record 1717. (pp. 46–54) Washington, DC:
Transportation Research Board, National Academy of Sciences.
Mercier, C. R., Shelley, M. C., Rimkus, J. B., & Mercier, J.M. (1997). Age and gender as predictors of
injury severity in head-on highway vehicular collisions. Transportation Research Record 1581
(Vol. 1581, pp. 37–46). Washington, DC: Transportation Research Board, National Academy of
Sciences.
Nagelkerke, N. J. D. (1991). A note on a general definition of the coefficient of determination.
Biometrike,78(3), 691–692.
Ratnayake, I. (2004). Identification of factors related to urban and rural highway crashes.Ames,IA:
Midwest Transportation Consortium.
Shanker, V., Mannering, F., & Barfield, W. (1996). Statistical analysis of accident severity on rural
freeways. Accident Analysis and Prevention,28(3), 391–401.
Stamatiadis, N., Jones, S., & Hall, L. A. (1999). Causal factors for accidents on southeastern low-
volume rural roads. Transportation Research Record 1652 (Vol. 1, pp. 111–117). Washington,
DC.: Transportation of Research Board, National Academy of Sciences.
U.S. Census Bureau. (2006). Income 2005. Retrieved April 2008, from http://www.census.
gov/hhes/www/income/income05/statemhi2.html.
U.S. Department of Transportation. (2006). Highway statistics 2005. Retrieved April 2008, from
http://www.fhwa.dot.gov/policy/ohim/hs05/index.htm.
U.S. Department of Transportation. (2008). Fatality Analysis Reporting System (FARS) web-based
encyclopedia. National Highway Traffic Safety Administration, National Center for Statistics
and Analysis. Retrieved April 2008, from http://www-fars.nhtsa.dot.gov.
Wade, M. G., Hammond, C., & Kim, C. G. (2004). Accident analysis of significant crash rates for
low to very low volume roadways in 10 Minnesota counties (MN/RC-2004-22). Minneapolis,
MN: Minnesota Department of Transportation.
Zegeer, C. V., Stewart, R., Council, F., & Neuman, T. R. (1994). Accident relationships of roadway
width on low-volume roads. Transportation Research Record 1445 (Vol. 1445, pp. 160–168).
Washington, DC: Transportation of Research Board, National Academy of Sciences.
Zhang, C., & Ivan, J. N. (2005). Effects of geometric characteristics on head-on crash incidence on
two-lane roads in Connecticut. Transportation Research Record 1908 (Vol. 1908, pp. 159–164.
Washington, DC: Transportation Research Board.
Downloaded by [Texas A&M University Libraries] at 22:38 13 April 2013