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Complementary parametric probit regression and nonparametric
classification tree modeling approaches to analyze factors
affecting severity of work zone weather-related crashes
Ali Ghasemzadeh
1
•Mohamed M. Ahmed
1
Received: 12 February 2018 / Revised: 26 November 2018 / Accepted: 28 November 2018 / Published online: 21 December 2018
The Author(s) 2018
Abstract Identifying risk factors for road traffic injuries
can be considered one of the main priorities of trans-
portation agencies. More than 12,000 fatal work zone
crashes were reported between 2000 and 2013. Despite
recent efforts to improve work zone safety, the frequency
and severity of work zone crashes are still a big concern for
transportation agencies. Although many studies have been
conducted on different work zone safety-related issues,
there is a lack of studies that investigate the effect of
adverse weather conditions on work zone crash severity.
This paper utilizes probit–classification tree, a relatively
recent and promising combination of machine learning
technique and conventional parametric model, to identify
factors affecting work zone crash severity in adverse
weather conditions using 8 years of work zone weather-
related crashes (2006–2013) in Washington State. The key
strength of this technique lies in its capability to alleviate
the shortcomings of both parametric and nonparametric
models. The results showed that both presence of traffic
control device and lighting conditions are significant
interacting variables in the developed complementary crash
severity model for work zone weather-related crashes.
Therefore, transportation agencies and contractors need to
invest more in lighting equipment and better traffic control
strategies at work zones, specifically during adverse
weather conditions.
Keywords Adverse weather Work zone Safety Crash
characteristics Probit model Decision tree
1 Introduction
The widespread aging of the US roads and the increase in
traffic demand have raised the need for more transportation
maintenance projects; hence, affecting both safety and
operations of roadways. Over 27% of 67,523 work zone
crashes in 2013 involved injuries or fatalities. In fact, over
579 fatalities were reported due to work zone-related cra-
shes in 2013 [1]. A number of studies have been conducted
on work zone crashes. Results from these studies showed
that crash rate and frequency are increased by the presence
of work zones [2–6]. Weng et al. [7] used association rules
to investigate factors that might have a significant effect on
work zone crash casualties. They found that driving under
the influence, the speed limit over 40 mph and work zones
without traffic control devices have the most significant
effects on work zone casualty risk. Debnath et al. [8]
identified the most frequent hazards at work zones from
road-worker perspective. They found that speeding vehi-
cles are the common work zone hazard. Wang and Qin [9]
investigated the severity of single-vehicle crashes at work
zones. They concluded that speeding is one of the key
factors affecting the severity of work zone crashes. Char-
acteristics of work zone rear-end crashes were analyzed by
Qi et al. [10], and they found that driving under the
influence, lighting condition, the presence of pedestrians,
and roadway defects have the highest effects on severity of
work zone rear-end crashes.
It is worth mentioning that there is no agreement among
different studies about the severity of work zone crashes.
More specifically, some studies reported that work zone
&Ali Ghasemzadeh
aghasemz@uwyo.edu
Mohamed M. Ahmed
mahmed@uwyo.edu
1
Department of Civil and Architectural Engineering,
University of Wyoming, Laramie, WY 82071, USA
123
J. Mod. Transport. (2019) 27(2):129–140
https://doi.org/10.1007/s40534-018-0178-6
crashes were significantly more severe than non-work zone
crashes [11]. On the other hand, some studies claimed that
work zone crashes were less severe than non-work zone
crashes [12,13]. There is another group of studies, which
mentioned that there is no significant difference between
the severity of work zone and non-work zone crashes
[14,15]. While these studies are important and useful to
understand factors affecting work zone crashes, it is largely
unknown whether the harmful effects of adverse weather
conditions can exacerbate the severity of work zone cra-
shes or not.
Prior experience from road safety studies suggested that
adverse weather conditions significantly affect the opera-
tions and safety of roadways [16–20]. More than 7,400
people are killed, and over 673,000 people are injured due
to weather-related crashes every year on the US roadways
[21]. Qin et al. [22] found that heavy rain leads to a fewer
number of crashes but more severe crashes. Yu et al. [23]
found that crashes are extremely affected by weather
conditions, especially those that occurred in mountainous
freeways. Huang et al. [24] found that the severity of fog-
and smoke-related crashes is higher compared with crashes
in clear weather condition. Eisenberg et al. [25] analyzed
effects of snowfalls on crashes injury severity. They found
that snowy days have less fatal crashes than dry days;
however, they have more injury and property damage only
(PDO) crashes. Ahmed et al. [26] analyzed the interaction
between roadway geometry and real-time weather and
traffic data on mountainous freeways. They found that the
probability of being involved in a crash could be doubled
during the snowy seasons. Another study depicted that both
injury and non-injury crash rates increase during the winter
season; however, injury crashes are more severe during
snowy winter season in comparison with other non-snow
seasons [27].
Nevertheless, there is still a lack of studies examining
the impact of weather conditions on work zone injury
severity. This paper utilized data from the second Strategic
Highway Research Program (SHRP2) Roadway Informa-
tion Datasets (RID) to shed some lights on the different
factors affecting work zone crash frequency and severity in
different weather conditions.
The contributions provided in this paper are emphasized
as follows. First, considering the fact that weather data
extracted from weather stations are not that accurate, this
study utilized weather information provided in police crash
reports. It is worth mentioning that a previous study by the
authors showed about 60% accuracy in identifying
weather-related crashes using the weather data obtained
from the weather stations [28]. Second, a new methodol-
ogy, which is based on combining the traditional probit
regression analysis and data mining decision tree tech-
nique, was utilized to overcome the limitations of each
standalone modeling technique. Third, factors affecting the
severity of work zone weather-related crashes were iden-
tified and discussed.
2 Data source
This study utilized 8 years (2006–2013) of crashes
including 3,028 weather-related crashes (1,887 PDO and
1,141 fatal ?injury) to determine factors affecting work
zone weather-related crashes in Washington State. The
crash data were extracted from the Strategic Highway
Research Program 2 (SHRP2) Roadway Information
Dataset (RID).
RID consists of roadway data collected from mobile
data collection project, government, public, and private
parties, in addition to supplemental crash history data
which is used in this study. For more information about
RID, see [29].
3 Methodology
In this study, factors affecting work zone weather-related
crashes were identified using a complementary parametric
and nonparametric crash severity model. In fact, both
parametric and nonparametric models have their own
advantages and disadvantages. For example, parametric
models such as probit and logistic regression can provide
the relationship between a response variable and predictors,
and the results obtained from them are easy to interpret and
understand [30]. However, the problem with these models
is that there are many pre-assumptions in parametric
models, which might negatively affect the accuracy of the
results. Risk factors can also exhibit various exposure
effects in different circumstances in parametric models
(hidden effects problem). These shortcomings cannot be
addressed using the common parametric models such as
logistic and probit regression models [31]. One of the
major solutions to address the hidden effects problem is to
split the full sample data into several sub-datasets using the
nonparametric classification tree method [31]. This method
might be an effective way to see the effects of risk factors’
hidden exposure in different circumstances. In addition,
using nonparametric models is beneficial as these models
have the ability to provide high prediction accuracy [31].
Therefore, this study utilized the probit–classification tree
method, which is a complementary method utilizing both
nonparametric (classification tree) and parametric (probit
regression) models, to analyze the effect of different risk
factors on work zone weather-related crashes. The depen-
dent variable in the model is the crash severity levels, and
the explanatory variables are the factors which influence
130 A. Ghasemzadeh, M. M. Ahmed
123 J. Mod. Transport. (2019) 27(2):129–140
crash severity levels. In this study, the crash severity is
defined as a binary variable, which has two levels including
severe crashes (injury and fatal crashes) and non-severe
crashes (PDO crashes).
3.1 Decision tree
A decision tree can be used for both continuous and
nominal target variables. When a decision tree is used to
predict a continuous target variable, it is called a regression
tree, and when it is used to classify a nominal target
variable, it is called a classification tree [32]. Two main
components of decision trees are the ‘‘root node’’ and the
‘‘leaf node.’’ The root node is the node located at the top of
the tree and contains all the data, and the ‘‘leaf node’’ refers
to the termination node and has the lowest impurity. More
specifically, based on the independent variable (splitter)
that creates the best homogeneity, the root node is divided
into two child nodes. This procedure (partitioning the target
variable recursively) will be continued until all the data in
each node reach their highest homogeneity; then, tree
growing will stop. This node, which does not have any
branches, is called the ‘‘leaf node,’’ and each path from the
top of the tree (the root node) to each leaf (the terminal
node) can be considered as a rule. It is worth mentioning
that data in each child node are purer (more homogenous)
than the data in the upper parent node [33]. In order to find
possible splits among all variables, a splitting criterion
(test) is performed. Splitting criterion is the main design
component of a decision tree [34]. More specifically, in the
decision tree learning algorithm, the splitting criterion’s
role is to measure the quality of each possible split among
all variables. Two common splitting criteria that can be
used to grow a decision tree are Chi-square and Gini
reduction. In this study, Gini splitting criterion is used to
select which variable and split pattern will be used to best
split the node.
Gini impurity shows the level of data impurity. More
specifically, it shows the incorrect classification probability
of a randomly chosen record from the specific node in the
subset. The procedure of selecting variables and split
scheme that can be used to best split the parent node is as
follows [35]:
1. Determine the node impurity: Considering the tas a
parent node, the node impurity i(t) can be calculated
using the Gini index definition, which is provided in
Eq. (1).
iðtÞ¼1X
M
j
nj
N
2
;ð1Þ
where Mrepresents the number of classes, njrepre-
sents the number of class jelements, and Ndepicts all
elements in the node.
If a node is homogeneous, then the value obtained
from Eq. (1) would be minimal. However, the value
would be higher for the less pure nodes.
2. Determine the impurity reduction (Di): For all possible
splits in the values for the variable x, the impurity
reduction on the parent node tcaused by a split sis
calculated as follows:
Diðx;s;tÞ¼iðtÞX
nt
j¼1
FjiðtjÞ;ð2Þ
where ntis the number of child nodes of the parent
node t;F
j
is the proportion of class jelements divided
by all elements in the node (the proportion mentioned
in the parenthesis in Eq. (1)). Di[0 indicates that
elements in the child nodes are purer than elements in
the parent node, and Di0 denotes that elements in
the child nodes are not purer than the parent node.
The best split which can be shown by s* associated
with the variable xcan be identified by comprehen-
sively searching all possible splits related to the vari-
able x. More clearly, s* causes the maximum impurity
reduction.
3. Determine the global maximum impurity reduction:
The previous step would be repeated, and the best
splits for all variables would be determined. Among all
the best splits, the split s* associated with the variable
x
*
determines the global maximum impurity reduction.
4. Determine the leaf node: If Di(x*, s*, t)[0, then
choose the variable x* and split s* to split the parent
node. If Di(x*, s*, t)B0, then the parent node will be
considered as the leaf node.
5. Stop the splitting: By satisfying one of these two
criteria, the splitting would be stopped:
(a) Any nodes cannot be further split (Di(x*, s*,
t)B0), or the number of elements in the node is
less than the preset minimum number.
(b) The current tree depth reaches the preset maxi-
mum tree depth. Otherwise, go to Step 1.
For more information about the decision tree method,
see [32].
3.2 Probit regression
Probit regression is a common statistical method that can
estimate the coefficients of predictors [36]. This method
was chosen to develop a separate probit regression for each
group identified by the decision tree model. The forward
Complementary parametric probit regression and nonparametric classification tree modeling…131
123
J. Mod. Transport. (2019) 27(2):129–140
selection method was used to find the best fitting model.
The advantage of using probit regression model is the
ability to estimate marginal effects. Probit regression is
accordingly implemented to each data group to find the
coefficient of each explanatory variable.
Probit regression has the S-shape and can be used for
dealing with binary response variables. Probit model
(probit PðxÞ
½
¼y) is shown as Eq. (3)[36].
y¼aþbx;ð3Þ
where ais the probability of response when explanatory
variables are the reference level (or when x= 0) and b
represents the change in the probability per unit change in
x, a parameter to be estimated.
The cumulative distribution function (CDF) F(x) for a
random variable xcould be defined as FðxÞ¼PðXxÞin a
way that xcould be varied between 1 and 1.By
increasing the x,F(x) increases from 0 to 1 because the
probability of having success would be increased. Let us
consider xas a continuous random variable and plot the
cumulative distribution function as a function of x; the
result looks like an S-shape when b[0[36].
The best definition for the relation of CDF, normal
distribution and probit model provided by Agresti [36]is
‘‘ when F is the CDF of a normal distribution, the model
provided in Eq. (3)is equivalent to the probit model.’’ This
statement is clearly shown in Eqs. (4), (5), and (6) as the
normal density function provided in Eq. (6) and the CDF of
normal distribution depicted in Eq. (5)[36].
PxðÞ¼FxðÞ:ð4Þ
As mentioned, assuming the Ffollows a normal
cumulative distribution:
FðxÞ¼UðxÞ¼ Z
x
1
/ðzÞdz;ð5Þ
where /ðzÞis the normal density function and defined as in
Eq. (6).
/ðzÞ¼
pexp ðzlÞ2
2r2
rffiffiffiffiffiffi
2p
p;zNð0;1Þ;l¼a
b;
r¼1
b
jj
;
ð6Þ
where zfollows the normal distribution with the mean of 0
and standard deviation equal to 1.
For more information about probit regression, see [36].
3.3 Variables description
Table 1shows the selected variables for developing the
work zone crash severity model in adverse weather
conditions. The dependent variable is crash severity with
two levels: severe crashes (fatal and injury crashes) and
non-severe crashes (PDO crashes). Explanatory variables
can be considered as driver behavior, roadway conditions,
environmental conditions, and crash characteristics.
4 Results and discussion
The dataset was divided into three sub-datasets (training,
validation, and testing). Among them, 60% of the data
were assigned to the training sub-dataset, 30% to the val-
idation sub-dataset, and 10% to the testing sub-dataset.
More clearly, 3023 observations were used and divided
among mentioned sub-datasets (i.e., 1813 observations
were assigned to the training sub-dataset, 906 observations
were assigned to the validation sub-dataset, and 302
observations were assigned to the testing sub-dataset). In
addition, the maximum tree depth of 10, which is suit-
able considering the number of variables, was selected. The
minimum number of data per node was selected as 40 so
that all the crash severity classes have enough data for the
subsequent probit analysis in each leaf node.
The Gini reduction test found any node at level four at
the significance level of 0.05 to be insignificant based on
the obtained results. Hence, the tree stops growing at this
level, and the tree comprising four leaf nodes is selected.
Optimal decision tree size ensures mitigating the overfit-
ting issue. Two criteria were considered: First, the mis-
classification rate for the training and validation datasets
should be similar to some extent; and second, the mis-
classification rate and average squared error should be as
low as possible. Misclassification rates for the training and
validation were obtained as 0.32 and 0.35, respectively.
The average square errors obtained were 0.21 and 0.22 for
the training and validation datasets, respectively. There-
fore, both criteria were satisfied based on the obtained
results.
Figure 1shows the selected decision tree structure for
the probit–classification tree model. As can be seen, col-
lision type, the presence of a traffic control device, and
lighting conditions were found to be significant interacting
variables. Based on the classification shown in Fig. 1, the
training dataset was divided into four groups representing
four leaf nodes, including
Group (1): collision type = 3 and 4 (sideswipe and other
crashes);
Group (2): collision type = 1 and 2 (rear-end and angle
crashes) and traffic control = 2 (none);
Group (3): collision type = 1 and 2 (rear-end and angle
crashes) and traffic control = 1 (stop/signal/yield sign/
other) and lighting condition = 2 (other);
132 A. Ghasemzadeh, M. M. Ahmed
123 J. Mod. Transport. (2019) 27(2):129–140
Table 1 Variables descriptions
Variable Description Type Definition Assigned
code
Crash severity level Severity of a crash Binary PDO 1
Fatal ?injury 2
Speed Maximum posted speed Binary Below 50 mph
Above 50 mph
1
2
Gender Driver’s gender Categorical Male 1
Female 2
Age Driver’s age Categorical Young \25 1
Middle (25–64) 2
Old [64 3
Land use If the crash occurred in an urban area Binary Urban 1
Rural 2
Vehicle involved Number of motor vehicles involved Categorical Greater than or equal to three 1
Less than three 2
Collision type Type of crash Categorical Rear-end 1
Angle 2
Sideswipe 3
Other 4
Driving under the
influence
If the driver was under the influence
of alcohol or drugs
Binary Sober 1
Drunk 2
Roadway characteristic If there is a curve at the crash location Binary No 1
Yes 2
Lighting condition If the crash occurred during the daylight Binary Yes 1
No 2
Weather Type of severe weather condition Categorical Rain 1
Snow 2
Fog 3
Other 4
Vehicle action before
crash
Vehicle last action before the crash Categorical Stopped 1
Making left or right turn 2
Changing lane 3
Slowing 4
Other (going straight, etc.) 5
Roadway type Roadway type in crash location Categorical One way 1
Two-way divided 2
Two-way undivided 3
Other 4
Traffic control devices Presence of traffic control devices at
crash location
Binary Stop/signal/yield sign/other 1
None 2
Vehicle age Vehicle age Categorical Less than 5 years 1
Between 5 and 10 years 2
Greater than 10 years 3
Vehicle type Whether the vehicle is considered as a big
vehicle, a small vehicle or a motorcycle
Categorical Big vehicles (bus, truck, pickup,
etc.)
1
Small vehicles (sedan, coupe, etc.) 2
Motorcycle 3
Complementary parametric probit regression and nonparametric classification tree modeling…133
123
J. Mod. Transport. (2019) 27(2):129–140
Table 1 continued
Variable Description Type Definition Assigned
code
Airbag Whether the vehicle is equipped with airbag or
not
Categorical Equipped 1
Not airbag equipped 2
Construction type Different construction types at crash location Categorical Construction 1
Maintenance 2
Utility 3
Other 4
Crash location Whether the crash is within work zone or in
external traffic backup caused by work zone
Binary Within work zone 1
In external traffic backup 2
Surface condition Surface condition at crash location Binary Dry 1
Other (wet, snow, etc.) 2
Fig. 1 Decision tree structure for the logistic-decision tree model
134 A. Ghasemzadeh, M. M. Ahmed
123 J. Mod. Transport. (2019) 27(2):129–140
Group (4): collision type = 1 and 2 (rear-end and angle
crashes) and traffic control = 1 (stop/signal/yield sign/
other) and lighting condition = 1 (daylight).
For each above-mentioned group, a separate probit
regression model was developed, and the marginal effect of
risk factors for work zone weather-related crashes was
calculated. For instance, in case of Group (2), 19 variables
are available for developing a probit model, since the
lighting condition is equal to 2, which means that this
variable is fixed in this model. It is worth mentioning that
for Group 2, collision type still has two categories (rear-end
and angle crashes), and therefore, this variable is not fixed
and will be used for further analysis in the probit model.
Table 2shows the results obtained from developing a
separate probit model for each classified group using the
estimated decision tree algorithm. In fact, four models were
estimated for work zone weather-related crashes using the
probit–classification tree procedure. To confirm the
suitability and fitness of the models, three statistics
including Akaike information criterion (AIC) statistic, the
Schwarz criterion (SC) statistic, and the -2 log-likelihood
statistic were used, and the results are given in Table 3.
As can be seen in model 1, the marginal effects of risk
factors on the crash severity of a driver who is involved in
collision types 3 and 4 (sideswipe and other) in work zone
weather-related crashes can be identified. Speed limit is
one of the factors found to be significant in model 1. In
fact, a higher speed limit dramatically increases the
severity of work zone weather-related crashes. More
specifically, drivers in work zone weather-related crashes
occurred in a segment with less than 55 mph posted speed
limit were 13% less likely to be involved in severe crashes
(the marginal effect is -0.13 in Table 2) in comparison
with the reference level (drivers who were driving in a
work zone segment with a posted speed limit greater than
55 mph). In fact, driving over the speed limit could be
risky because it provides insufficient time for
Table 2 Estimation of probit classification tree regression for work zone weather-related crash severity
Model Variable Coefficient SE Wald Chi-
square
Pvalue Marginal effect
dy/dxSE
Model 1 Intercept 0.5876 0.2132 7.5971 0.0058 – –
Speed limit 1 -0.3769 0.0972 15.0471 0.0001 -0.1353255 0.0313671
Vehicle age 1 -0.3709 0.1120 10.9751 0.0009 -0.1333592 0.0309113
Vehicle age 2 -0.0637 0.1046 0.3715 0.5422 -0.0262309 0.0060800
Sobriety 1 -0.5067 0.1833 7.6390 0.0057 -0.1323963 0.0306881
Gender 1 -0.1876 0.0928 4.0818 0.0433 -0.0548812 0.0127209
Roadway characteristic 1 0.2864 0.0987 8.4145 0.0037 -0.0665939 0.0154358
Collision type 3 -0.2600 0.0948 7.5265 0.0061 -0.0746425 0.0173014
Model 2 Intercept -1.0630 0.5961 3.1806 0.0745 – –
Roadway type 2 1.1801 0.2017 34.2453 \0.0001 0.3710220 0.0917906
Speed limit 1 -0.2757 0.1092 6.3771 0.0116 -3.6055224 0.0182795
Vehicle type 1 -0.1790 0.0776 5.3202 0.0211 -2.5847597 0.6394681
Crash location 1 -0.2710 0.0982 7.6225 0.0058 -0.1153495 0.0285374
Roadway characteristic 1 -0.2302 0.1041 4.8938 0.0270 -0.0930068 0.0230098
Surface condition 2 0.8450 0.2979 8.0437 0.0046 0.2948777 0.0729526
Collision type 1 -0.4907 0.2117 5.3725 0.0205 -0.1845932 0.0456683
Model 3 Intercept 6.7347 334.7 0.0004 0.9839 – –
Sobriety 1 -1.3562 0.3125 18.8339 \0.0001 -0.4300327 0.1684546
Airbag 1 -0.4780 0.2352 4.1319 0.0421 -0.1320891 0.0517426
Vehicle involved 2 -0.6947 0.1659 17.5375 \0.0001 -0.2196478 0.0860416
Model 4 Intercept -0.7614 0.3911 3.7887 0.0516 – –
Vehicle action before crash 1 0.2731 0.1345 4.1238 0.0423 0.0793240 0.0205579
Vehicle action before crash 2 -1.0430 0.5113 4.1618 0.0413 -0.3807359 0.0986730
Speed limit 1 -0.3002 0.1405 4.5622 0.0327 -0.1242374 0.0321978
Weather condition 1 0.9319 0.3227 8.3385 0.0039 0.1333412 0.0345572
Land use 1 0.3460 0.1459 5.6216 0.0177 0.1054947 0.0273404
SE standard error
Complementary parametric probit regression and nonparametric classification tree modeling…135
123
J. Mod. Transport. (2019) 27(2):129–140
suitable response to control and handle unexpected situa-
tions, and this might be exacerbated during adverse
weather conditions such as heavy rain or fog.
The findings indicated that among those drivers who had
sideswipe and other types of crashes (all crashes except
rear-end and angle crashes), female drivers had a higher
casualty risk in comparison with male drivers. Two factors
have been identified for the higher risk of being injured
associated with the female drivers at work zone crashes in
the literature, i.e., risk-taking behavior, which is higher in
younger female drivers, and increased number of female
drivers (exposure effect) [31,37]. Based on the identified
marginal effects for model 1, male drivers were 5% less
likely to be involved in severe crashes in comparison with
female drivers.
Vehicle age is another factor that turned out to be a
significant predictor in model 1. Results showed that older
vehicles were severely impacted in work zone weather-
related crashes. This result confirms previous studies,
which depicted the impact of vehicle age on driver injury
severity [38,39]. More specifically, vehicles less than
5 years old were 13% less likely to be involved in severe
work zone weather-related crashes in comparison with
those over 10 years old. It was also found that 5–10-year-
old vehicles were 2% less involved in severe work zone
weather-related crashes in comparison with older vehicles.
Driving under the influence is another factor that came
out to be significant in model 1. Particularly, sober drivers
were 13% less likely to be involved in severe work zone
weather-related crashes in comparison with drivers under
the influence, which supports previous studies [40,41].
Roadway characteristics (presence of a curve) were also
found to have a significant effect in this model. More
specifically, drivers who were involved in a work zone
weather-related crash at non-curved sections were 6% less
likely to be involved in severe crashes in comparison with
drivers who were involved in a work zone weather-related
crash at a curve. The presence of curves at work zone
segments could adversely affect the sight distance and
handling of the vehicle in critical situations. The adverse
weather might exacerbate this negative effect. Risky
overtaking might be another reason for severe crashes at
work zones on road curves.
The model also estimated the effect of collision type
(sideswipe crashes) on the severity of crashes. More
clearly, drivers who were involved in sideswipe crashes
were 7% less likely to be involved in severe crashes in
comparison with other collision types. It is worth men-
tioning that most of the sideswipe crashes were not severe
in comparison with head-on crashes at work zones, which
will be discussed in model 2 interpretation.
Model 2 indicates the results of the probit model for
those drivers who were involved in rear-end and angle
crashes, in locations with no traffic control devices. Par-
ticularly, model 2 showed that route type is a contributing
factor in crash severity model. Drivers who were involved
in work zone weather-related crashes in rural or secondary
routes were 37% more likely to be involved in severe
Table 3 Pure probit regression
Parameter Estimate SE Wald Chi-
square
Pvalue Marginal effect
dx/dySE
Intercept -0.4316 0.1834 5.5401 0.0186 – –
Vehicle action before crash 1 0.1439 0.0650 4.9053 0.0268 0.0613226 0.0088342
Vehicle action before crash 2 -0.5228 0.1567 11.1332 0.0008 -0.1802264 0.0259636
Roadway type 1 -0.4321 0.1938 4.9698 0.0258 -0.1553926 0.0223860
Roadway type 2 0.2769 0.0990 7.8209 0.0052 0.0938238 0.0135164
Roadway type 3 0.3120 0.1003 9.6716 0.0019 0.1096382 0.0157946
Speed limit 1 -0.1901 0.0627 9.1990 0.0024 -0.0718147 0.0103457
Traffic control 2 -0.1597 0.0534 8.9583 0.0028 0.0551023 0.0079381
Sobriety 2 0.6802 0.1291 27.7685 \0.0001 -0.2363750 0.0340524
Gender 1 -0.1469 0.0487 9.1061 0.0025 -0.0533711 0.0076887
Roadway characteristic 2 0.2216 0.0645 11.7957 0.0006 -0.0803298 0.0115724
Surface condition 2 0.2705 0.1374 3.8766 0.0490 0.0793566 0.0114322
Land use 1 -0.1587 0.0666 5.6741 0.0172 0.0563574 0.0081189
Vehicle involved 1 -0.1547 0.0490 9.9761 0.0016 -0.0548034 0.0078950
Collision type 1 0.2220 0.0673 10.8795 0.0010 0.0742384 0.0106949
Collision type 2 0.5739 0.1374 17.4388 \0.0001 0.1945923 0.0132321
Collision type 3 -0.2636 0.0969 7.4078 0.0065 -0.0918510 0.0132321
136 A. Ghasemzadeh, M. M. Ahmed
123 J. Mod. Transport. (2019) 27(2):129–140
crashes in comparison with drivers who were driving on
interstate highways. This could be because most of the
rural roads are narrow two-way two-lane undivided roads
which do not have enough shoulder width. Even secondary
roads do not have the same quality as interstate roadways,
which might intensify the severity of crashes in rural and
secondary roads.
Vehicle type was found to be a significant factor in
model 2. Drivers who were driving passenger cars and
involved in work zone weather-related crashes were 2.5
times less likely to be involved in severe crashes in com-
parison with those driving other vehicles.
Crash location was found to be another significant factor
in this model. The results showed that drivers who were
involved in crashes within a work zone area were 11% less
likely to be involved in severe crashes in comparison with
drivers who were involved in crashes in external traffic
backup caused by work zone. This finding is supported by
other studies which noted lane closure might increase the
traffic conflicts, as a road work mostly requires closing a
part of the roadway [42]. This situation might be worse in
adverse weather conditions as the low visibility for drivers
could prevent them to perform appropriate maneuver in
critical circumstances.
The model also showed the significant effect of surface
conditions on the severity of crashes. Drivers who were
involved in work zone crashes were 29% more likely to be
involved in severe crashes if the surface is wet in com-
parison with a dry surface condition. The marginal effect of
rear-end crashes (collision type = 1) is given in Table 2,
which indicated that drivers who were involved in rear-end
crashes (most common crashes in work zones) were 18%
less likely to be involved in severe crashes in comparison
with angle crashes during adverse weather conditions.
Model 3 specifies the results of the probit model for
those drivers who were involved in rear-end and angle
crashes, with the presence of traffic control devices and in
the absence of daytime lighting conditions. Similar to
model 1, sobriety came out to be significant, which means
that the crash severity is affected by this factor. The mar-
ginal effect of a risk factor on crash severity showed that
drivers equipped with airbags were 13% less likely to be
involved in severe crashes, which is consistent with a
previous study [31].
In addition, results showed that crashes with fewer
vehicles involved were 21% less likely to be severe. This
could be because of the severity of chain crashes. Asking
drivers to keep the safe following distance and avoid tail-
gating might be helpful. Installing dynamic message signs
at work zones could be beneficial to provide advisory
messages for drivers.
Finally, model 4 reveals the results of the probit model
for those drivers who were involved in rear-end and angle
crashes, with the presence of traffic control devices and in
daytime lighting conditions. Vehicle action before crash,
speed limit, weather conditions, and land use came out to
be significant factors affecting crash severity model.
Indeed, vehicles making a left or right turn before a crash
were 38% less likely to be involved in severe crashes in
comparison with vehicles going straight (category 5 in
Table 1).
It was also found that drivers who were driving on roads
with posted speed limits less than 55 mph were 12% less
likely to be involved in severe crashes. In addition, drivers
who were involved in rainy weather condition crashes were
13% more likely to be involved in severe crashes. Finally,
drivers who were driving in a rural area were 10% more
likely to be involved in severe work zone weather-related
crashes in comparison with those driving on urban road-
ways. This might be due to the fact that risky behaviors
such as not wearing seatbelts are more common among
rural drivers [43].
As mentioned earlier, another conventional probit model
with all variables was developed to compare the results
with complementary probit–classification tree models. All
the 20 variables used for developing probit–classification
tree were considered in developing the conventional probit
model as well. Forward stepwise selection method was
used to find the best model fit. The results of the probit
regression model are given in Table 3.
As can be seen, 11 variables came out to be significant
in the conventional probit model. However, some impor-
tant contributing factors including vehicle age, vehicle
type, crash location, airbag, number of vehicles involved,
lighting, and weather conditions are not represented in this
model. The conventional probit model fit statistics are
provided in Table 4.
Receiver operating characteristic (ROC) curve was used
to visualize models’ performance. The predictive capabil-
ity of the probit–classification tree models and conven-
tional probit (base model) is shown in Fig. 2using ROC
curves. ROC curve shows the models’ performance by
plotting sensitivity versus 1-specificity. More clearly, if
there are no relevant information and bias results, the ROC
curve would be closer to the diagonal line. On the other
hand, the best performed model would be close to the
upper left corner.
Figure 2shows that for training dataset which contains
most of the data, all developed probit–classification tree
models performed better than the conventional probit
model. It is also worth mentioning that even though small
portions of dataset were assigned to validation and testing
datasets (in comparison with training dataset), still using
probit–classification tree method showed a better perfor-
mance in comparison with a conventional probit model.
Complementary parametric probit regression and nonparametric classification tree modeling…137
123
J. Mod. Transport. (2019) 27(2):129–140
5 Conclusions
This study explored the effects of vehicle, driver behavior,
and environmental factors on work zone weather-related
crashes severity using a method that combines both data
mining technique and conventional parametric modeling.
In addition, the obtained results from both conventional
probit model and proposed probit–classification tree model
were compared to better understand the advantages of the
proposed model using the 8 years of work zone weather-
related crashes.
The complementary methodology utilized in this study
has the advantage of being used in safety analysis, as this
model can compensate for the weak points of parametric
and nonparametric models.
In comparison with the probit–classification tree model,
some important contributing factors, such as vehicle age,
vehicle type, crash location, airbag, number of the vehicles
involved, lighting, and weather conditions, were excluded
in the conventional probit model, which shows the capa-
bility of the developed model in identifying risk factors
affecting work zone weather-related crashes.
The most interesting finding of this study is that both the
presence of traffic control device and lighting conditions
were found to be significant interacting variables in the
developed complementary crash severity model for work
zone weather-related crashes. This finding shows that more
attention should be paid to the effect of weather conditions
in different stages of work zone projects by transportation
agencies and contractors. It is highly recommended to
transportation agencies and contractors to invest in
Fig. 2 Comparision among all models using ROC chart
Table 4 Model fit statistics for four models obtained from probit–classification tree
Model 1 Model 2 Model 3 Model 4 Conventional probit
Intercept
only
Intercept
and
covariates
Intercept
only
Intercept
and
covariates
Intercept
only
Intercept
and
covariates
Intercept
only
Intercept
and
covariates
Intercept
only
Intercept
and
covariates
Model fit statistics
AIC 1119.4 1081.9 1714.4 1604.7 446.5 371.1 665.1 631.5 4003.28 3844.92
SC 1124.3 1120.5 1719.6 1682.0 450.3 408.8 669.3 682.1 4009.30 3965.19
-2 Log-likelihood 1117.4 1065.9 1712.4 1574.7 444.5 351.1 663.1 607.5 4001.28 3804.92
138 A. Ghasemzadeh, M. M. Ahmed
123 J. Mod. Transport. (2019) 27(2):129–140
adequate lighting equipment for nighttime work, which is
the only option in most urban areas. In 2013, the American
Traffic Safety Services Association developed the first and
the most comprehensive set of nighttime lighting guideli-
nes for work zones called ‘‘Nighttime Lighting Guidelines
for Work Zones: A guide for developing a lighting plan for
nighttime work zones’’ [44]. The manual provides a simple
procedure for designing a nighttime lighting system for
work zones that can be easily adopted by engineers,
designers, and contractors without prior experience in
illumination. However, more studies are needed to clarify
and characterize driver behavior in different lighting, vis-
ibility, and weather conditions.
This study found that the presence of a traffic control
device is a significant contributing factor to crash injury
severity. Improving the temporary traffic control (TTC),
including but not limited to the portable variable speed
limit (VSL), to adjust speed limits during adverse weather
conditions can be beneficial in this regard.
Portable changeable message signs (PCMS) are also highly
recommended to warn drivers about work zones to reduce
the severity of work zone crashes.
Acknowledgements This work was conducted under the second
Strategic Highway Research Program (SHRP2), which is adminis-
trated by the Transportation Research Board (TRB) of the National
Academies of Sciences, Engineering, and Medicine, and it was
sponsored by the Federal Highway Administration (FHWA) in
cooperation with the American Association of State Highway and
Transportation Officials (AASHTO).
Open Access This article is distributed under the terms of the
Creative Commons Attribution 4.0 International License (http://
creativecommons.org/licenses/by/4.0/), which permits unrestricted
use, distribution, and reproduction in any medium, provided you give
appropriate credit to the original author(s) and the source, provide a
link to the Creative Commons license, and indicate if changes were
made.
References
1. Ullman GL, Pratt M, Fontaine MD et al (2018) Estimating the
safety effects of work zone characteristics and countermeasures: a
guidebook. Natl Coop Highw Res Progr Rep. https://doi.org/10.
17226/25007
2. Ghasemzadeh A, Ahmed MM (2017) A tree-based ordered probit
approach to identify factors affecting work zone weather-related
crashes severity in North Carolina using the highway safety
information system dataset. In: 96th Transportation research
board annual meeting, Washington, D.C.
3. Ghasemzadeh A, Ahmed MM (2016) Crash characteristics and
injury severity at work zones considering adverse weather con-
ditions in Washington using SHRP 2 roadway information data-
base. In: 95th Transportation research board annual meeting,
Washington, D.C.
4. Khattak AJ, Khattak AJ, Council FM (2002) Effects of work zone
presence on injury and non-injury crashes. Accid Anal Prev
34:19–29. https://doi.org/10.1016/S0001-4575(00)00099-3
5. Schrock SA, Ullman GL, Cothron AS, Cothron AS (2004) An
analysis of fatal work zone crashes in Texas. Texas Transporta-
tion Institute, Texas
6. Akepati SR, Dissanayake S (2011) Characteristics and contribu-
tory factors of work zone crashes. In: Transportation Research
Board 90th annual meeting
7. Weng J, Zhu J-Z, Yan X, Liu Z (2016) Investigation of work zone
crash casualty patterns using association rules. Accid Anal Prev
92:43–52
8. Debnath AK, Blackman R, Haworth N (2015) A comparison of
self-nominated and actual speeds in work zones. Transp Res Part
F Traffic Psychol Behav 35:213–222
9. Wang K, Qin X (2014) Use of structural equation modeling to
measure severity of single-vehicle crashes. Transp Res Rec J
Transp Res Board 2432:17–25
10. Qi Y, Srinivasan R, Teng H, Baker R (2013) Analysis of the
frequency and severity of rear-end crashes in work zones. Traffic
Inj Prev 14:61–72
11. Garber N, Zhao M (2002) Distribution and characteristics of
crashes at different work zone locations in Virginia. Transp Res
Rec 1794:19–25
12. Garber NJ, Woo T-SH (1990) Accident characteristics at con-
struction and maintenance zones in urban areas. No. VTRC
90-R12. Virginia Transportation Research Council
13. Hargroves BT (1981) Vehicle crashes in highway work zones.
J Transp Eng 107:525–539
14. Chambless J, Chadiali AM, Lindly JK, McFadden J (2002)
Multistate work zone crash characteristics. ITE J 72(5):46–50
15. Hall JW, Lorenz VM (1989) Characteristics of construction zone
crashes. In: Transportation research record: journal of the trans-
portation research board. TRB, National Research Council,
Washington, D.C, pp 20–27
16. Ghasemzadeh A, Ahmed MM (2018) Utilizing naturalistic driv-
ing data for in-depth analysis of driver lane-keeping behavior in
rain: non-parametric MARS and parametric logistic regression
modeling approaches. Transp Res Part C Emerg Technol
90:379–392. https://doi.org/10.1016/j.trc.2018.03.018
17. Hammit BE, Ghasemzadeh A, James RM et al (2018) Evaluation
of weather-related freeway car-following behavior using the
SHRP2 naturalistic driving study database. Transp Res Part F
Traffic Psychol Behav 59:244–259
18. Ghasemzadeh A, Ahmed MM (2017) Drivers’ lane-keeping
ability in heavy rain: preliminary investigation using SHRP 2
naturalistic driving study data. Transp Res Rec J Transp Res
Board. https://doi.org/10.3141/2663-13
19. Ghasemzadeh A, Hammit BE, Ahmed MM, Young RK (2018)
Parametric ordinal logistic regression and non-parametric deci-
sion tree approaches for assessing the impact of weather condi-
tions on driver speed selection using naturalistic driving data.
Transp Res Rec. https://doi.org/10.1177/0361198118758035
20. Ahmed MM, Ghasemzadeh A (2018) The impacts of heavy rain
on speed and headway behaviors: an investigation using the
SHRP2 naturalistic driving study data. Transp Res Part C Emerg
Technol 91:371–384. https://doi.org/10.1016/j.trc.2018.04.012
21. Colyar J, Zhang L, Halkias J (2003) Identifying and assessing key
weather-related parameters and their impact on traffic operations
using simulation. In: Institute of Transportation Engineers 2003
Annual Meeting and Exhibit (held in conjunction with ITE Dis-
trict 6 Annual Meeting) Institute of Transportation Engineers
22. Qin X, Noyce D, Lee C, Kinar J (2006) Snowstorm event-based
crash analysis. Transp Res Rec J Transp Res Board
1948:135–141
Complementary parametric probit regression and nonparametric classification tree modeling…139
123
J. Mod. Transport. (2019) 27(2):129–140
23. Yu R, Xiong Y, Abdel-Aty M (2015) A correlated random
parameter approach to investigate the effects of weather condi-
tions on crash risk for a mountainous freeway. Transp Res part C
Emerg Technol 50:68–77
24. Huang H, Abdel-Aty M (2010) Multilevel data and Bayesian
analysis in traffic safety. Accid Anal Prev 42:1556–1565
25. Eisenberg D, Warner KE (2005) Effects of snowfalls on motor
vehicle collisions, injuries, and fatalities. Am J Public Health
95:120–124
26. Ahmed M, Abdel-Aty M, Yu R (2012) Assessment of interaction
of crash occurrence, mountainous freeway geometry, real-time
weather, and traffic data. Transp Res Rec J Transp Res Board
2280:51–59
27. Khattak A, Knapp K (2001) Interstate highway crash injuries
during winter snow and nonsnow events. Transp Res Rec J
Transp Res Board 1746:30–36
28. Ahmed M, Abdel-Aty M, Lee J, Yu R (2014) Real-time assess-
ment of fog-related crashes using airport weather data: a feasi-
bility analysis. Accid Anal Prev 72:309–317. https://doi.org/10.
1016/j.aap.2014.07.004
29. Smadi O, Hawkins N, Hans Z, Bektas BA, Knickerbocker S,
Nlenanya I, Souleyrette R, Hallmark S (2015) Naturalistic driving
study: development of the roadway information database. Federal
Highway Administration. SHRP 2 Report No. S2-S04A-RW-1
30. Abdel-Aty M, Abdelwahab H (2004) Modeling rear-end colli-
sions including the role of driver’s visibility and light truck
vehicles using a nested logit structure. Accid Anal Prev
36:447–456
31. Weng J, Meng Q, Wang DZW (2013) Tree-based logistic
regression approach for work Zone Casualty Risk Assessment.
Risk Anal 33:493–504
32. Osei-Bryson K-M, Ngwenyama O (2014) Advances in research
methods for information systems research. Springer, Berlin
33. Weng J, Meng Q (2011) Decision tree-based model for estima-
tion of work zone capacity. Transp Res Rec J Transp Res Board
2257:40–50
34. Kovalerchuk B, Vityaev E (2000) Data mining in finance:
advances in relational and hybrid methods. Springer, Berlin
35. Weng J, Meng Q (2012) Effects of environment, vehicle and
driver characteristics on risky driving behavior at work zones. Saf
Sci 50:1034–1042
36. Agresti A (2007) An introduction to categorical data analysis,
2nd edn. Wiley, New York
37. Kostyniuk LP, Molnar LJ, Eby DW (2000) Are women taking
more risks while driving? A look at Michigan drivers. In:
Women’s travel issues second national conference
38. National Highway Traffic Safety Administration (2013) How
vehicle age and model year relate to driver injury severity in fatal
crashes. US Dep Transp
39. Glassbrenner D (2012) An analysis of recent improvements to
vehicle safety. NHTSA Tech Rep (Report No DOT HS 811 572)
40. DeJong W, Hingson R (1998) Strategies to reduce driving under
the influence of alcohol. Annu Rev Public Health 19:359–378
41. Keall MD, Frith WJ, Patterson TL (2004) The influence of
alcohol, age and number of passengers on the night-time risk of
driver fatal injury in New Zealand. Accid Anal Prev 36:49–61
42. Weng J, Meng Q, Yan X (2014) Analysis of work zone rear-end
crash risk for different vehicle-following patterns. Accid Anal
Prev 72:449–457. https://doi.org/10.1016/j.aap.2014.08.003
43. Hao W, Daniel J (2016) Driver injury severity related to incle-
ment weather at highway–rail grade crossings in the United
States. Traffic Inj Prev 17:31–38
44. American Traffic Safety Services Association (2013) Nighttime
lighting guidelines for work zones. https://www.workzonesafety.
org/files/documents/training/fhwa_wz_grant/night_lighting_
guide.pdf
140 A. Ghasemzadeh, M. M. Ahmed
123 J. Mod. Transport. (2019) 27(2):129–140
