# Analysis of Rear-End Crash on Thai Highway: Decision Tree Approach

Authors: Thanapong Champahom; Sajjakaj Jomnonkwao; Vuttichai Chatpattananan; Ampol Karoonsoontawong; Vatanavongs Ratanavaraha
Journal: Journal of Advanced Transportation
 (2019)

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## Abstract

Objective. Among crash types on Thai highways, rear-end crashes have been found to cause the largest number of fatalities. This study aims to find ways to decrease rear-end crashes and fatal rear-end crashes. Methods. Classification and regression tree (CART) was used to analyze the complicated relationship of variables of big data. The analysis was conducted by creating two models: (1) a model which indicates the causes of rear-end crashes by applying Quasi-Induced Exposure to at-fault driver characteristics; (2) a determined model which studies fatal crashes. Results. Predictor variables in the model of at-fault and not-at-fault drivers found that driver age is most significant, followed by number of lanes and median opening area. For the mode of fatality, the use of safety equipment was found to be of most importance. Conclusion. The model results can be used to develop guidelines for public awareness programs for motorists and to propose policy changes to the Department of Highway in order to reduce the severity of rear-end crashes. Moreover, this paper discusses the variables that may result in both the perspective of rear-end crash number and the fatality rate of rear-end crashes as strategies in future research.


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## Body

## 1. Introduction

Crash trends on Thailand highways are continuously on the increase [1–3]. Crash type statistics reveal that rear-end collision is the second most common type of collision. However, the highest number of fatalities occur as a result of rear-end collisions (Figure 1). Therefore, finding strategies to decrease the number and severity of rear-end crashes is urgently needed.Figure 1
Crash on Thai highways by crash type.There are two important issues in the study of rear-end crashes at intersections. First, a study of the causes of rear-end crashes, focusing on at-fault and not-at-fault drivers, has found that most crashes are caused by drivers not leaving enough space between their own car and cars in front [4]. Therefore, the cause of rear-end collisions, is the car behind [5]. This study focuses on the driver characteristics of the at-fault driver, that is, the driver of the car behind that crashes into the car in front, by applying Quasi-Induced Exposure Methods [6]. These methods have been widely used in the field of traffic accident research. The principle of these methods is to predict the at-fault driver based on the accident report [7, 8] by supposing that the distribution of not-at-fault drivers closely represents the distribution of exposure to accident hazards [9, 10]. Second, this research explores the relevance of the high fatality rate caused by rear-end crashes. Fatal crashes must be considered from a characteristic study of rear-end crashes by focusing on ways to reduce fatalities. Sullivan and Flannagan [11] studied fatal crash risks and found that darkness is the risk factor causing the greatest number of fatalities, due to the invisibility of vehicles parked along the roadside. Wiacek, et al. [12] found that the greater the difference in velocity of the struck car and the striking car, the higher the number of rear-end crash fatalities. However, if a truck is involved in a rear-end crash, the chances of fatality are further increased.There are numerous factors affecting the causes of rear-end crashes. These include driver characteristics that affect driving decision making, such as driver characteristics (gender, age, alcohol use) [13–15], environment (time, weather conditions), roads (surface condition, physical characteristics) [16, 17], vehicle type [18], and number of traffic lanes [14, 19, 20].Previous research has found that factors causing death in rear-end crashes included driver characteristics affecting braking, such as gender, age, and alcohol or substance abuse [21]. Use of a seatbelt has been found to be another important contributing factor to rear-end fatalities [22]. Vehicle type is an important factor in all accident types [23], but especially in rear-end crashes. If the types of vehicle involved in a crash are very different, the chances of severity are higher [24]. Speed limit factors also affect the severity of the crash [12]. Other important characteristics of fatal crashes are physical road characteristics and visibility [21].A statistical analysis of rear-end crashes involves independent variables, such as weather conditions, vehicle type, seat belt use, and dependent variables, such as at-fault driver and not-at-fault driver, and fatal and nonfatal rear-end crash. The distribution analysis method has been widely used to generalize whether an estimated parameter exists. If there is an estimated parameter, the relationship between independent and dependent variables is considered. If there is no estimated parameter, data are investigated proportionally. Yan and Radwan [9] have stated that there are limitations to the use of parametric analysis (binary logistic regression) due to the difficulty in using it to investigate the relationship between two variables. Thus, an appropriate alternative is nonparametric analysis, or Decision tree or classification tree (DT). This is an algorithmic arrangement to perceive proportions of data according to determined dependent variables (also known as data mining) [25]. Thus, appropriate data can be used to analyze complex independent data [9, 26]. A decision tree is a structure that includes a root node, branches, and leaf nodes [27]. Yan and Radwan [9] have used DT to study rear-end crash data in Florida, USA, by analyzing two models. The first was an analysis of which accidents involved rear-end crashes, and the second was an analysis of driver characteristics of individuals who could potentially become at-fault-drivers.In choosing a model for this study, other models that can analyze the relationship between independent variables and target or categorical variables were considered. A traditional model using multiple logistic regression which has been widely used [24]. Another common model is the multinomial logit model which theoretically analyzes data using the nested logit model (NLM), which can examine hierarchical dependent variables [28]. Odds ratio is used to interpret probability. The advantage of this method is the ability to compare the effects of explanatory variables on dependent variables, especially when independent variables result in statistical significance. However, the limitation of each of these models is their inability to find relationships between explanatory variables. The Decision Tree Model (DT), however, potentially solves this problem. As mentioned earlier, rear-end crashes are the cause of high fatalities. Therefore, the presentation of this model simultaneously identifies relationships between independent variables, which may allow for the application of findings to policy development. For example, an examination of whether the different ages of drivers in different traffic lanes affects the role of the driver (at-fault/not-at-fault) in a crash can influence the development of effective policy. Research by Khan et al. [29], which compared DT and ordinal discrete choice model, confirmed that DT can help to address issues of multicollinearity and variable redundancy.Among studies that have analyzed rear-end crashes (Table1), most have analyzed crash frequency, followed by crash severity (fatal/nonfatal). One study has analyzed both crash frequency and severity outcome [30]. However, the crash data used in that study came from a country with different roads, conditions, driver behaviors to Thailand, leading to the development of a very different model. No concentrated road crash study of highways in Thailand has been conducted which applies the DT model to the reduction of the number of rear-end crash fatalities and fatal rear-end crashes. This research will discuss model consistency with the number of fatalities, by comparing the two with previous studies as a guideline for conducting future research.Table 1
Comparison with others studies in analysis of rear-end crash field.
Studies/model
At-fault/not-at-fault
Fatal injury
Comparison of two models
Raised issues
This study
✓
✓
✓
Case accidents in Thailand; comparison of the result of two model.
Yan et al. [10]
✓
Rear-end crash at signalized intersections.
Yan and Radwan [9]
✓
Model#1: Rear-end vs Nonrear-end, Model#2: At-fault/not-at-fault.
Chandraratna and Stamatiadis [7]
✓
Evaluation of not-at-fault assumption.
Meng and Qu [20]
✓
At Urban road tunnels.
Ma and Yan [5]
✓
Focused on age of driver.
Weng et al. [23]
✓
On work zone.
Chen et al. [21]
✓
Hybrid approach.
Chen et al. [22]
✓
Hybrid classifier.
Sullivan and Flannagan [11]
✓
Lighting conditions.
Joon-Ki et al. [40]
✓
Probability of freeway rear-end crash occurrence.
Das and Abdel-Aty [30]
✓
✓
✓
Genetic programing approach, rear-end crash in Florida.
Note: At-fault or not-at-fault driver are assumed related to the rear-end crash frequency.


## 2. Highway Crash Reporting

This study used Department of Highway (DOH) road accident data from 2011 to 2015. These data included dates, road segments, physical characteristics of accident scenes (e.g., straight road, curved road, work zone, median, intersection), environmental conditions (e.g., rain, lighting conditions, time of accident), cause-and-effect data (e.g., driving over the speed limit) and injury data (including fatalities, serious injuries and minor injuries). The information provided by the DOH may not cover all accidents. In cases of minor collisions, where victims came to an agreement, accidents were not recorded.Rear-end type collisions were selected from these data, and divided into three main types according to the movement of the front car prior to the collision [5]. These three are (1) going straight, with the front car traveling at normal speed, (2) decelerating speed, with the front car decelerating, such as when turning the car or executing a u-turn, and (3) stopping, with the front car parked on the roadside or on the hard shoulder or stopped at traffic lights. After screening, there were 2,096 cases of rear-end collision. As vehicle data had to be considered in this analysis, driver and vehicle factors were added to the model. The dataset comprised 5,445 vehicles involved in accidents.Descriptive statistics, shown in Table2, define the dependent variables: (1) The at-fault driver is the driver of the striking car, while the not-at-fault driver is the driver of the struck vehicle, (2) Fatal rear-end crash refers to a collision with at least one fatality either at the accident scene or at the hospital, while nonfatal rear-end crash denotes rear-end crash without fatality. For all 22 independent variables of the two models, they exhibited with the values of the two dependent variables. Data description was displayed to help illustrate the overall picture created by the data [31, 32]. After cleaning the data for driver exposure, there were 2,458 at-fault drivers and 2,096 not-at-fault drivers. With regard to crash fatalities, 1,156 vehicles were involved in fatal rear-end crashes, and 3,396 vehicles were involved in nonfatal rear-end crashes. According to vehicle type (Veh_type), medium cars, such as private cars and pickup trucks had a 28.0% chance of being at-fault. According to fatal rear-end collisions, larger vehicles were the cause of 11.7% of collisions, and small vehicles, such as motorcycles, were the cause of 8.5% of accidents (Figure 2(a)). Light condition (env_light) was the dominant environmental factor affecting fatalities, with 42.2% of rear-end collision fatalities occurring at night in the absence of light, 27.9% occurring at night with light, and 22% occurring in the daytime (Figure 2(b)).Table 2
Categorical Variables’ characteristics and descriptive statistics.
Driver exposure
Fatal injury
Not-at-fault
At-fault
Fatal crash
Nonfatal crash
Count
%
Count
%
Count
%
Count
%
Veh_type
Small
718
15.8%
833
18.3%
387
8.5%
1164
25.6%
Middle
1078
23.7%
1274
28.0%
533
11.7%
1819
39.9%
Large
300
6.6%
351
7.7%
236
5.2%
415
9.1%
Crashtype
Stopped
1344
29.5%
1611
35.4%
721
15.8%
2234
49.1%
Decelerating
645
14.2%
705
15.5%
347
7.6%
1003
22.0%
Go Straight
107
2.3%
142
3.1%
88
1.9%
161
3.5%
Gender
Female
1731
38.0%
2037
44.7%
1000
22.0%
2768
60.8%
Male
365
8.0%
421
9.2%
156
3.4%
630
13.8%
Main_road
Other wise
1895
41.6%
2193
48.2%
1070
23.5%
3018
66.3%
Yes
201
4.4%
265
5.8%
86
1.9%
380
8.3%
Entran_exit
Other wise
2084
45.8%
2448
53.8%
1154
25.3%
3378
74.2%
Yes
12
0.3%
10
0.2%
2
0.0%
20
0.4%
Nonrepairing road
Other wise
54
1.2%
59
1.3%
28
0.6%
85
1.9%
Yes
2042
44.8%
2399
52.7%
1128
24.8%
3313
72.7%
Road_lane
2
710
15.6%
792
17.4%
385
8.5%
1117
24.5%
3
10
0.2%
11
0.2%
4
0.1%
17
0.4%
4
926
20.3%
1083
23.8%
573
12.6%
1436
31.5%
5
9
0.2%
8
0.2%
5
0.1%
12
0.3%
6
155
3.4%
202
4.4%
63
1.4%
294
6.5%
7
0
0.0%
2
0.0%
0
0.0%
2
0.0%
8
160
3.5%
205
4.5%
92
2.0%
273
6.0%
9
3
0.1%
4
0.1%
5
0.1%
2
0.0%
10
33
0.7%
59
1.3%
21
0.5%
71
1.6%
12
60
1.3%
65
1.4%
8
0.2%
117
2.6%
14
30
0.7%
27
0.6%
0
0.0%
57
1.3%
Road_isle
No median
779
17.1%
861
18.9%
399
8.8%
1241
27.3%
Flush
115
2.5%
133
2.9%
96
2.1%
152
3.3%
Raised
452
9.9%
561
12.3%
298
6.5%
715
15.7%
Depressed
513
11.3%
612
13.4%
264
5.8%
861
18.9%
Barrier
237
5.2%
291
6.4%
99
2.2%
429
9.4%
Asphalt
Other wise
242
5.3%
309
6.8%
124
2.7%
427
9.4%
Yes
1854
40.7%
2149
47.2%
1032
22.7%
2971
65.2%
Straight
Other wise
125
2.7%
172
3.8%
96
2.1%
201
4.4%
Yes
1971
43.3%
2286
50.2%
1060
23.3%
3197
70.2%
Slope
Other wise
2039
44.8%
2358
51.8%
1090
23.9%
3307
72.6%
Yes
57
1.3%
100
2.2%
66
1.4%
91
2.0%
Intersection
Nonintersection
1725
37.9%
2013
44.2%
985
21.6%
2753
60.5%
Intersection
371
8.1%
445
9.8%
171
3.8%
645
14.2%
Median_opening
Other wise
1853
40.7%
2129
46.8%
985
21.6%
2997
65.8%
Yes
243
5.3%
329
7.2%
171
3.8%
401
8.8%
Env_surfaces
Dry
1951
42.8%
2284
50.2%
1073
23.6%
3162
69.4%
Wet
145
3.2%
174
3.8%
83
1.8%
236
5.2%
Weather
Otherwise
1947
42.8%
2266
49.8%
1063
23.3%
3150
69.2%
Clean
149
3.3%
192
4.2%
93
2.0%
248
5.4%
Env_light
Day
1413
31.0%
1629
35.8%
669
14.7%
2373
52.1%
Nigh without light
217
4.8%
243
5.3%
194
4.3%
266
5.8%
Night with light
466
10.2%
586
12.9%
293
6.4%
759
16.7%
SafetyEqui
Other wise
1312
28.8%
1585
34.8%
856
18.8%
2041
44.8%
Use
784
17.2%
873
19.2%
300
6.6%
1357
29.8%
Alcohol
Other wise
2070
45.5%
2433
53.4%
1131
24.8%
3372
74.0%
Yes
26
0.6%
25
0.5%
25
0.5%
26
0.6%
SpeedExc
Other wise
651
14.3%
734
16.1%
387
8.5%
998
21.9%
Yes
1445
31.7%
1724
37.9%
769
16.9%
2400
52.7%Figure 2
Relationship between dependent variables and some independent variables.
(a)
(b)The distribution of continuous variables is shown in Table3. With regard to driver age distribution, there was little difference between the ages of at-fault drivers and not-at-fault drivers. The average age of at-fault drivers was 38.04 years and of not-at-fault driver was 38.58 years. The mean value of trucks involved in fatal rear-end crashes was 18.2% and in nonfatal rear-end crashes was 16.2%. The DT model was then used for further analysis. Predictions could then be presented as logical if-then conditions at the terminal node. Thus, data did not require normal distribution. In other words, the relationships between independent and dependent variables was not obligatory for the existence of linear relationships [33].Table 3
Descriptive statistics of continuous variables.
Driver exposure
Fatal injury
Not-at-fault
At-fault
Fatal crash
Nonfatal crash
Mean
Std. Dev.
Min.
Max.
Mean
Std. Dev.
Min.
Max.
Mean
Std. Dev.
Min.
Max.
Mean
Std. Dev.
Min.
Max.
Person_age
38.6
14.0
9.0
86.0
38.0
13.9
11.0
85.0
39.8
14.3
12.0
86.0
37.8
13.8
9.0
85.0
Veh_involve
2.2
0.5
2.0
8.0
2.4
0.8
2.0
8.0
2.3
0.7
2.0
7.0
2.3
0.7
2.0
8.0
AADT60
33,318
53,089
183
270,050
33,779
52,363
163
270,050
26,583
39,286
483
270,050
35,943
56,342
163
270,050
PerCTruck
16.4
10.6
0.0
68.0
17.0
10.8
0.0
68.0
18.2
11.9
1.1
68.0
16.2
10.2
0.0
59.4
Note: Person_age = age of deriver; Veh_involve = number of vehicle involvement; AADT60 = average annual traffic volume on 2017; PerCTruck = average truck volume (%).Relationships between the independent variables are shown in the pairwise coefficient correlation model (Table4). Two highly correlated pairs were found: (1) road surface factor (env surface) correlated with weather condition (r=0.840). This was particularly evident in cases where there were unusual conditions, such as rain resulting in a wet road surface; (2) Factor of the number of traffic lanes and median type (r=0.621). This relationship is rational, as roads in Thailand typically have four or more traffic lanes and median types usually include a depressed median and barrier. Some pairs exhibited no relationship, such as driver age and road slope, or driver gender and road surface type.Table 4
Correlation among independent variables.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
(1) Vehicle types
1.00
−0.05
0.11
−0.20
0.07
0.02
−0.01
0.14
0.16
−0.03
−0.05
0.05
−0.03
0.02
0.07
0.08
0.06
−0.02
−0.02
0.09
0.15
0.03
(2) CrashType
1.00
0.01
0.02
−0.09
0.00
0.01
−0.10
−0.10
0.00
0.04
−0.07
0.16
0.16
−0.10
−0.08
−0.02
−0.05
0.00
−0.16
−0.10
−0.23
(3) Person_age
1.00
−0.13
−0.01
−0.02
−0.01
0.02
0.03
−0.01
0.02
0.00
0.01
0.02
0.00
0.01
−0.01
0.00
0.02
0.01
0.00
−0.04
(4) Gender
1.00
−0.02
−0.01
−0.01
−0.05
−0.04
0.00
0.02
−0.02
0.03
−0.03
−0.02
−0.02
−0.08
0.04
−0.01
−0.04
−0.04
0.00
(5) Main_Road
1.00
−0.02
−0.01
0.40
0.23
−0.17
0.06
−0.04
−0.05
−0.04
0.01
0.01
0.08
0.04
−0.01
0.35
0.07
0.06
(6) Entran_Exit
1.00
0.01
0.13
0.05
−0.01
0.02
−0.01
0.02
−0.03
−0.02
−0.02
0.00
0.00
−0.01
0.13
0.02
0.03
(7) Normal
1.00
0.06
0.05
−0.03
0.02
0.00
0.00
0.00
0.03
0.03
0.00
−0.02
0.02
0.05
0.01
−0.03
(8) Road_lane
1.00
0.62
−0.22
0.11
−0.09
−0.12
0.05
−0.01
−0.01
0.12
0.06
−0.05
0.60
0.17
0.09
(9) Road_isle
1.00
−0.13
0.12
−0.08
−0.12
0.16
0.02
0.03
0.09
0.09
−0.04
0.48
0.26
0.06
(10) Asphalt
1.00
−0.05
0.04
−0.06
−0.08
0.06
0.03
−0.10
0.07
0.03
−0.10
−0.04
−0.06
(11) Straight
1.00
−0.39
0.03
0.03
−0.11
−0.08
0.03
0.05
0.01
0.07
−0.07
0.01
(12) Slope
1.00
−0.05
−0.04
0.05
0.04
−0.02
−0.07
0.00
−0.06
0.09
−0.04
(13) Intersection
1.00
0.08
−0.07
−0.06
0.00
−0.06
0.03
−0.11
−0.05
−0.09
(14) Median_open
1.00
−0.02
−0.03
−0.01
−0.01
0.00
−0.05
0.03
−0.11
(15) Env_surfaces
1.00
0.84
−0.02
0.00
−0.01
−0.03
0.04
0.07
(16) Weather
1.00
0.02
0.00
0.01
−0.03
0.04
0.06
(17) Env_light
1.00
−0.05
0.02
0.10
0.06
0.04
(18) SafetyEqui
1.00
−0.01
0.08
−0.01
0.00
(19) Alcohol
1.00
−0.04
−0.04
−0.08
(20) AADT60
1.00
0.03
0.12
(21) PerCTruck
1.00
0.03
(22) SpeedExc
1.00
Note: Bold number represented correlation, which is significant at the 0.05 level (2-tailed).


## 3. Methods

### 3.1. Variable Setting

The dependent variables were determined as categorical values, such as fatal = 1, nonfatal = 0. According to independent variables, there were two variable types: (1) categorical variables, the values of which were divided according to variable characteristics in numeric form, for example, gender (0 = male, 1 = female), vehicle types (1 = small vehicle, i.e., motorcycle, 2 = medium vehicle, i.e., car, pickup truck, 3 = large vehicle, i.e., six-wheel truck), crash types (1 = going straight, 2 = decelerating, 3 = stopped), and (2) continuous variables, such as number of lanes (2,3,4, ...). “PerCTruck” was the proportion of trucks traffic volume.


### 3.2. Classification Tree and Building Model

This study used a decision tree or classification tree (DT) model for rear-end crash data analysis, which started by determining target variables (dependent variables). Two models were constructed. Model#1 analyzed at-fault/not-at-fault drivers. In order to consider this variable, the driver factor was only selected for the first and second vehicles, as the first vehicle was clearly identifiable as accident-prone. Therefore, 4,192 vehicles (2,096 rear-end crashes) were analyzed in the model. Model#2 was an analysis of factors resulting in fatal and nonfatal rear-end collisions. Therefore, data included the two or more vehicles involved in a rear-end crash. Out of a total of 4,554 vehicles, 2,096 were involved in those crashes.The DT model consists of three components. These are decision node, branches, and leaf nodes. Within the DT structure, each decision node displays the variable, and each branch displays one variable value based on decision rules, while leaf nodes exhibit the expected values of target variables [34].SPSS was used to conduct the analysis. In order to create the DT, the full dataset was first split according to root node, which was the proportion of values in the target variable. This was then split into a number of smaller subsets. Several SPSS types can be used to carry out splitting and growing, including CHAID, CART, and QUEST. Each of these types has advantages and disadvantages. This study chose CRT for two reasons. First, CRT is capable of analyzing binary node splitting, which is suitable for the interpretation of accident data analysis results [9]. Second, CRT can potentially analyze influence variables. This research sought to find the relationship between target variables and other variables expressed in form of the rank of each independent (predictor) variable according to its importance to the model [35]. A great deal of previous research has used CRT to analyze accident data [36–38], as CRT functions to emphatically focus on maximizing within-node homogeneity. The extent to which a node does not represent a homogenous subset of cases is an indication of impurity [35].Choosing the correct splitting algorithm is also important. SPSS CRT offers two types of splitting, Gini and Twoing. Gini-splits, which are widely used function, to maximize the homogeneity of child nodes with respect to the values of the dependent variables. Gini is based on squared probabilities of membership for each category of the dependent variable [35, 36, 39]. For CART acceptance, splitting was achieved by using unit misclassification costs. This is the proportion of observed and predicted data comparisons [29].In order to determine the optimal tree model, ten-fold cross-validation was undertaken, which is one of several cross-validation techniques to select for appropriate tree size. To avoid over-fitting the model, the maximum tree depth was five nodes, minimum cases in the parent node were 150, and minimum cases in child node were 75 [29].


## 3.1. Variable Setting

The dependent variables were determined as categorical values, such as fatal = 1, nonfatal = 0. According to independent variables, there were two variable types: (1) categorical variables, the values of which were divided according to variable characteristics in numeric form, for example, gender (0 = male, 1 = female), vehicle types (1 = small vehicle, i.e., motorcycle, 2 = medium vehicle, i.e., car, pickup truck, 3 = large vehicle, i.e., six-wheel truck), crash types (1 = going straight, 2 = decelerating, 3 = stopped), and (2) continuous variables, such as number of lanes (2,3,4, ...). “PerCTruck” was the proportion of trucks traffic volume.


## 3.2. Classification Tree and Building Model

This study used a decision tree or classification tree (DT) model for rear-end crash data analysis, which started by determining target variables (dependent variables). Two models were constructed. Model#1 analyzed at-fault/not-at-fault drivers. In order to consider this variable, the driver factor was only selected for the first and second vehicles, as the first vehicle was clearly identifiable as accident-prone. Therefore, 4,192 vehicles (2,096 rear-end crashes) were analyzed in the model. Model#2 was an analysis of factors resulting in fatal and nonfatal rear-end collisions. Therefore, data included the two or more vehicles involved in a rear-end crash. Out of a total of 4,554 vehicles, 2,096 were involved in those crashes.The DT model consists of three components. These are decision node, branches, and leaf nodes. Within the DT structure, each decision node displays the variable, and each branch displays one variable value based on decision rules, while leaf nodes exhibit the expected values of target variables [34].SPSS was used to conduct the analysis. In order to create the DT, the full dataset was first split according to root node, which was the proportion of values in the target variable. This was then split into a number of smaller subsets. Several SPSS types can be used to carry out splitting and growing, including CHAID, CART, and QUEST. Each of these types has advantages and disadvantages. This study chose CRT for two reasons. First, CRT is capable of analyzing binary node splitting, which is suitable for the interpretation of accident data analysis results [9]. Second, CRT can potentially analyze influence variables. This research sought to find the relationship between target variables and other variables expressed in form of the rank of each independent (predictor) variable according to its importance to the model [35]. A great deal of previous research has used CRT to analyze accident data [36–38], as CRT functions to emphatically focus on maximizing within-node homogeneity. The extent to which a node does not represent a homogenous subset of cases is an indication of impurity [35].Choosing the correct splitting algorithm is also important. SPSS CRT offers two types of splitting, Gini and Twoing. Gini-splits, which are widely used function, to maximize the homogeneity of child nodes with respect to the values of the dependent variables. Gini is based on squared probabilities of membership for each category of the dependent variable [35, 36, 39]. For CART acceptance, splitting was achieved by using unit misclassification costs. This is the proportion of observed and predicted data comparisons [29].In order to determine the optimal tree model, ten-fold cross-validation was undertaken, which is one of several cross-validation techniques to select for appropriate tree size. To avoid over-fitting the model, the maximum tree depth was five nodes, minimum cases in the parent node were 150, and minimum cases in child node were 75 [29].


## 4. Results and Discussion

According to the results from the CART of the two models, when considering misclassification costs for predictive accuracy (Table5), Model#1 had overall correctness of 52.9% and Model#2 of 65.1%. Despite these low values, as confirmed by Khan et al. [29], Kashani and Mohaymany [36], they can be accepted and interpreted.Table 5
Misclassification costs.
Model#1
Observed
Predicted
Not-at-fault
At-fault
Percent correct
Not-at-fault
1654
442
78.9%
At-fault
1538
558
26.6%
Overall
76.2%
23.8%
52.9%
Model#2
Observed
Predicted
Nonfatal crash
Fatal crash
Percent correct
Nonfatal crash
2332
1066
68.6%
Fatal crash
522
634
54.8%
Overall
62.7%
37.3%
65.1%


### 4.1. Model#1

Model#1 (Figure3) found six major variables related to the target variables. The most significant variable is driver’s age (person_age). Drivers aged less than 21 years were at-fault drivers in 57.3% of accidents. This may be because younger drivers are less careful. Ma and Yan [5], Chandraratna and Stamatiadis [7] found that young drivers are more likely to be at fault than middle-aged drivers. Those aged over 21 years were at-fault only 48.9%. The significant variable was road lane, which can be interpreted that if a driver aged more than 21 years drives on a road with 10 or more traffic lanes (considering at only 10 lanes as there is no frequency of seven lanes), the chances of being at-fault drivers are 61.7%. This is consistent with research by Pande et al. [38]. This may be because roads with many lanes provide greater opportunities for speeding and vehicles are often parked on the roadside. Some less observant older drivers may be at fault for rear-end collisions. For accidents occurring at the median (median_opening), where the median is on a road with fewer than 10 traffic lanes, drivers older than 21 years were more likely to be at-fault. Due to the characteristics of median openings, front car drivers are more likely to reduce car speed in order to turn or execute a u-turn. If the car behind is too close, the chances of a rear-end collision are high. Dividing drivers into less and more than 25 years is a variable that has not previously been investigated. This research found that drivers in these two age ranges potentially consist of not-at fault drivers. When considering drivers aged over 25 years together with median type, there are more at-fault drivers when driving on unoccupied streets with a raised or flush median, with a greater chance of being at-fault than drivers on roads with barriers or depressed medians. The causes of these results were raised median, no median, and painted median. In Thailand, most of these median types are used on roads with low traffic flow, such as in residential areas or urban streets. Therefore, when driving too close, there is a chance of rear-end collision. This is consistent with research conducted by Joon-Ki et al. [40], Baldock et al. [41], who concluded that spacing on low-speed roads is a major cause of rear-end collisions. However, a study by Das and Abdel-Aty [30] indicated that median type had no effect on the frequency of rear-end collisions.Figure 3
Tree model#1.Overall policy and public relations, therefore, should promote the reduction of rear-end collisions in the following ways: driver training should place special emphasis on drivers under 21 years of age, focusing on driving at the legal speed limit, and maintaining an appropriate distance from the vehicle in front. For drivers aged 21 years and older, it is important to pay special attention to roads with more than 10 lanes, and to take greater care of median openings on roads with fewer lanes. In other words, drivers should observe whether the car in front is executing a u-turn. Drivers aged 25 years or older, should take special care on roads with no median, with a raised median, or with a depressed median, and they should maintain a greater distance from the car in front.


### 4.2. Model#2

The results of Model#2 (Figure4) reveal 14 variables essential to fatal/nonfatal crashes. The most significant variable was safety equipment (SafertEqui), such as seatbelts or helmets. Those who did not use safety equipment were at 29.5% risk of dying in a rear-end collision. This is consistent with other research which has found that the use of safety equipment can reduce accident severity [21, 41]. The next most significant variable was visibility, with a rear-end crash at night with no light having a 49% risk of fatality. This result supports findings by Sullivan and Flannagan [11], Chen et al. [21]. Low light driving leads to rear-end crashes against cars parked along roadsides. In addition, a lower quantity of night-time traffic leads to drivers driving at higher speeds, which, in turn, causes a greater number of fatalities due to high velocity while crashing. In the case of sufficient light (in the daytime and at night with light), the variable of roads with a minimum of 2–8 traffic lanes on which a large number of trucks are parked, the chances of rear-end crashes are high. Moreover, the second variable, vehicle type (Veh_type), shows that large cars and trucks with six wheels or more result in 39.7% of deaths. This is relevant to the findings of Chen et al. [21], Chang and Chien [39], who found that the chances of fatality while decelerating and going straight were 53.1% (60/113 of crash accidents). Large vehicles which hit small vehicles on 2–4 lane roads have a high chance of fatality due to the vehicle body size factor [24]. With regard to other crash types, stopped crash type has a 33% chance of fatality (80/240 crash accidents). In other words, rear-end crashes, occurring when the front cars are stopping, have a high fatality rate. With regard to medium and small vehicles, the chances of fatal crashes are high when the driver is aged more than 36 years (31.4%).Figure 4
Tree model#2.For drivers who use seatbelts, the second variable of raised and flush median led to a higher chance of fatality than other median types as these two types exist in areas of low-speed driving. If drivers violate the rules, the chances of rear-end collisions will be very high. For example, roads with a flush median type usually have no auxiliary lane to separate turning cars. Therefore, if a speeding car comes from behind, the resulting rear-end crash will be severe. This is consistent with the second variable, median opening, where there is a 48.8% probability of death. For other median types, two to four traffic lanes had 16.2% fatal rear-end crashes. With regard to leaf node,envi_light was found to be in accordance with Chen et al. [22], who found that collisions occurring at night both with light and no light have a greater chance of fatality than collisions occurring during the daytime.Policy recommendations to reduce fatalities from rear-end collisions are as follows: promoting awareness of seatbelt use by focusing on the driving license test, and increasing the strictness of law enforcement. For light conditions affecting visibility, drivers must be made aware of the danger of driving on roads with no lights, especially at night. Relevant authorities should consider increasing light installation on roads where the risk of rear-end collision is high. With regard to vehicle type, truckers must increase their awareness of parking their vehicles on roads with a high risk of rear-end collision, such as where there are no parking lanes and no light. In other words, the relevant departments, such as the DOH, should consider setting up illuminated roadside rest stops for trucks.


### 4.3. Discussion of the Two Models

Considering the overall picture of the two models, similar variables result in frequent rear-end collisions and fatalities. The first variable is the small number of lanes (2–4 traffic lanes), which is common in Thailand. The results of the models differed. Model#1 found fewer at-fault drivers in cases of a small number of traffic lanes, while model#2, found a high chance of fatalities. Future research should analyze this issue with regard to how different traffic lanes affect the frequency and severity of rear-end collisions. Another variable which was significant in both models was median type. Barrier and depressed median types result in a small number of rear-end collisions, and a low fatal crash rate. Therefore, when subordinate units of the DOHs make road improvements, these two median types should be considered. With regard to median opening point, both models found that rear-end collisions occurring at the median opening had a high incidence of at-fault, and caused high proportion of fatal crashes as the front vehicle decelerated or executed a u-turn. In these conditions, there is a high probability for the occurrence of a rear-end collision. In the case of fatal crashes, if the following vehicle has not seen the turning signal, a serious rear-end collision will occur.


## 4.1. Model#1

Model#1 (Figure3) found six major variables related to the target variables. The most significant variable is driver’s age (person_age). Drivers aged less than 21 years were at-fault drivers in 57.3% of accidents. This may be because younger drivers are less careful. Ma and Yan [5], Chandraratna and Stamatiadis [7] found that young drivers are more likely to be at fault than middle-aged drivers. Those aged over 21 years were at-fault only 48.9%. The significant variable was road lane, which can be interpreted that if a driver aged more than 21 years drives on a road with 10 or more traffic lanes (considering at only 10 lanes as there is no frequency of seven lanes), the chances of being at-fault drivers are 61.7%. This is consistent with research by Pande et al. [38]. This may be because roads with many lanes provide greater opportunities for speeding and vehicles are often parked on the roadside. Some less observant older drivers may be at fault for rear-end collisions. For accidents occurring at the median (median_opening), where the median is on a road with fewer than 10 traffic lanes, drivers older than 21 years were more likely to be at-fault. Due to the characteristics of median openings, front car drivers are more likely to reduce car speed in order to turn or execute a u-turn. If the car behind is too close, the chances of a rear-end collision are high. Dividing drivers into less and more than 25 years is a variable that has not previously been investigated. This research found that drivers in these two age ranges potentially consist of not-at fault drivers. When considering drivers aged over 25 years together with median type, there are more at-fault drivers when driving on unoccupied streets with a raised or flush median, with a greater chance of being at-fault than drivers on roads with barriers or depressed medians. The causes of these results were raised median, no median, and painted median. In Thailand, most of these median types are used on roads with low traffic flow, such as in residential areas or urban streets. Therefore, when driving too close, there is a chance of rear-end collision. This is consistent with research conducted by Joon-Ki et al. [40], Baldock et al. [41], who concluded that spacing on low-speed roads is a major cause of rear-end collisions. However, a study by Das and Abdel-Aty [30] indicated that median type had no effect on the frequency of rear-end collisions.Figure 3
Tree model#1.Overall policy and public relations, therefore, should promote the reduction of rear-end collisions in the following ways: driver training should place special emphasis on drivers under 21 years of age, focusing on driving at the legal speed limit, and maintaining an appropriate distance from the vehicle in front. For drivers aged 21 years and older, it is important to pay special attention to roads with more than 10 lanes, and to take greater care of median openings on roads with fewer lanes. In other words, drivers should observe whether the car in front is executing a u-turn. Drivers aged 25 years or older, should take special care on roads with no median, with a raised median, or with a depressed median, and they should maintain a greater distance from the car in front.


## 4.2. Model#2

The results of Model#2 (Figure4) reveal 14 variables essential to fatal/nonfatal crashes. The most significant variable was safety equipment (SafertEqui), such as seatbelts or helmets. Those who did not use safety equipment were at 29.5% risk of dying in a rear-end collision. This is consistent with other research which has found that the use of safety equipment can reduce accident severity [21, 41]. The next most significant variable was visibility, with a rear-end crash at night with no light having a 49% risk of fatality. This result supports findings by Sullivan and Flannagan [11], Chen et al. [21]. Low light driving leads to rear-end crashes against cars parked along roadsides. In addition, a lower quantity of night-time traffic leads to drivers driving at higher speeds, which, in turn, causes a greater number of fatalities due to high velocity while crashing. In the case of sufficient light (in the daytime and at night with light), the variable of roads with a minimum of 2–8 traffic lanes on which a large number of trucks are parked, the chances of rear-end crashes are high. Moreover, the second variable, vehicle type (Veh_type), shows that large cars and trucks with six wheels or more result in 39.7% of deaths. This is relevant to the findings of Chen et al. [21], Chang and Chien [39], who found that the chances of fatality while decelerating and going straight were 53.1% (60/113 of crash accidents). Large vehicles which hit small vehicles on 2–4 lane roads have a high chance of fatality due to the vehicle body size factor [24]. With regard to other crash types, stopped crash type has a 33% chance of fatality (80/240 crash accidents). In other words, rear-end crashes, occurring when the front cars are stopping, have a high fatality rate. With regard to medium and small vehicles, the chances of fatal crashes are high when the driver is aged more than 36 years (31.4%).Figure 4
Tree model#2.For drivers who use seatbelts, the second variable of raised and flush median led to a higher chance of fatality than other median types as these two types exist in areas of low-speed driving. If drivers violate the rules, the chances of rear-end collisions will be very high. For example, roads with a flush median type usually have no auxiliary lane to separate turning cars. Therefore, if a speeding car comes from behind, the resulting rear-end crash will be severe. This is consistent with the second variable, median opening, where there is a 48.8% probability of death. For other median types, two to four traffic lanes had 16.2% fatal rear-end crashes. With regard to leaf node,envi_light was found to be in accordance with Chen et al. [22], who found that collisions occurring at night both with light and no light have a greater chance of fatality than collisions occurring during the daytime.Policy recommendations to reduce fatalities from rear-end collisions are as follows: promoting awareness of seatbelt use by focusing on the driving license test, and increasing the strictness of law enforcement. For light conditions affecting visibility, drivers must be made aware of the danger of driving on roads with no lights, especially at night. Relevant authorities should consider increasing light installation on roads where the risk of rear-end collision is high. With regard to vehicle type, truckers must increase their awareness of parking their vehicles on roads with a high risk of rear-end collision, such as where there are no parking lanes and no light. In other words, the relevant departments, such as the DOH, should consider setting up illuminated roadside rest stops for trucks.


## 4.3. Discussion of the Two Models

Considering the overall picture of the two models, similar variables result in frequent rear-end collisions and fatalities. The first variable is the small number of lanes (2–4 traffic lanes), which is common in Thailand. The results of the models differed. Model#1 found fewer at-fault drivers in cases of a small number of traffic lanes, while model#2, found a high chance of fatalities. Future research should analyze this issue with regard to how different traffic lanes affect the frequency and severity of rear-end collisions. Another variable which was significant in both models was median type. Barrier and depressed median types result in a small number of rear-end collisions, and a low fatal crash rate. Therefore, when subordinate units of the DOHs make road improvements, these two median types should be considered. With regard to median opening point, both models found that rear-end collisions occurring at the median opening had a high incidence of at-fault, and caused high proportion of fatal crashes as the front vehicle decelerated or executed a u-turn. In these conditions, there is a high probability for the occurrence of a rear-end collision. In the case of fatal crashes, if the following vehicle has not seen the turning signal, a serious rear-end collision will occur.


## 5. Conclusion

This research sought to explore two issues related to rear-end crashes. First, to find the factors which increase the number of rear-end collisions. This was achieved by focusing on the driver and environmental characteristics that cause rear-end collisions. Second, to find the factors causing fatal rear-end collisions. Using highway rear-end collision data from 2011 to 2015, nonparametric analysis was conducted on the significance of other variables which affect target variables, using an overview of factors, including drivers, the driving environment, and physical road characteristics. The model results were found to be able to predict rear-end collisions and fatalities with acceptable accuracy. The factors can contribute to a reduction in the number of at-fault drivers, and a reduction in the fatality rate of rear-end collisions.The factors acquired from this analysis can be used to develop transportation office and rural road office policy and public relations practices, in order to reduce the number and severity of rear-end collisions.It is recommended that future research parametric and nonparametric analysis to compare these factors in order to better understand the factors affecting crashes. In addition, a further investigation of lane numbers, median type, and median opening affecting the number of rear-end collisions, and fatal crashes, is called for, as these three variables were imperative for both models.



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*Source: 2568978-2019-11-27.xml*