# Analyzing the Impact of Traffic Violation Behaviors on Traffic Fatal Crashes Using Multilevel Models on Expressways

Authors: Huajing Ning; Yunyan Yu; Lu Bai
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

This study is intended to explore the impact of traffic violation behaviors on traffic fatal crashes on expressways. Based on the generalized additive model method, for independent traffic violation data and traffic fatal crash data from the Traffic Administration Bureau of Anhui Provincial Public Security Department, the relationship among the violations and traffic fatal crashes was discussed. Applying the proposed multilevel analysis method, which can effectively show the evolution trend among traffic violations and traffic fatal crashes influenced by time, space, and inter-reaction. The results show that hierarchical data structures should not be ignored. Meanwhile, in order to avoid fatal traffic collisions, we should reduce traffic violations, especially the control of speed on expressways This is because speeding is the most common traffic violation behavior and has a significant impact on traffic fatal crashes. The results could help strengthen our focus on key traffic violations and provide a reference for traffic safety management and decision-making.


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## Body

## 1. Introduction

Traffic crashes can lead to traffic congestion, property damage, and human casualties, which seriously threaten people’s safety. The number of deaths by road crashes globally remains unacceptably high, with an estimated 1.35 million deaths each year and 50 million injuries [1]. Serious injuries caused by traffic crashes in China are still not good. Take Anhui Province for example, according to the 2017–2021 yearbook statistics of Anhui Province [2], the crash fatality rate [3] in the past 5 years exceeded 20%, and reached the peak of 23.57% in 2019. This shows that more efforts are needed to prevent traffic crashes.Compared with common traffic crashes, the traffic fatal crashes have the basic characteristics of latent, causality, irreversibility, suddenness and so on, and the most significant feature is harmfulness. The standards of harm in traffic crashes vary from country to country. Based on the Ministry of Public Security of the People’s Republic of China, according to the accident severity, accident types can be divided into serious accidents, major accidents, ordinary accidents, and minor accidents [4]. In Britain, the accident severity is a different classification. These are fatal traffic accidents, serious accidents, slight accidents, and damage-only accidents [5]. In the USA, depending on the degree of injury, the traffic accident classification contains five categories. These are a fatal injury, a suspected serious injury, a suspected minor injury, a possible injury, and no apparent injury [6]. Although definitions of the severity of a crash vary from country to country, when a person is killed in a crash, it is considered a serious one. In the study, a crash in which a person dies due to a traffic crash is a fatal crash, which could have grave consequences for all of us.Fatal crashes tend to happen on expressways. At this point, that is why a maximum speed limit has been set for the expressway. According to the 67th of the Road Traffic Safety Law of the People’s Republic of China [7]; the two-way, multi-lane expressway has a designed speed of 120 kilometers per hour. Due to the requirements of speed, vehicles usually drive at a high speed on the expressway. In this condition, once a crash occurs, it will often lead to serious traffic consequences. The relationship between traffic crash severity and speed is well documented [8]. In recent years, the crash fatality rate of expressway traffic crashes was 10 percentage points higher than the fatality rate of common traffic crashes in the same period [9]. These crashes happening on the expressway should be paid more attention by the traffic authorities, transport management departments, and traffic safety researchers.Since traffic crashes lead to a large number of deaths and injuries, it is, therefore, necessary to explore the intrinsic characteristics of crashes and identify their contributing factors for traffic safety management. There have been numerous research results about the influence factors on traffic crashes from various aspects worldwide. From the macroscopic point of view, the research mainly focuses on road characteristics, such as highway mileage [10, 11], road density [12, 13], and intersection density [14–17]; traffic flow characteristics, including limiting-velocity [18, 19], average speed [20, 21], traffic flow [16, 22], number of motor vehicles [22]; the weather characteristics, for example, rainfall [23], snowfall [24], temperature [19, 25], visibility [23, 26]; driver characteristic, for instance, age of the driver [27]; social, economic, demographic characteristics [22, 27, 28], and land use [29–31] and so on. From the microscopic point of view, traffic crashes are mainly analyzed in terms of intersections [32], sections [33, 34], traffic monitoring settings [35], and so on.Among numerous factors, one thing worthy of particular note is traffic violation behaviors [36, 37]. Zhu [38] research results indicated that traffic violation behaviors were an important cause of traffic crashes. Wang et al. [39] claimed that traffic violations had become major cause of crashes and road fatalities, contributing to 75% of road crashes in China, 50% of fatal crashes in Europe, and 56% of fatal crashes in the United States. Hong et al. [36] studied commercial driver’s traffic violations and freight truck-involved crashes on mainlines of expressway, developing more accurate crash probability estimation by explaining the endogenous driver traffic violations. Wu and Hsu [40] claimed that traffic violations and improper driving were behaviors that primarily contribute to traffic crashes. In addition, they predicted at-fault driver frequency using fusion deep learning with city-level traffic violation data. Hosseinlou et al. [37] validated some traffic violations which caused crashes on freeways and determined their amount of influence through statistical models. Rezapour and Ksaibati [41] combined violation and crash data to model injury severity of truck crashes.In order to better explore traffic violation behaviors affecting the crash, some more research methods were introduced, such as correlation relation [42], fault tree analysis [42], K-nearest neighbor [43], classification decision making, [44], rough set [45], structural equation [46] and so on. Moreover, some advanced methods were applied, notably machine learning model [47, 48], such as SVM [49], BP neural network [50], Petri net model [51], etc.The generalized additive model is one of the effective methods to study the influence of factors on dependent variables. In 1985, Stone [52] proposed the additive model, in which each additive term is estimated by a single smooth function, and in each additive term, how parameters change with the change of independent variables can be explained. Hastie and Tibshirani [53] extended the application scope of the additive model and proposed the generalized additive model, which has been further popularized and applied. The advantage of this method is that the parameters do not need to satisfy the assumption of linearity and can flexibly detect the complex relationship among data. At present, this method has been applied to scientific research [54, 55].The relationship between crashes and factors is complex and diverse. The characteristics of data should not be ignored in the modeling process. The distribution of traffic violation behaviors and crash data tends to be accompanied by spatial correlation and temporal correlation. Due to the strictness of local traffic law enforcement and the behavior characteristics of local drivers, these data have a certain degree of aggregation. That is, the characteristics of crash data and offense data in the same region or the same period tend to be consistent. And for different regions or periods, the opposite is true. Analysis of the impact of traffic violation behaviors on traffic crashes, if the independent event is taken as the basic unit of analysis, the estimation of regression coefficient and its standard error will be biased. If the group level is taken as the basic unit of analysis, and independent events are aggregated to the group level, the differences of individual variation are underestimated. If the data structures are ignored, the fitting performance and prediction accuracy of the traffic crash model would be seriously affected, and even wrong conclusions may be drawn [56].Multilevel analysis fully considers the hierarchical structure of data and decomposes the error terms to different levels, which provides a new analytical thinking and framework for solving such problems. So far, there is some research utilizing this method in traffic safety, such as Wu et al. [57] applied this method for analysis of driver injury severity in single-vehicle crashes on rural and urban roadways. Usman et al. [58] adopted this method to evaluate injury severity. Peng et al. [59] examined the crash severity on divided rural multi-lane highway segments using multilevel logistic models. Adanu et al. [60] utilized the multilevel analysis of the role of human factors in regional disparities in crash outcomes.At present, there is a finite amount of literature regarding traffic violations and traffic fatal crashes as two independent parts and studying how traffic violations influence traffic fatal crashes. This study takes the traffic violation behaviors and traffic fatal crashes as the breakthrough point to study the relationship between them. This study would solve the following problems:(1)
Is there any correlation between traffic fatal crashes and traffic violation behaviors?(2)
How do traffic violation behaviors affect fatal crashes? Is it affected by the hierarchical structure of time and space?Accordingly, this study aims to provide evidence of the impact of traffic violations on traffic fatal crashes. In Section2, we will collect, prepare and analyze the traffic violation behaviors data and traffic fatal crashes data; Section 3 introduces the methods we need to use; Section 4 analyzes the influence of traffic violations on traffic fatal crashes. Section 5 provides the conclusion of the research.


## 2. Data Sources

### 2.1. Research Scope

The research data of this study came from the traffic safety integrated service management platform of the Traffic Administration Bureau of Anhui Provincial Public Security Department. On the platform, there were public data on traffic violation behaviors of vehicles and public data of drivers responsible for traffic fatal crashes in Anhui Province. The scope of this study is the administrative regions of all cities in Anhui Province. Each administrative region has different administrative codes, a total of 16. The study covered a 1-year period from April 1, 2017 to March 31, 2018.


### 2.2. Research Data

In the statistical data within the time range of the study, there were 245 traffic fatal crashes on expressways in Anhui Province. Crash data showed that each crash resulted in at least one death, and all crashes belonged to traffic fatal crashes.In the statistical data within the time range of the study, 8428 violations were reported on the platform on expressways in the province of Anhui. The data on traffic violations mainly included the following five types. The first offense is when a vehicle travels exceeding the prescribed speed by 20% no more than 50%, which is defined as X1. According to Article 67 of the Road Traffic Safety Law [7]; the maximum speed per hour indicated by speed limit signs on expressways shall not exceed 120 km/h. When driving on expressways, the driver must control his or her speed within the range of the posted maximum and minimum speed limit. When a vehicle drives at a speed of more than the speed limit of 20% (144 km/h), but less than the speed limit of 50% (180 km/h), which is recognized as a violation behavior.The second offense is when a vehicle exceeds the speed limit by more than 50%, which is markedX2. When a vehicle drives at a speed of more than the speed limit of 50% (180 km/h), it is identified as a traffic violation behavior.This is calledX3, which refers to behaviors that violate laws and regulations. According to Article 101 of the Road Traffic Safety Law [7]; this offense refers to the behavior leading to a major crash, the illegal behavior constituting a crime, or an offense of the ban marks.The fourth category of traffic violation behavior refers to a driver driving a defective vehicle or failing to comply with license restrictions, which is calledX4. According to Article 96 of the Road Traffic Safety Law [7]; this offense refers to a driver driving a defective vehicle, driving a vehicle without a driving license, forging or altering a vehicle registration certificate, using a forged or altered vehicle number plate or a driving license.The fifth offense is that the driver is under the influence of alcohol or drugs, which is defined asX5. According to Article 91 of the Road Traffic Safety Law [7]; driving under the influence of alcohol or drugs belongs to traffic violation behaviors.The proportion of various traffic violations is shown in Table1. Among all traffic violation behaviors, X2 (exceeding the speed limit by 50% or more) accounts for the largest proportion, reaching 81.2% of all traffic violation behaviors. This is because with multi-lane, fully road transportation facilities and good road conditions, drivers are prone to speeding if they ignore the real-time speed of the vehicle. X1 (exceeding the speed limit by 20% no more than 50%) accounts for 13.9% of all offenses. Both X1 (exceeding the speed limit by 20% no more than 50%) and X2 (exceeding the speed limit by 50% or more) belong to the category of speeding behavior, which accounts for 95% of all violations. For X3 (violations of laws and regulations), the proportion of all traffic violation behaviors is around 2%. And X4 (driving a defective vehicle or failure to comply with license restrictions) accounts for about 2% of total traffic violations. The X5 (driving under the influence of alcohol or drugs) holds 1% of all traffic violation behaviors. This part is only a small part of all traffic violations because people’s safety awareness is gradually increasing, realizing the harm of alcohol and narcotic drugs. “Drink not to drive, drive not to drink” regulation is deeply rooted in the public, so the proportion of such traffic violation behaviors on the highway is less.Table 1
Table of the proportion of traffic violations.
NameDescriptionNumberPercentage (%)X1Exceeding the speed limit by 20% no more than 50%117513.9X2Exceeding speed limit by 50% or more684481.2X3Violations of laws and regulations1641.9X4Driving a defective vehicle or failure to comply with license restrictions1672.0X5Driving under the influence of alcohol or drugs780.9According to the natural discontinuity point classification method (Jenks). Violations in all administrative regions of Anhui province can be divided into five levels in the statistical period, as shown in Figure1. The cities with the largest number of violations are Anqing City, Hefei City, and Huangshan City. The cities with the lowest number of violations are Huaibei City and Huainan City.Figure 1
The distribution of traffic violation behaviors in Anhui province.According to the natural discontinuity point classification method (Jenks). Traffic fatal crashes in all administrative regions of the province of Anhui can be divided into 5 levels in the statistical period, as shown in Figure2. Cities with the highest number of traffic fatal crashes are Fuyang City and Liu’an City. Hefei City and Suzhou City have the second highest number of traffic fatal crash cities among all cities.Figure 2
The distribution of traffic fatal crashes in Anhui province.According to the distribution statistics of traffic violation behaviors and traffic fatal crashes in Anhui province, the scatter distribution forms of traffic violation behaviors and traffic fatal crashes have similar distribution forms. Cities with the highest number of fatal crashes, such as Fuyang City and Lu’an City, also have a relatively high number of traffic violations among all cities. The cities with the least number of traffic fatal crashes, namely Huaibei City and Huainan City, also have the lowest number of traffic violations among all cities.


## 2.1. Research Scope

The research data of this study came from the traffic safety integrated service management platform of the Traffic Administration Bureau of Anhui Provincial Public Security Department. On the platform, there were public data on traffic violation behaviors of vehicles and public data of drivers responsible for traffic fatal crashes in Anhui Province. The scope of this study is the administrative regions of all cities in Anhui Province. Each administrative region has different administrative codes, a total of 16. The study covered a 1-year period from April 1, 2017 to March 31, 2018.


## 2.2. Research Data

In the statistical data within the time range of the study, there were 245 traffic fatal crashes on expressways in Anhui Province. Crash data showed that each crash resulted in at least one death, and all crashes belonged to traffic fatal crashes.In the statistical data within the time range of the study, 8428 violations were reported on the platform on expressways in the province of Anhui. The data on traffic violations mainly included the following five types. The first offense is when a vehicle travels exceeding the prescribed speed by 20% no more than 50%, which is defined as X1. According to Article 67 of the Road Traffic Safety Law [7]; the maximum speed per hour indicated by speed limit signs on expressways shall not exceed 120 km/h. When driving on expressways, the driver must control his or her speed within the range of the posted maximum and minimum speed limit. When a vehicle drives at a speed of more than the speed limit of 20% (144 km/h), but less than the speed limit of 50% (180 km/h), which is recognized as a violation behavior.The second offense is when a vehicle exceeds the speed limit by more than 50%, which is markedX2. When a vehicle drives at a speed of more than the speed limit of 50% (180 km/h), it is identified as a traffic violation behavior.This is calledX3, which refers to behaviors that violate laws and regulations. According to Article 101 of the Road Traffic Safety Law [7]; this offense refers to the behavior leading to a major crash, the illegal behavior constituting a crime, or an offense of the ban marks.The fourth category of traffic violation behavior refers to a driver driving a defective vehicle or failing to comply with license restrictions, which is calledX4. According to Article 96 of the Road Traffic Safety Law [7]; this offense refers to a driver driving a defective vehicle, driving a vehicle without a driving license, forging or altering a vehicle registration certificate, using a forged or altered vehicle number plate or a driving license.The fifth offense is that the driver is under the influence of alcohol or drugs, which is defined asX5. According to Article 91 of the Road Traffic Safety Law [7]; driving under the influence of alcohol or drugs belongs to traffic violation behaviors.The proportion of various traffic violations is shown in Table1. Among all traffic violation behaviors, X2 (exceeding the speed limit by 50% or more) accounts for the largest proportion, reaching 81.2% of all traffic violation behaviors. This is because with multi-lane, fully road transportation facilities and good road conditions, drivers are prone to speeding if they ignore the real-time speed of the vehicle. X1 (exceeding the speed limit by 20% no more than 50%) accounts for 13.9% of all offenses. Both X1 (exceeding the speed limit by 20% no more than 50%) and X2 (exceeding the speed limit by 50% or more) belong to the category of speeding behavior, which accounts for 95% of all violations. For X3 (violations of laws and regulations), the proportion of all traffic violation behaviors is around 2%. And X4 (driving a defective vehicle or failure to comply with license restrictions) accounts for about 2% of total traffic violations. The X5 (driving under the influence of alcohol or drugs) holds 1% of all traffic violation behaviors. This part is only a small part of all traffic violations because people’s safety awareness is gradually increasing, realizing the harm of alcohol and narcotic drugs. “Drink not to drive, drive not to drink” regulation is deeply rooted in the public, so the proportion of such traffic violation behaviors on the highway is less.Table 1
Table of the proportion of traffic violations.
NameDescriptionNumberPercentage (%)X1Exceeding the speed limit by 20% no more than 50%117513.9X2Exceeding speed limit by 50% or more684481.2X3Violations of laws and regulations1641.9X4Driving a defective vehicle or failure to comply with license restrictions1672.0X5Driving under the influence of alcohol or drugs780.9According to the natural discontinuity point classification method (Jenks). Violations in all administrative regions of Anhui province can be divided into five levels in the statistical period, as shown in Figure1. The cities with the largest number of violations are Anqing City, Hefei City, and Huangshan City. The cities with the lowest number of violations are Huaibei City and Huainan City.Figure 1
The distribution of traffic violation behaviors in Anhui province.According to the natural discontinuity point classification method (Jenks). Traffic fatal crashes in all administrative regions of the province of Anhui can be divided into 5 levels in the statistical period, as shown in Figure2. Cities with the highest number of traffic fatal crashes are Fuyang City and Liu’an City. Hefei City and Suzhou City have the second highest number of traffic fatal crash cities among all cities.Figure 2
The distribution of traffic fatal crashes in Anhui province.According to the distribution statistics of traffic violation behaviors and traffic fatal crashes in Anhui province, the scatter distribution forms of traffic violation behaviors and traffic fatal crashes have similar distribution forms. Cities with the highest number of fatal crashes, such as Fuyang City and Lu’an City, also have a relatively high number of traffic violations among all cities. The cities with the least number of traffic fatal crashes, namely Huaibei City and Huainan City, also have the lowest number of traffic violations among all cities.


## 3. Methodology

### 3.1. Generalized Additive Model

The purpose of the generalized additive model is to determine whether traffic violation behaviors have an impact on traffic fatal crashes. Statistical data of traffic fatal crashes in administrative regions by quarter were collected. The advantage of this method is that the parameters do not need to satisfy the assumption of linearity and can flexibly detect the complex relationship among data. Besides the linear relationship, whether there are other possible response states between traffic violation behavior variables and traffic fatal crashes. The formula of the generalized additive model is as follows:(1)Y=β0+f1X1+f2X2+f3X3+f4X4+fnX5,where Y is the number of traffic fatal crashes; X1 is the traffic violation number of exceeding the speed limit by 20% no more than 50%; X2 is the traffic violation number of exceeding the speed limit by 50% or more; X3 is the traffic violation number of violations of laws and regulations; X4 is the traffic violation number of driving a defective vehicle or failure to comply with license restrictions; X5 is the traffic violation number of driving under the influence of alcohol or drugs; β0 is the error.


### 3.2. Multilevel Analysis Model

Multilevel data is the basis of the development and application of multilevel statistical models. The main feature of data is that the distribution of response variables is not independent among individuals, but there is aggregation within a geographical distance or a specified time range. To model further, we collated all traffic violation data and traffic fatal crash data by region and date of occurrence.Construct a multilevel logistic regression model, and the 2-level logistic regression model is expressed as:(2)logitpij=β0+uoj+β1xijpij,u0j=β0j−β0,whereu0j∼N0,σu02,where pij is the observed value of the reaction, and xij is the explained value of the observation. β1 is the effect parameter of the fixed factor, also known as fixed effects. u0j is the difference between the logit mean βoj of level 2 units and the total mean β0, also known as random effects or a high level residual. The variance σu02 is also known as a random coefficient, reflecting the difference in ratio among high-level units. The larger the data σu02 is, the more aggregated it is in high-level units. When σu02 is 0, the model evolves into 2-level zero model, which can be expressed as follows:(3)logitPij=β0+uoj,uoj=β0j−β0,where pij is the observed value of the reaction, βoj is the mean value of logit of level 2 units, β0 is the total mean value, and uoj is the difference between the mean of the logit βoj and the mean β0 of the total at level 2.As the data has more hierarchies, it can evolve into a regression model with 3 levels. The 3-level logistic regression model is expressed as:(4)logitpij=β0jk+βijkxijk,β0jk=β0+νok+uojk,whereνok∼N0,σν02,uojk∼N0,σu02,where pij is the observed value of the reaction, and xijk is the explained value of the observation. βijk is the effect parameter of the fixed factor, also known as fixed effects. νok is the random effects of level 3, and its variance is σν02. β0jk is the random effects of level 2, and its variance is σu02.For hypothesis testing of fixed part parameter estimation, three methods can be adopted: (1) hypothesis testing is carried out by establishing separate confidence intervals and joint intervals of parameters; (2) Wald test; (3) log-likelihood ratio test. The results of the three tests are generally similar. This paper adopts the third method. The log-likelihood ratio statistic or deviance statistic is constructed as:(5)D01=−2lnλ0λ1,where λ0 and λ1 are the likelihood values of the model. D01 is the deviance statistic, and obeys χ2 distributed.


## 3.1. Generalized Additive Model

The purpose of the generalized additive model is to determine whether traffic violation behaviors have an impact on traffic fatal crashes. Statistical data of traffic fatal crashes in administrative regions by quarter were collected. The advantage of this method is that the parameters do not need to satisfy the assumption of linearity and can flexibly detect the complex relationship among data. Besides the linear relationship, whether there are other possible response states between traffic violation behavior variables and traffic fatal crashes. The formula of the generalized additive model is as follows:(1)Y=β0+f1X1+f2X2+f3X3+f4X4+fnX5,where Y is the number of traffic fatal crashes; X1 is the traffic violation number of exceeding the speed limit by 20% no more than 50%; X2 is the traffic violation number of exceeding the speed limit by 50% or more; X3 is the traffic violation number of violations of laws and regulations; X4 is the traffic violation number of driving a defective vehicle or failure to comply with license restrictions; X5 is the traffic violation number of driving under the influence of alcohol or drugs; β0 is the error.


## 3.2. Multilevel Analysis Model

Multilevel data is the basis of the development and application of multilevel statistical models. The main feature of data is that the distribution of response variables is not independent among individuals, but there is aggregation within a geographical distance or a specified time range. To model further, we collated all traffic violation data and traffic fatal crash data by region and date of occurrence.Construct a multilevel logistic regression model, and the 2-level logistic regression model is expressed as:(2)logitpij=β0+uoj+β1xijpij,u0j=β0j−β0,whereu0j∼N0,σu02,where pij is the observed value of the reaction, and xij is the explained value of the observation. β1 is the effect parameter of the fixed factor, also known as fixed effects. u0j is the difference between the logit mean βoj of level 2 units and the total mean β0, also known as random effects or a high level residual. The variance σu02 is also known as a random coefficient, reflecting the difference in ratio among high-level units. The larger the data σu02 is, the more aggregated it is in high-level units. When σu02 is 0, the model evolves into 2-level zero model, which can be expressed as follows:(3)logitPij=β0+uoj,uoj=β0j−β0,where pij is the observed value of the reaction, βoj is the mean value of logit of level 2 units, β0 is the total mean value, and uoj is the difference between the mean of the logit βoj and the mean β0 of the total at level 2.As the data has more hierarchies, it can evolve into a regression model with 3 levels. The 3-level logistic regression model is expressed as:(4)logitpij=β0jk+βijkxijk,β0jk=β0+νok+uojk,whereνok∼N0,σν02,uojk∼N0,σu02,where pij is the observed value of the reaction, and xijk is the explained value of the observation. βijk is the effect parameter of the fixed factor, also known as fixed effects. νok is the random effects of level 3, and its variance is σν02. β0jk is the random effects of level 2, and its variance is σu02.For hypothesis testing of fixed part parameter estimation, three methods can be adopted: (1) hypothesis testing is carried out by establishing separate confidence intervals and joint intervals of parameters; (2) Wald test; (3) log-likelihood ratio test. The results of the three tests are generally similar. This paper adopts the third method. The log-likelihood ratio statistic or deviance statistic is constructed as:(5)D01=−2lnλ0λ1,where λ0 and λ1 are the likelihood values of the model. D01 is the deviance statistic, and obeys χ2 distributed.


## 4. Results of Data Analysis

Spearman’s correlation coefficient [61] can indicate the correlation between traffic violation behaviors and traffic fatal crashes. It is represented by relations between traffic violations and traffic fatal crashes from Table 2. X1 (exceeding the speed limit by 20% no more than 50%), X2 (exceeding the speed limit by 50% or more), X3 (violations of laws and regulations), X4 (driving a defective vehicle or failure to comply with license restrictions) are significant for traffic fatal crashes. While the Spearman’s correlation coefficient can not reveal the effect of each traffic violation behavior on traffic fatal crashes intuitively.Table 2
Spearman’s correlation coefficient between traffic violation behaviors and traffic fatal crashes.
VariableX1X2X3X4X5Value−0.034∗∗−0.142∗∗0.120∗∗0.089∗∗0.009∗∗for P value ≤ 0.05.Using the generalized additive model (GAM), we can get the correlation between traffic violation behaviors and traffic fatal crashes. SinceX5 (driving under the influence of alcohol or drugs) does not meet the correlation test, X5 (driving under the influence of alcohol or drugs) is not considered in this model. Based on Table 3, the results show that the nonlinear effects of these traffic violation behavior variables on fatal crashes are significant. The regression model can explain 84.9% of the overall variance of the response variables (R2 = 0.849), indicating that these traffic violation behaviors variables can explain 84.9% of the variance at the logarithmic level of the fatal crashes, and the fitting results are excellent.Table 3
Parametric coefficients.
VariableEstimateSEChi-squaredP-valueIntercept0.8710.0969.041<0.001∗∗∗X18.1868.69430.50<0.001∗∗∗X28.5198.87728.27<0.001∗∗∗X38.0808.71160.04<0.001∗∗∗X47.1587.93915.800.040∗∗for P value ≤ 0.1. ∗∗for P value ≤ 0.05. ∗∗∗for P value ≤ 0.01. R2=0.849.Figure3 shows the relationship between four kinds of traffic violation behaviors and traffic fatal crashes. The s-value on the vertical axis represents the probability of a fatal crash in each city per quarter. The horizontal axis represents the range of distribution of all violation behaviors in each district in each quarter. The curve represents the probability of traffic fatal crashes as the number of four types of violations increases.Figure 3
The impact of traffic violation behaviors on traffic fatal crashes.Figure3 illustrates the increasing gradient of X1 (exceeding the speed limit by 20% no more than 50%), the vertical axis can be described as the logarithm of the traffic fatal crashes changing with the change of X1 (exceeding the speed limit by 20% no more than 50%). The number of X1 (exceeding the speed limit by 20% no more than 50%) in each quarter of each administrative region is evenly distributed in the range of 0–50, and there are outliers in the range of X1 (exceeding the speed limit by 20% no more than 50%) equal to 10 and 20. However, the curve characteristics seem to be piecewise, with some fluctuation in some locations, but the overall number of X1 (exceeding the speed limit by 20% no more than 50%) shows a trend of slow rise. The results show that X1 (exceeding the speed limit by 20% no more than 50%) has a promoting effect on traffic fatal crashes.On the increasing gradient ofX2 (exceeding the speed limit by 50% or more), the logarithm of traffic fatal crashes, described as the vertical axis, varies with the change of X2 (exceeding the speed limit by 50% or more). X2 (exceeding the speed limit by 50% or more) is most concentrated in the range of 0–150 in each administrative region in each quarter, and the log value of the fatal crashes in this part has a significant upward trend, indicating that X2 (exceeding the speed limit by 50% or more) has a certain influence on the fatal crashes. There will be extreme values and fluctuations in the range of 150–400.On the increasing gradient ofX3 (violations of laws and regulations), the logarithm of the fatal crashes described as the vertical axis changes with the change of X3 (violations of laws and regulations). However, from the point of view of the characteristics of the curve, it seems to be segmented and shows local volatility. X3 (violations of laws and regulations) districts are mostly in the 0–8 range each quarter, and the number of such violations is low. The logarithm of the fatal crashes fluctuates with X3 (violations of laws and regulations) and the curve comes growing. When the value exceeds 8, it is affected by some extreme values and shows obvious fluctuation, which has an obvious impact on the curve.On the increasing gradient ofX4 (driving a defective vehicle or failure to comply with license restrictions), the logarithm of the fatal crashes varies with the change of X4 (driving a defective vehicle or failure to comply with license restrictions). For X4 (driving a defective vehicle or failure to comply with license restrictions), most of the districts fall within the 0–9 range in each quarter and the number of such offences is low. X4 (driving a defective vehicle or failure to comply with license restrictions) is evenly distributed within the range of 0–8, and some locations will be affected by outliers. Although the number of serious traffic crashes increases and the number of traffic violations decreases locally, the overall trend of fluctuation increases. This trend indicates that X4 (driving a defective vehicle or failure to comply with license restrictions) has a certain influence on the fatal crashes.According to the analysis results of the influence of these four kinds of traffic violation behaviors on the traffic fatal crashes, it shows that these four kinds of traffic violation behaviors do have an impact on traffic fatal crashes.In a real situation, we would need to consider that every traffic violation behavior and traffic fatal crash have two attributes: time and place. The statistical time and place of traffic violation behaviors are different, as are the traffic fatal crashes, so multilevel models can be constructed. There are three multilevel models, model A, model B, model C. Model A is a 2-level model, and shown in Figure4. Level 2 of model A is time (all traffic violation behaviors events and traffic fatal crashes are counted within a day), and level 1 is each independent event (including traffic violation behaviors events and traffic fatal crashes). Model B is a 2-level model, and shown in Figure 5. Level 2 of model B is the illegal region (taking the administrative region as the unit, counting all traffic violation behaviors events and traffic fatal crashes in a city), level 1 is each event (including traffic violation behaviors events and traffic fatal crashes). Model C is a 3-level model, and shown in Figure 6. Level 3 of model C is an illegal area (taking the administrative region as the unit, counting all traffic violation behaviors and traffic fatal crashes within a city), level 2 is the time (all traffic violation behaviors events and traffic fatal crashes are counted within a day), and level 1 is each independent event (including traffic violation behaviors events and traffic fatal crashes).Figure 4
Hierarchical structure of model A.Figure 5
Hierarchical structure of model B.Figure 6
Hierarchical structure of model C.Three multilevel zero models are constructed without any explanatory variables. Explore the relationship between traffic fatal crashes and traffic violations in time and space and the interaction of time and space. That is, whether the multilevel model is meaningful. Construct two 2-level zero models of model A and model B, and a 3-level zero model of model C. The results are shown in Table4.Table 4
The table of different multilevel zero models.
EffectsParametersCoefficientModel Ax2Model Bx2Model Cx2Fixed effectsβ0−3.494 (0.086)1652.517∗∗∗−3.496 (0.071)2424.522∗∗∗−3.488 (0.083)1766.025∗∗∗Random effectsLevel 2σu021.089 (0.193)642.478∗∗∗4.892 (0.532)84.557∗∗∗0.712 (0.184)14.974∗∗∗σv02——3.867 (0.529)56.236∗∗∗Level 11 (0.000)1 (0.000)1 (0.000)∗for P value ≤ 0.1. ∗∗for P value ≤ 0.05. ∗∗∗for P value ≤ 0.01.The results of the three models are statistically significant. The data has a hierarchical structure relationship for traffic violation behaviors and traffic fatal crashes. That means, although various kinds of traffic violation behaviors will affect traffic fatal crashes, the degree of impact is affected by time, administrative location, and the interaction of time and space. Since time and administrative location cannot be ignored, traffic violation behavior variables are introduced to study the impact of traffic violation behaviors on traffic fatal crashes. Specific analysis results are shown in Table5.Table 5
The logistics regression models for multilevel analysis.
EffectsParametersCoefficientModel AEstimatex2Model BEstimatex2Model CEstimatex2Fixed effectsβ0−0.240 (0.150)1.2712.560∗−0.286 (0.149)1.3283.633∗∗∗−0.265 (0.154)1.3032.961∗∗β1−3.975 (0.284)53.250195.901∗∗∗−3.970 (0.286)52.932191.249∗∗∗−3.948 (0.283)51.832194.617∗∗∗β2−3.803 (0.172)44.835488.873∗∗∗−3.797 (0.176)44.567465.432∗∗∗−3.774 (0.175)43.554465.080∗∗∗β3−3.760 (0.609)42.94838.119∗∗∗−3.736 (0.606)41.88837.862∗∗∗−3.734 (0.602)41.84638.473∗∗∗β4−2.853 (0.534)17.34028.544∗∗∗−2.842 (0.538)17.15027.905∗∗∗−2.827 (0.531)16.89528.344∗∗∗Random effectsLevel 3σv020.595 (0.187)—10.124∗∗∗Level 2σu020.631 (0.182)—12.020∗∗∗0.834 (0.365)—5.221∗∗∗0.388 (0.422)—0.845∗Level 11——1——1——∗for P value ≤ 0.1. ∗∗for P value ≤ 0.05. ∗∗∗for P value ≤ 0.01.The research results in Table5 show that for model A, time is at a high level and independent event is at a low level, not considering the region. From the perspective of time, the traffic violation behaviors variables X1 (exceeding the speed limit by 20% no more than 50%), X2 (exceeding the speed limit by 50% or more), X3 (violations of laws and regulations) and X4 (driving a defective vehicle or failure to comply with license restrictions) that affect the occurrence of traffic fatal crashes have statistical significance. Under the condition that other factors remain unchanged, the occurrence of X1 (exceeding the speed limit by 20% to no more than 50%) impacting fatal crashes will be 53.25 times more likely than that without X1 (exceeding the speed limit by 20% no more than 50%). Compared with no X2 (exceeding speed limit by 50% or more) behaviors, the possibility of fatal crashes will increase by 44.835 times in a day. Compared with X3 (violations of laws and regulations) behaviors, the possibility of fatal crashes will increase 42.948 times. Compared with no X4 (driving a defective vehicle or failure to comply with license restrictions) behaviors, the possibility of fatal crashes will increase by 17.340 times.Model B shows high levels in areas and low levels for each event, not considering time. In other words, from the space level, the traffic violation behaviors variablesX1 (exceeding the speed limit by 20% no more than 50%), X2 (exceeding the speed limit by 50% or more), X3 (violations of laws and regulations) and X4 (driving a defective vehicle or failure to comply with license restrictions) that affect the traffic fatal crashes have statistical significance. Under the condition that other factors remain unchanged, for the same area, the X1 (exceeding the speed limit by 20% no more than 50%) impacting the fatal crashes will be 52.932 times more likely than that without X1 (exceeding the speed limit by 20% no more than 50%) behaviors. Compared with no X2 (exceeding speed limit by 50% or more) behaviors, the possibility of traffic fatal crashes will increase by 44.567 times. Compared with X3 (violations of laws and regulations) behaviors, the possibility of traffic fatal crashes will increase by 41.888 times. Compared with no X4 (driving a defective vehicle or failure to comply with license restrictions) behaviors, the possibility of traffic fatal crashes will increase by 17.150 times.Model C shows that the time is level 3, the illegal area is level 2, and each event is level 1. The results are shown in Table5, X1 (exceeding the speed limit by 20% to no more than 50%), X2 (exceeding the speed limit by 50% or more), X3 (violations of laws and regulations), and X4 (driving a defective vehicle or failure to comply with license restrictions), which are all statistically significant, are related to the interaction of time and space. Under the condition that other factors remain unchanged, at the same time, areas with high levels of X1 (exceeding the speed limit by 20% to no more than 50%) compared with areas with low levels of X1 (exceeding the speed limit by 20% to no more than 50%), and fatalities are 51.832 times. Compared with no X2 (exceeding speed limit by 50% or more) behaviors, the possibility of fatal crashes will increase by 43.554 times for different regions at the same time. Under different space conditions and the same period, compared with X3 (violations of laws and regulations) behaviors, the possibility of fatal crashes will increase 41.846 times. Compared with no X4 (driving a defective vehicle or failure to comply with license restrictions) behaviors, the possibility of fatal crashes will increase by 16.895 times for different regions at the same time.The goodness of fit of the multi-level model is better than that of the single-level model, which is manifested by smaller residuals standard error. As shown in Table6, the variable effect value estimated by the 1-level model is relatively large, because it includes the differences between the whole regions as well as the differences in each time period of the whole time range. The multilevel model separates this difference. For example, the residual standard obtained by Model A includes only the difference in each time period. The residual standard obtained by model B only includes the difference between each region. The residual obtained by Model C takes into account the difference between each time period and each region, and its deviation value is the smallest. It can be seen that the traditional model has disadvantages in dealing with multi-level structure data and estimating the effect of variables at different levels. At this point, the multi-level model is more reasonable.Table 6
Comparison of different models of residuals standard error.
1-level model2-level model of model A2-level model of model B3-level model of model C−2 log likelihood1745.4851745.241715.0361600.723In Table6, comparing the 1-level model and 2-level model of model A, the likelihood ratio hypothesis test statistic D01 = 1745.485–1745.24 = 0.265. Since this deviation degree of freedom is 0 (that is, there is no parameter increase between the two models), it can be considered that the 2-level model of Model A is superior to the 1-level regression model. Using the same method for model checking, it can be seen that the 3-level model of the Model C model is optimal, which reflects that the quasi-cooperative use of the model can be improved when the hierarchical structure of variables is considered.


## 5. Summary and Conclusions

The results show that traffic violation behaviors have a significant impact on traffic fatal crashes. As lawbreaking increases, so does the likelihood of traffic fatal crashes. In order to avoid the occurrence of traffic fatal crashes, we should start with reducing traffic violation behaviors, especially for the control of speed on the expressway. This is because speeding is the most common traffic violation behavior and has a remarkable influence on traffic fatal crashes. ForX3 (violations of laws and regulations) and X4 (driving a defective vehicle or failure to comply with license restrictions), although these two kinds of traffic violation behaviors account for a small proportion of all traffic violation behaviors, once such traffic violation behaviors occur, they also have a significant impact on traffic fatal crashes, which should not be ignored.By using multilevel models, we can conclude that traffic violations have a significant impact on traffic fatal crashes in terms of time and region. In other words, the possibility of traffic fatal crashes increases with the time when the traffic violation behaviors are more intensive. In addition, districts with a higher number of violations are more prone to traffic fatal crashes than other regions. The traffic fatal crashes are affected dramatically by the traffic violation behaviors which in traffic black spots and in the crash-prone period. If these two unfavorable conditions are limited, the probability of a traffic fatal crash is less than the probability of a single disadvantage. The quantified analysis results are well proven in this conclusion. That’s because the more restrictions there are, the less likely it is to happen.The contribution of this study: (1) A generalized additive model was used to verify the correlation between traffic violation behaviors and traffic fatal crashes. By traffic violation behaviors and traffic fatal crashes data visualization, risk behaviors were evident. Although the crash curve was very sensitive to outliers, showing local fluctuations, the overall curves mainly presented an upward trend. (2) According to the characteristics of the data of traffic violation behaviors and traffic fatal crashes, multilevel analysis models were constructed based on a single event, time dimension, and space dimension. The results showed that traffic violation behaviors and traffic fatal crashes would have spatial aggregation, time aggregation, and space-time aggregation interaction.In general, this study provides some valuable information for traffic safety research. To reduce the traffic fatal crashes, based on the current research results, the expressway should further strengthen the supervision and control of traffic violation behaviors, such as speeding. In addition, further improvements are required. First, a more complex multilevel hierarchy could be added to the study or use other methods to study the crash mechanism. It is beneficial to help us to have a clear understanding of the factors that affect traffic fatal crashes. This paper only considers the traffic fatal crashes and traffic violation behaviors in one year. In future studies, the data volume will be further expanded, the crash curve will be further improved, and the influence of individual outliers will be further eliminated.



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*Source: 9917877-2022-09-06.xml*