Multivariate dynamic Tobit models with lagged observed dependent variables: An effectiveness analysis of highway safety laws

Accident Analysis and Prevention 113 (2018) 292–302

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Multivariate dynamic Tobit models with lagged observed dependent variables: An effectiveness analysis of highway safety laws

T

⁎

Chunjiao Donga,c, , Kun Xieb,c, Jin Zengc, Xia Lid a

Center for Transportation Research, Tickle College of Engineering, University of Tennessee, 600 Henley Street, Knoxville, TN 37996, USA Department of Mechanical, Aerospace, & Biomedical Engineering, College of Engineering, University of Tennessee, 1512 Middle Drive, 414 Dougherty, Knoxville, TN 37996-2210, USA c School of Traffic & Transportation, Beijing Jiaotong University, Beijing 100044, China d School of Management and Economics, Beijing Institute of Technology, Beijing 100181, China b

A R T I C L E I N F O

A B S T R A C T

Keywords: Traffic safety Multivariate dynamic Tobit models Safety laws Temporal correlation Interdependency issues

Highway safety laws aim to influence driver behaviors so as to reduce the frequency and severity of crashes, and their outcomes. For one specific highway safety law, it would have different effects on the crashes across severities. Understanding such effects can help policy makers upgrade current laws and hence improve traffic safety. To investigate the effects of highway safety laws on crashes across severities, multivariate models are needed to account for the interdependency issues in crash counts across severities. Based on the characteristics of the dependent variables, multivariate dynamic Tobit (MVDT) models are proposed to analyze crash counts that are aggregated at the state level. Lagged observed dependent variables are incorporated into the MVDT models to account for potential temporal correlation issues in crash data. The state highway safety law related factors are used as the explanatory variables and socio-demographic and traffic factors are used as the control variables. Three models, a MVDT model with lagged observed dependent variables, a MVDT model with unobserved random variables, and a multivariate static Tobit (MVST) model are developed and compared. The results show that among the investigated models, the MVDT models with lagged observed dependent variables have the best goodness-of-fit. The findings indicate that, compared to the MVST, the MVDT models have better explanatory power and prediction accuracy. The MVDT model with lagged observed variables can better handle the stochasticity and dependency in the temporal evolution of the crash counts and the estimated values from the model are closer to the observed values. The results show that more lives could be saved if law enforcement agencies can make a sustained effort to educate the public about the importance of motorcyclists wearing helmets. Motor vehicle crash-related deaths, injuries, and property damages could be reduced if states enact laws for stricter text messaging rules, higher speeding fines, older licensing age, and stronger graduated licensing provisions. Injury and PDO crashes would be significantly reduced with stricter laws prohibiting the use of handheld communication devices and higher fines for drunk driving.

1. Introduction States across the United States (US) have enacted highway safety laws to influence driving behaviors, such as impaired driving and distracted driving. The enacted highway safety laws are intended to enhance traffic safety and reduce traffic crashes and deaths, injuries, and related outcomes and costs. Currently, there are 11 types of highway safety laws by issues in the US (Governors Highway Safety Association), as shown in Table 1. However, no state has enacted all of those 11 key highway safety laws (Advocates for Highway & Auto Safety, 2016) and there are still far too many people being killed and injured in motor vehicle crashes. The latest fatality and injury data from the federal ⁎

government show that 35,092 people were killed and 2.443 million people were injured in traffic crashes in 2015, a 7.17% and 4.49% increase from 2014 (National Highway Traffic Safety Administration, 2016). To save more lives and reduce the outcomes of motor vehicle crashes, the effects of the key highway safety laws on traffic safety have to be better understood. Results from analyses and modeling of the relationship between highway safety laws and crash counts across severities could be used by decision makers, policy makers, and lawmakers to refine/amend existing laws and develop new legislation. For example, the implementation of the seat belt laws is estimated to save more than 10,000 lives annually (Advocates for Highway & Auto Safety,

Corresponding author. E-mail address: [email protected] (C. Dong).

https://doi.org/10.1016/j.aap.2018.01.039 Received 25 September 2017; Received in revised form 17 November 2017; Accepted 29 January 2018 0001-4575/ © 2018 Elsevier Ltd. All rights reserved.

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Table 1 Summary of the investigated state highway safety laws and related research. Highway safety laws

Brief description/explanation

# states have passed laws*

# states have no laws*

Relevant research

Aggressive driving

Passed laws specifically defining aggressive driving actions

11

39

Child passenger safety

Booster seats or other appropriate devices for children who have outgrown their child safety seats but are still too small to use an adult seat belt safely Children younger than two years of age to be in a rear-facing child seat Seat belt requirements for school buses

48

2

Dula and Geller (2003), Nesbit et al. (2007), Shinar and Compton (2004), Jovanović et al. (2011) and Constantinou et al. (2011) Arbogast et al. (2004), Elliott et al. (2006), Nakanara et al. (2015) and Winston et al. (2007)

4

46

5

45

Hand-held cell phone ban (for all drivers)

14

36

Text Messaging Ban (for all drivers)

46

4

Graduated driver licensing

Learner stage (16 years old) Full privilege stage (18 years old) Intermediate stage (Nighttime Driving Restriction) Intermediate stage (Passenger Restriction)

8 8 48 46

42 42 2 4

Ferguson et al. (1996), Hedlund et al. (2006) and Williams (2009)

Helmets

Motorcycle Helmets (Universal helmet law) Bicycle helmets

19 21

31 29

Weiss et al. (2010), McCartt et al. (2011), Passmore et al. (2010) and Brown et al. (2009)

Impaired driving

Drugs (Zero tolerance) Drugs (Per se) Marijuana drug-impaired Driving laws (Zero tolerance or non-zero per se laws for marijuana) Alcohol (Administrative license suspension on the first offense) Alcohol (Mandatory or highly incentivized ignition interlock law) Sobriety checkpoints

16 6 18

34 44 32

Elder et al. (2011), Mercer et al. (2010) and McCartt et al (2015)

42

8

22

28

38

12

Mature drivers

Special provisions for mature drivers

33

17

Seat belts

For front seat occupants Seat belt use for all rear seat passengers

49 28

1 22

Speed limits

Different speed limits for cars and trucks Highest speed limits higher than 70 mph

7 14

43 36

Welki and Zlatoper (2007), Welki and Zlatoper (2009) and Dong et al. (2016a,b)

Automated enforcement laws

Speed cameras Speed cameras implementation Red light cameras Red light cameras implementation

13a + 9b 12 10c + 21d 24

28 38 19 26

Montella et al. (2012), Shin et al. (2009) and Tay, 2010 McCartt and Hu (2014), Hu et al. (2011), Retting and Kyrychenko (2002) and Hallmark et al. (2010)

Work zones

Double the fine for committing traffic violations Workers to be present Signs must be posted

33 24 42

17 26 8

Lin et al. (2004) and Ullman et al., 1997

Distracted driving

Jacobson et al. (2012), Goodwin et al., 2012, Welki and Zlatoper (2014) and Kwon et al. (2014) Atchley et al. (2011), Hallett et al., 2012, Harrison (2011) and Ehsani et al. (2014)

Siren and Meng (2012), Hakamies-Blomqvist (2006), Fitten (2003) and Langford et al. (2004a,b) Nichols et al. (2012), Strine et al. (2010), Conner et al. (2010), Cohen and Einav (2003) and Shults and Beck (2012)

Note: *The data are based as of the year 2015. a Prohibit (with very narrow exceptions) the use of speed cameras. b Permit or limit the use of speed cameras. c Prohibit the use of red light cameras. d Permit the use of red light cameras.

crashes (as opposed to total crashes) can reveal new insights that would support the law making. To analyze the effects of state highway safety laws on crashes across severities, multivariate regression models are needed, since the crash counts are interdependent. In this research, we proposed a multivariate dynamic Tobit (MVDT) model to analyze the crash data. The proposed models have two merits. The proposed models can address the issues of differential censoring in crash counts across crash types, while account for the possible contemporaneous error correlation resulting from unobserved heterogeneity in the samples. The proposed models can also address potential temporal correlation issues in the interdependent crash counts.

2016). Some states have enacted it as a secondary law, which allows law enforcement officers to issue a citation for unbelted occupants when the driver commits a separate offense. In addition, some states require seat belt use only for front seat occupants, without requiring other occupants to wear seat belts. A better understanding of the relative effectiveness of enacted primary and secondary seat belt laws on crash counts across severities could help states develop better laws and even more lives could be saved. Furthermore, it is possible that a particular highway safety law that enacted to reduce one specific type of crash might increase the number and severity of other crashes. For example, automated red-light camera enforcement laws have been shown to be effective in reducing the incidences of red-light running and the number of red-light running crashes. However, several studies (Llau et al., 2015; Hallmark et al., 2010; Shin and Washington, 2007) showed that the implementation of red-light cameras increases the number of rear-end collisions. Modeling the counts of specific types of

2. Literature review Several studies have examined the effectiveness of enacted highway safety laws. Voas et al. (2000) analyzed the relationship between three 293

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major alcohol safety laws – administrative license revocation laws, 0.10 illegal per se, and 0.08 illegal per se laws - and the number of “drunk” drivers in fatal crashes using data for 50 states and the District of Columbia. The results showed that each of the three laws has a significant relationship to the downward trend in alcohol-related fatal crashes in the United States over a period of 16 years (1982–1997). The study also pointed out that the long-term trend is the result of the growing impact of several laws over time plus the effects of some other factors. Shults et al. (2004) conducted a systematic review on the effectiveness of primary enforcement seat belt laws and enhanced enforcement of seat belt laws. Their results showed that primary seat belt laws are more effective than secondary laws in increasing safety belt use and decreasing fatalities and that enhanced enforcement is effective in increasing seat belt use. Another study (Farmer and Williams, 2005) showed that if these remaining secondary laws were amended to primary laws, an additional 696 deaths per year could be prevented. Branas and Knudson (2001) analyzed motorcycle rider death rates between states with full motorcycle helmet laws and those without. The results showed that death rates in states with full helmet laws were lower on average than death rates in states without full helmet laws, after controlling for other factors that affect motorcycle rider fatalities. Traffic safety laws can vary across states. Take aggressive driving laws as an example. Aggressive driving is defined by the National Highway Traffic Safety Administration (NHTSA) as "the operation of a motor vehicle in a manner that endangers or is likely to endanger persons or property". Nonetheless, states should define what constitutes aggressive driving and stipulate the related fines and penalties according to their respective laws and regulations, practices, and the public understanding. Dula and Geller (2003) addressed the need for consistent definition of aggressive driving. Other studies (Nesbit et al., 2007; Shinar and Compton, 2004; Jovanović et al., 2011; Constantinou et al., 2011) examined factors that contribute to aggressive driving behaviors—these include personality traits, mood, and situation. Currently, 11 states have passed laws specifically defining aggressive driving, while others have no laws to address this issue. Though some states have enacted the laws that define what constitutes aggressive driving, the effects of aggressive driving laws on traffic safety are not fully understood. There is a need to evaluate the effects of the differences in the enacted highway safety laws on traffic safety. Consider studies related to distracted driving laws as an example. Some states enacted distracted driving laws, including a ban on the use by drivers of hand held mobile phones and text messaging ban as primary laws, while some other states enacted them as secondary laws, and yet other states do not have such laws. To evaluate the effectiveness of distracted driving laws, some studies compared states with primary laws to those with secondary laws, and some studies evaluated the effects when changing from secondary to primary laws. However, their findings are not consistent or conclusive. Some research (Goodwin et al., 2012; Hallett et al., 2012; Harrison, 2011) showed that the decrease in mobile phone use did not significantly differ between the states that have the distracted driving laws and the states that did not have such laws. Other studies (Jacobson et al., 2012; Welki and Zlatoper, 2014, Ehsani et al., 2014) showed that the distracted driving laws have reduced hand held mobile phone use and fatal crash rates. Because of differences in the enacted laws, and differences in the methodologies used to assess changes following the law’s enactment, summarizing the results of highway safety law evaluations is difficult. Table 1 provides a summary of studies that analyzed the effectiveness of enacted highway safety laws. In summary, to determine the effects of enacted state highway safety laws on traffic safety, before and after analyses were conducted based on the crash frequencies and severities. Though a “longer” time period is desirable, few studies have been able to include more than one or two years of data before and after a law was enacted. There is no question that one specific highway safety law could potentially affect the results of studies that evaluated the effectiveness

of another highway safety law. But, studies typically analyze the effects of individual highway safety laws on traffic safety. In addition, many studies considered only fatal crashes (or total crash counts) as the dependent variables, though highway laws have potential effects on injury crashes and PDO crashes as well. To understand and analyze the effects of highway safety laws on the counts of specific types of crashes, multivariate regression models are needed, because the counts of specific crash types are not independent. The intent of this study is to propose a new methodology – using multivariate dynamic Tobit (MVDT) models to assess the effectiveness of highway safety laws on traffic safety. To address the temporal correlation issues in crash counts, lagged observed dependent variables are incorporated in the models. Key factors that associated with highway safety laws, including the status of state enacted highway safety law programs, fines for violations, and other penalties associated with the laws have been taken into account and analyzed. The socio-demographic and traffic characteristic related factors have been incorporated as controlled indicators. The aggregated crash counts at state level, including fatal crash counts, injury crash counts, and PDO crash counts are analyzed as dependent variables. The performance of the proposed models, including goodness-of-fit and predictive accuracy, have been compared with the multivariate static Tobit models (MVST) and MVDT models with lagged random variables. 3. Methodologies The analyses of dependent variables show that the observed samples are truncated at zero and over-dispersed. Based on the data characteristics, the Tobit distribution is considered. Compared to the traditional Tobit regression models that deal with the total crash counts as a whole, the multivariate static Tobit (MVST) models can address the issues of differential censoring in crash counts across severities, while accounting for the possible contemporaneous error correlation resulting from unobserved heterogeneity in the samples. Previous research (Anastasopoulos et al., 2012) has shown that MVST models have the potential to provide a fuller understanding of the factors determining crash rates on specific roadway segments. Though the MVST models can explicitly consider the correlation among the injury severity levels for each roadway segment, they become inappropriate in crash-frequency modeling when the same roadway segments generate multiple observations, and these observations may be correlated because many of the unobserved effects remain the same over time. In other words, the MVST models cannot account for the temporal correlation issues. From a statistical perspective, ignoring the potential temporal correlation in dependent variables could adversely affect the precision of parameter estimates and it also may result in the loss of important insights. To address potential temporal correlation issues in interdependent crash counts, multivariate dynamic Tobit (MVDT) models have been proposed to analyze the crash-frequency data. If yt = (y1t, y2t, …, ynt)′ is a vector of n types of crashes across severities, the dynamic Tobit model with unobserved effect is described as follows (Chang, 2011; Wooldridge, 2005):

y * ifyit* > 0 yit = ⎧ it ⎨ 0 otherwise ⎩

fori = 1, 2, ⋯, N

t = 1, 2, ⋯, T (1)

where yit is the number of observed crashes for crash type i in period t and yit* is the expected number of crashes for crash type i in period t. The censoring threshold is assumed to be zero for notational convenience without losing generalization, where yit equals to zero with a positive probability, but it is continuously distributed over strictly positive values. The random variable yit* is given by k−p

yit* =

p

∑ βij xijt + ∑ λij yi,t−j + ci + uit j=1

j=1

(2)

where xjt (1 ≤ j ≤ k − p) is the explanatory variable that can be a factor 294

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conventional hill-climbing optimization techniques—Newton’s method, BFGS have proven to have good performance even for non-smooth optimizations (Anastasopoulos et al., 2012). Ten draws are used to form the GHK simulator. For comparison, three models have been estimated in this research: 1) a MVDT model with lagged observed dependent variables (hereinafter referred to as Model 1); 2) a MVDT model with unobserved random variables (hereinafter referred to as Model 2); and 3) and a MVST model (hereinafter referred to as Model 3). Model 2 can p p be obtained from Eq. (2) by replacing the ∑j = 1 λij yi, t − j with ∑j = 1 λij yi*, t − j . The simulation likelihood function of Model 2 can be obtained in the same way as Model 1 except that yi*, t − j is used in Eqs. (5)–(7), instead of using yi,t-j. Detailed information regarding the estimation process for Model 3 can be found in Anastasopoulos et al. (2012). The residual sum of squares (RSS), Akaike’s information criterion (AIC), and Schwarz Bayesian criterion (SBC) are estimated to evaluate the models’ goodness-of-fit. For these evaluation statistics, given a set of candidate models for the data, the preferred model is the one with the minimum values.

related to highway safety laws and k is the total number of estimated parameters, βij (1 ≤ j ≤ k − p) and λij (1 ≤ j ≤ p) are the estimable parameters, p is the number of lagged observed dependent variables, ci is an unobserved individual specific random disturbance that is constant over time, and ui is an idiosyncratic error that varies across time and observed samples; ci and uit are assumed to follow a Gaussian distribution conditional on xj1, xj2, …, xjT. Note that the proposed model is characterized by lagged observed dependent variables yi,t-j instead of random variables yi*, t − j , which can capture the dynamics and to allow the proposed model to account for temporal correlation in crash data. Let θ denote the parameter set {βi1, βi2, …, βi,k-p, λi1, λi2, …, λip}, correspondingly we define the vectors xi = (xi1t, xi2t, …, xi,k-p,t, yi,t-1, yi,t2, …, yi,t-p)’ and εi = (εi1, εi2, …, εiT)’, where εit=ci+uit. We can write εi = Aδi, where A is a lower triangular matrix and δi ∼ N(0, 1) and δi = (δi1, δi2, …,δiT)’. According to the sequential decomposition methods proposed by Hendry and Richards (1992), the joint density function of yit and yit* can be decomposed into the products of different forms of conditional densities,

g (yit , yit* yi, t − 1 , yi*, t − 1) = q (yit yi, t − 1 , yi*, t − 1) × h (yit* yit , yi, t − 1 , yi*, t − 1)

(3)

4. Data

where q is a conventional Tobit likelihood function and h is a sampling density from which the latent variables yit* can be drawn. Hence, the likelihood function for the MVDT model with lagged observed dependent variables can be written as: N

L=

0

The dataset includes three parts: yearly aggregated fatal crashes, injury crashes, and property damage only (PDO) crashes as the dependent variables, characteristics of key highway safety laws as the explanatory variables, and sociodemographic factors as the control variables for each individual state. For consistency and reliability, all the data were obtained from the jurisdictional agencies in the United States from 2010 to 2014. The dependent variables (fatal, injury, and PDO crash counts) that aggregated at the state level were obtained from the Insurance Institute for Highway Safety (IIHS) and the National Highway Traffic Safety Administration (NHTSA). In total, the dataset consisted of 250 observations for each crash severity. Fatal crash counts per year in the 50 states range from 42 in Vermont in 2014 to as high as 3193 in Texas in 2014, with a mean of 602.79 and a standard deviation of 607.53. The injury crash counts ranged from a low of 467 in the Rhode Island in 2012 to a high of 161,094 in California in 2010, with a standard deviation of 39,253.75. The PDO crash counts have a mean of 82,591 and a standard deviation of 74,707. The independent and dependent variables and their descriptive statistics are shown in Table 2. The empirical crash frequency distributions are presented in Fig. 1. Compared to a standard normal distribution, significant censoring appears in the observed crash counts across severities. For instance, there are more observed samples with values less than 500 than the rest of the distribution in fatal crashes. For the analyses, the natural logarithms of the dependent variables are used, since there are significant differences between the raw data and normal distribution. With the log transformation, the observed distributions of the fatal, injury, and PDO crashes are more close to the normal distributions, as shown in Fig. 1. However, in the histograms of fatal, injury, and PDO crash distributions, several spikes are noted to be higher than the others, which show the excess number of observed samples. In addition to the histograms, several QQ plots of observed crash counts versus standard normal distributions are presented in Fig. 1, which also confirms that the empirical crash frequency distributions are different compared to the normal distributions, regardless of raw data or log transformed data. For each state, characteristics of key highway safety laws, including the status of enacted highway safety laws and the penalties for traffic violations have been collected as key indicators. The information was obtained from state Departments of Transportation (DOT), State Highway Safety Offices (SHSO), the Insurance Institute for Highway Safety (IIHS), and the Governors Highway Safety Association (GHSA). To compare and assess the differences in state highway safety laws, the variables of the status of enacted laws have been coded as dummy variables. An initial analysis of the law status data show that no state has all 11 key highway safety laws enacted. According to the report of the 2016 Roadmap of State Highway Safety Laws, only 13 states

T

0

∏ ∫−∞ ⋯ ∫−∞ ∏ g (yit , yit* yi,t−1 , yi*,t−1) dyi* i=1

(4)

t=1

yi*

In this study, the number of dimensions for is three [1–3 for fatal crashes, injury crashes and property damage only (PDO) crashes, respectively] and yi0* are assumed to be zero in the likelihood simulation. To obtain a computationally practical simulation estimator for the proposed MVDR model with complicated dependence structures, the log-likelihood function has been maximized and simulated through procedures based on a recursive algorithm formulated by GewekeHajivassiliou-Keane (GHK) simulator (Hajivassiliou et al., 1996). The GHK simulator is selected because it allows current information to feedback to the simulation procedure. In other words, yit* can be drawn from not only the past, but also the current sample information. Thus, the simulated log-likelihood function based on the GHK simulator with R simulation draws can be written as

1 lˆR = R

R

T

1

φ(

tt

r=1 i=1 t=1

k−p

y͠ it(r ) =

N

∑ ∑ ∑ [A

yit − y͠ it I −y͠ )] it [Φ ( it )]1 − Iit Att Att t−1

p

∑ βij xjt − ∑ λij yi,t−j − ∑ Atk δik(r ) j=1

(5)

j=1

k=1

(6)

where Iit is a censored indicator function, for crash type i, if Iit = 1 then yit* is observed and yit = yit* . On the other hand, yit* is censored and its value is not observed (i.e., yit = 0); φ is the standard normal density function and Φ is the cumulative standard normal function; δik(r ) is the truncated normal random variables that can be estimated by (r )

δit(r )

⎧ Φ−1 (η (r ) Φ ( −y͠ it )) for t ∈ {t1, t2, ⋯, tmi } ⎪ it Att = ⎨ yit*(r ) − y͠ it(r ) for t ∉ {t1, t2, ⋯, tmi} ⎪ Att ⎩

(7)

where ηit is the random variables from the uniform random number generator on [0, 1], Att is the element at tth row and tth column of the lower triangular matrix A. Thus, a practical simulation estimator of θ can be obtained through Eq. (5) by maximizing the simulated log-likelihood function. The ConstrOptim procedure in R software was used as the optimization subroutine, and the Broyden–Fletcher–Goldfarb–Shanno (BFGS), which is an iterative method for solving unconstrained nonlinear optimization problems, has been used for the maximization. Compared to the 295

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Table 2 Summary statistics of investigated continuous variables. Variables

Brief description

Mean

Std. Dev.

Min.

Max.

Independent variables Fatal crashes Injury crashes PDO crashes

The natural logarithm of fatal crashes per year The natural logarithm of injury crashes per year The natural logarithm of PDO crashes per year

5.97 9.78 10.86

0.97 1.34 1.04

3.74 6.15 8.02

8.07 11.99 12.66

Explanatory variables Fines for aggressive driving Fines for holding a cellphone Fines for text messaging Fines for drunk driving Fines for not wearing helmet Fines for not wearing seat belt Fines for speeding Fines for a violation issued by a speed camera Fines for a violation issued by a red light camera

Fines Fines Fines Fines Fines Fines Fines Fines Fines

3.06 0.40 0.83 13.38 0.47 0.43 2.91 0.35 0.56

14.46 0.65 0.81 12.45 0.79 0.38 2.83 1.43 1.37

0 0 0 3.00 0 0.10 0.20 0 0

100.00 2.50 5.00 62.50 5.00 1.62 10.00 11.50 10.00

State population (Millions) The percentage of people 25 years and older who have completed an advanced degree (%) Employment/population ratio for the population ages 16–64 (%) Mean travel time to work of workers ages 16 and older who did not work at home (Minutes) Median Family Income (10,000 dollars)

6.27 10.44

6.95 2.56

0.56 6.30

38.80 18.00

68.13 23.75

4.56 3.50

59.00 16.10

79.00 32.60

6.39

1.01

4.55

8.97

Total licensed drivers (Millions) Annual vehicle miles traveled (Billions) The length of public road in states (Thousand Miles) < 60 (Thousand Miles) 60–220 (Thousand Miles) > 220 (Thousand Miles) The number of bridges in states (in Thousand) Bridges having structurally deficient (in Thousand) Bridges having functionally obsolete (in Thousand)

4.23 59.53 81.58 1.75 148.27 1.27 12.12 1.24 1.66

4.39 60.35 53.68 1.42 176.17 1.54 9.84 1.23 1.59

0.42 4.59 4.37 0.04 0.89 0.02 0.75 0.03 0.12

24.81 332.86 313.23 5.46 556.85 9.37 52.90 5.22 8.87

Control variables Socio-demographic factors Population Rate of advanced degree Rate of employment Average travel time to work Median family income Traffic factors Licensed drivers Annual vehicle miles traveled Public Road Length Road condition (Measured by IRI)

All bridges Structurally deficient Functionally obsolete

of of of of of of of of of

first first first first first first first first first

offense offense offense offense offense offense offense offense offense

(100 (100 (100 (100 (100 (100 (100 (100 (100

Dollars) Dollars) Dollars) Dollars) Dollars) Dollars) Dollars) Dollars) Dollars)

Fig. 1. Empirical distribution of dependent variables compared with normal distribution.

296

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(Alabama, California, Georgia, Illinois, Louisiana, Maryland, New Jersey, New Mexico, New York, North Carolina, Oregon, Tennessee, Washington) made progress in advancing key laws to encourage seat belt and motorcycle helmet use, curbing drunk driving, protecting young drivers, and requiring booster seats for young children. Seven states (Alaska, Arkansas, Montana, Rhode Island, South Dakota, West Virginia, and Wyoming) were noted to be dangerously lagging behind, with less than half of the 11 key highway safety laws enacted. The other 30 states have serious gaps in implementing recommended basic highway safety laws. The penalties for traffic violations, including fines, driving license suspensions, penalty points, mandatory participation in rehabilitation programs, and vehicles confiscation are considered and analyzed in the study. The variables of fines have been coded as continuous variables, since they have consistency measurements as dollars. Other penalty variables have been coded as dummy variables, since they are more complicated and difficult to interpret in continuous variable formats. The sociodemographic factors, including population, proportion of the population with advanced educational degree(s), rate of employment, average travel time to work, and median family income that might have potential significant effects on crash counts across severities were obtained from the Population Reference Bureau (PRB) and the United States Census Bureau. They are considered as control variables. Besides that, several other exposure related factors, including the number of licensed drivers, annual vehicle miles traveled, length of public roads, road condition, the number of bridges, and bridge condition were obtained from the Bureau of Transportation Statistics and the Federal Highway Administration. They are also considered as the control variables. The International Roughness Index (IRI), which measures the cumulative deviation from a smooth surface in inches per mile, is used to identify roadway pavement condition. Based on IRI, the public road length has been classified in three categories: 1) the length of public road with IRI < 60; 2) from 60 to 220; and 3) greater than 220. Bridge conditions are characterized by the number of structurally deficient and functionally obsolete bridges. Though road condition and bridge condition might have potential effects on traffic safety, few studies have analyzed them and so they are incorporated in our study. The aforementioned control variables have been considered as continuous variables. The sociodemographic data and fatal crash data can be obtained easily and the newest data are the data for the year 2015. Data related to highway safety laws are not easy to obtain; the newest data we can find for the 50 states are for the year 2014. For consistency, the newest data we used is from the year 2014. However, it is to be noted that several highway safety laws and regulations were enacted more recently. For example, Washington enacted the first law specifically banning all drivers from texting, effective January 1, 2008. After that, the text messing ban was implemented in several other states. In 2010, ten states still didn’t have such laws. We selected 2010 as the beginning year of the analysis time period because we want to include the laws that were enacted recently, such as the text messaging ban. The years of 2008 and 2009 were not chosen as the beginning years of study, because these years didn’t have enough observed samples for all the categories. The analyzed continuous and categorical independent variables and their summary descriptive statistics are shown in Tables 2 and 3, respectively.

Table 3 Summary statistics of investigated categorical variables. State highway safety laws

Variable

Frequency

Percent

Aggressive driving

State passed laws specifically defining aggressive driving actions Yes No

55 195

22 78

85 165

34 66

220 30

88 12

180 70

72 28

207 43

82.8 17.2

95 155

38 62

105 145

42 58

89 161

35.6 64.4

90 160

36 64

155 95

62 38

190 60

76 24

Special provisions for mature drivers Yes No

126 124

50.4 49.6

Seat belt use for all rear seat passengers Yes No

140 110

56 44

Highest speed limits higher than 70 mph Yes No

76 174

30.4 69.6

62 48 140

24.8 19.2 56

47 105 98

18.8 42 39.2

165 85

66 34

120 130

48 52

Distracted driving

Graduated driver licensing

Helmets

Impaired driving

Mature drivers

Seat belts

Speed limits

Hand-held cell phone ban (for all drivers) States have passed laws States have no laws Text Messaging Ban (for all drivers) States have passed laws States have no laws Learner stage Younger than 16-year-old 16-year-old Full privilege stage Younger than 18-year-old 18-year-old Motorcycle Helmets (Universal helmet law) Universal helmet law No law Bicycle helmets Have a law for bicyclists No laws Drugs (Zero tolerance) Having a law No law Marijuana drug-impaired Driving laws (Zero tolerance or non-zero per se laws for marijuana) Having a law No law Alcohol (Mandatory or highly incentivized ignition interlock law) Having a law No law Sobriety checkpoints Conducted Otherwise

Automated enforcement laws Speed cameras Prohibit the use Permit the use No law Red light cameras Prohibit the use Permit the use No law

5. Modeling results

Work zones

5.1. Comparison of model performances The comparison results of model fit are presented in Table 4. The results show that Model 1 provides superior statistical fit, with the smallest RSS value of 34.26, indicating that the posterior predictive distributions are proximity to the observed data. Model 3 has the greatest RSS value of 144.29, indicating that there are relative discrepancies between the posterior predictive distribution and the 297

Double the fine for committing traffic violations Yes Otherwise Workers to be present Yes No

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Table 4 Comparison of model performances. Model performances

Model 1

Model 2

Model 3

Goodness-of-fit RSS AIC SBC

34.26 865.58 1254.42

63.54 1035.19 1424.03

144.29 1141.83 1530.68

Property of prediction Fatal crashes MAE (crash counts) MAPE (%) VAPE (%)

0.147 2.398 0.023

0.196 3.327 0.047

0.288 4.852 0.074

Injury crashes MAE (crash counts) MAPE (%) VAPE (%)

0.245 2.546 0.022

0.404 4.154 0.029

0.454 4.815 0.099

PDO crashes MAE (crash counts) MAPE (%) VAPE (%)

0.256 2.386 0.018

0.348 3.223 0.039

0.555 5.136 0.076

Overall MAE (crash counts) MAPE (%) VAPE (%)

0.216 2.443 0.021

0.316 3.568 0.039

0.432 4.934 0.083

observed data. The performances of Model 2 are between Model 1 and Model 3, with a RSS of 63.54. The conclusions are also confirmed by the AIC and SBC statistics, which are 865.58 and 1254.42 for Model 1, 1,035.19 and 1,424.03 for Model 2, and 1141.83 and 1530.68 for Model 3, respectively. Model 1 has the smallest AIC and SBC statistics, indicating its superiority among the three models for the investigated dataset. The findings show that, compared to the MVST models, the MVDT models that can account for temporal correlation issues in crash count data provide a better goodness-of-fit. For the MVDT models, the ones with lagged observed dependent variables have better fit than the ones with unobserved random variables. In other words, considering the lagged dependent variables as the input variables can better address temporal correlation issues. The model performances are further assessed by the property of prediction. To obtain out-of-samples predictions, a five year dataset has been divided into two groups. One is a training set, which includes the data from the year 2010 to 2013. Another is a validating set, which is the observed data of the year 2014. The investigated models are fitted using the training set. The fitted models are used to predict the crash count in the validating set. The prediction results from Model 1 are compared with other investigated models for the fatal, injury, and PDO crash counts. Both the absolute and relative indices are used in this paper to assess the prediction accuracy and stability. The Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) are employed to assess the prediction accuracy, and the Variance of Absolute Percentage Error (VAPE) is employed to assess the prediction stability. The comparison results are summarized in Table 4. Table 4 suggests that Model 1 predicts better than the Models 2 and 3. Model 1 has the superior predication accuracy with overall MAE of 0.216 and MAPE of 2.443%. The MAE and MAPE for Model 2 and Model 3 are 0.316, 3.568%, 0.432, and 4.934%, respectively. We hypothesize that Model 1 better addresses the issue of temporal correlations and accounts for censoring in the dependent variables. Of importance, Model 1 provides superior prediction stability, with a VAPE of 0.021. The results show that MVDT models have better estimation property compared to the MVST, regardless prediction accuracy or stability. The results also indicate that the MVDT models with lagged observed variables have better prediction accuracy and stability, compared to the MVDT models with lagged unobserved variables. The findings confirm that MVDT model with lagged observed variables can better handle the stochasticity and dependency in the temporal

Fig. 2. Comparison between the observed crash counts and the predicted values.

evolution of the crash counts. Fig. 2(a)–(c) presents the predicted values versus observed values of three investigated models for fatal crashes, injury crashes, and PDO crashes, respectively. The results show that the predicted values from Model 1 are more close to the observed values compared to Models 2 and 3. Fig. 2 also indicates a tight fit of the Model 1 to the data. Since Model 1 provides the best goodness-of-fit in three models, the estimated results of Model 1 are discussed and interpreted in the following section. 5.2. Interpretations and discussions of results of Model 1 The estimated results of Model 1 are shown in Table 5. A total of 16 variables are included in Table 5, besides the intercept parameter. Among them, ten variables, including three highway safety law related factors [text messaging ban (for all drivers), learner stage (younger than 16 years old), full privilege stage (younger than 18 years old)], one penalty factor (fines for speeding), two sociodemographic factors 298

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Table 5 Fitting results of Model 1. Parameter

Intercept Hand-held cell phone ban (for all drivers) Text messaging ban (for all drivers) Learner stage (younger than 16 years old) Full privilege stage (younger than 18 years old) Motorcycle helmets (universal helmet law) Special provisions for mature drivers Highest speed limits higher than 70 mph Permitting the use of red light cameras Fines for drunk driving Fines for speeding Population Median family income Annual vehicle miles traveled Public road length of IRI > 220 Lagged observed variable yt-1 Lagged observed variable yt-2

Fatal crashes

Injury crashes

PDO crashes

Estimate

Std.Err

t Value

Pr > |t|

Estimate

Std.Err

t Value

Pr > |t|

Estimate

Std.Err

t Value

Pr > |t|

0.17

0.53

0.32

0.753

−0.24 0.31 0.18 −0.15

0.05 0.05 0.04 0.06

−4.48 6.24 4.56 −2.31

< 0.0001 < 0.0001 < 0.0001 0.022

0.56 −0.22 −0.20 0.17 0.11

0.54 0.03 0.03 0.02 0.02

1.04 −6.61 −7.24 7.00 5.57

0.298 < 0.0001 < 0.0001 < 0.0001 < .0001

0.42 −0.18 −0.21 0.30 0.20

1.42 0.03 0.06 0.06 0.07

0.30 −6.59 −3.44 5.01 2.98

0.765 < 0.0001 0.001 < 0.0001 0.003

< 0.0001 < 0.0001

0.002

< 0.0001

−6.37 5.30

−3.14

4.70

0.02 0.03

0.05

0.05

−0.11 0.14

−0.16

0.24

0.023 < 0.0001 < 0.0001 < 0.0001 < 0.0001 0.004 < 0.0001

−0.18 −0.10 0.14 −0.23 0.07 0.25 0.80 0.21

0.02 0.03 0.01 0.02 0.00 0.02 0.05 0.06

−7.28 −3.41 11.25 −13.17 13.48 14.78 14.82 3.66

< .0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001 < 0.0001

0.14 −0.14 −0.11 0.33 −0.40 0.13 0.56 0.34 0.27

0.04 0.02 0.02 0.03 0.05 0.02 0.04 0.12 0.06

3.37 −6.31 −5.67 10.14 −7.90 6.14 12.91 2.79 4.53

0.001 < .0001 < 0.0001 < 0.0001 < 0.0001 < .0001 < 0.0001 0.006 < 0.0001

−0.12 0.28 −0.44 0.13 0.50 0.42 0.23

0.05 0.02 0.03 0.01 0.03 0.15 0.05

−2.30 11.37 −12.68 14.76 15.19 2.89 5.20

have a three-stage GDL law, state lawmakers decide what age is the learner stage, intermediate stage, and full privilege driver license. The youngest age to get a learner driver license is 14 years old and the youngest age to get a full privilege driver license is 15.5 years old. Previous research shows that teenage drivers have an increased risk for being involved in traffic crashes compared with middle aged drivers. Our results show that the variables of learner stage (younger than 16 years old) and full privilege stage (younger than 18 years old) are significantly associated with the increases of fatal, injury, and PDO crashes. The findings confirm the research results of Ferguson et al (1996) and Williams (2009), which showed that the states with supervised driving by 16 years old are associated with lower crash rates compared to the states allowing unsupervised driving by 16 years old. According to our study, older licensing age and stronger graduated licensing provisions are a possible countermeasure for the high crash rates among young drivers. Five variables, including the hand-held cell phone ban (for all drivers), motorcycle helmets (universal helmet law), special provisions for mature drivers, highest speed limits higher than 70 mph, and permitting the use of red light cameras are found to have different effects on crash frequencies across severities. Enacted hand-held cell phone ban (for all drivers) and special provisions for mature drivers are found to have significant effects on reducing injury and PDO crashes. Compared to text messaging, talking on a hand-held cell phone while driving needs less visual, manual, and cognitive attention and has been considered as a secondary alarming distraction. Even so, talking on a handheld cell phone can delay reaction time and decrease awareness and could increase the crash risk. The variable of motorcycle helmets (universal helmet law) is found to be significantly associated with fatal crash reduction. NHTSA (2016) estimates that the number of deaths on motorcycles was over 30 times the number in cars for per mile traveled in 2011. Helmets are found about 67 percent effective in preventing brain injuries and 37 percent effective in preventing motorcycle deaths by Deutermann (2005). However, since the U.S. congress revoked federal authority to assess penalties for noncompliance universal motorcycle helmet laws in 1976, currently, only 19 states and the District of Columbia mandate helmet use by all riders. The remaining 31 states either require helmets for specific riders or do not have a motorcycle helmet law. Numerous states considered repealing existing all-rider helmet laws in 2004. However, the example of Louisiana has been an inspiration to stop the repealing, which experienced a 100 percent increase in motorcycle rider deaths since it repealed its law in 1999. The findings show that the all-rider motorcycle helmet laws are needed to reduce the injuries and deaths of

(population and median family income), two traffic factors (annual vehicle miles traveled and public road length with IRI > 220), and two legged observed variables are found to have significant effects on all crash types, regardless of injury severities. Three variables, hand-held cell phone ban (for all drivers), special provisions for mature drivers, and fines for drunk driving have significant effects on injury crashes and PDO crashes, but not significant for fatal crashes. One variable, highest speed limits higher than 70 mph has a significant effect on fatal crashes and injury crashes, but is not significant for PDO crashes. One variable, permitting the use of red light cameras, is found to have significant effects on only PDO crashes. And the variable of motorcycle helmets (universal helmet law) is only significant for fatal crashes. In summary, the estimated results in Table 5 show that 12 variables have significant effects on fatal crashes, including five highway safety law related factors, one penalty factor, two sociodemographic factors, two traffic factors, and two lagged observed variables. For injury crashes, 14 variables are significant, including six highway safety law related factors, two penalty factors, two sociodemographic factors, two traffic factors, and two lagged observed variables. The number of significant variables for the PDO crashes is the same as for the injury crashes. However, the variable of highest speed limits higher than 70 mph has significant effects on injury crashes, but is not significant for the PDO crashes. And the variable of permitting the use of red light cameras has significant effects on the PDO crashes, which is not significant for the injury crashes. The findings show that the control variables, including sociodemographic factors and traffic factors have consistent effects on crashes, regardless of the severity types. In other words, if a control variable is significant, it would have significant effects on fatal, injury, and PDO crashes and the direction of significant variable would be the same for these crash types. The highway safety law related variables, including enacted law status and penalty factors have different effects on crashes across severity types. Among eight variables of highway safety law status in Table 5, three have significant effects for fatal, injury, and PDO crashes. The results show that an enacted text messaging ban (for all drivers) has significant effects on reducing the frequencies of fatal, injury, and PDO crashes. The findings are consistent with the previous research (Dong et al., 2016a,b), which showed texting messages when driving can impair driver performances and increase crash risk. The findings indicate that primary text messaging laws might be an effective way to reduce the distraction-affected crashes. Graduated driver licensing (GDL) laws have been used to reduce crash risk of teenage drivers by making sure they gradually build up driving experiences under lower-risk conditions. Though all 50 states 299

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reductions. The variable of fines for speeding is found to have significant effects on reducing the frequencies of fatal, injury, and PDO crashes. Speeding is one of the most critical factors contributing to traffic crashes and deaths in the United States. The findings show that speeding fines would be effective for restricting driver behaviors, and hence, reducing crash frequencies and improving traffic safety. Among the control variables, population, annual vehicle miles traveled, and public road length of IRI > 220 are found to be significantly associated with the increase of crash frequencies regardless of crash types. The variable of median family income is significantly associated with crash reduction. The population, median family income, and annual vehicle miles traveled have been used as the control variables in numerous studies. The results are consistent with previous research. Public road length, road conditions, the number of bridges, and the bridge conditions that are examined in this study, have been rarely used before. In our study, only road condition factor, public road length of IRI > 220 is found to have significant effects on crashes. The results are expected. Road condition affects vehicle operation. The road friction will reduce as the IRI increase, which affects the stopping ability and maneuverability of vehicles. Poor road surfaces and unexpected changes in the pavement condition, such as potholes or very rough pavement, can lead to crashes. Two lagged observed variables are found to have significant effects for crash frequencies. Compared to the observed variable yt-2, yt-1 has stronger impacts on crash frequency prediction, regardless of crash types. In other words, yt-1 has closer relationship with crash counts in the year of yt, which also confirms the temporal correlation between the observed crash counts. In further studies, we would like to include more observed variables in the model as the input and investigate their significates for the prediction. To provide some insights into the implications of the estimation results, the elasticities are calculated. For a continuously measured attribute, the elasticities provide the change in the percent of crashes given a one percent change in any explanatory variables. For a categorical variable, a pseudo-elasticity can be calculated to estimate an approximate elasticity of the investigated variable. More relevant information can be found in Dong et al. (2016c). The average elasticities calculated for the fatal crashes, injury crashes, and PDO crashes are shown in Table 6. The elasticity provides a good indication of the relative importance of variables. For example, if a state enacted a text messaging ban, the fatal crashes, injury crashes, and PDO crashes would be reduced by 27.00%, 21.62%, and 23.37% respectively. A one percent increase in population causes 0.77%, 0.91%, and 2.09% increases in fatal crashes, injury crashes, and PDO crashes, respectively. More detailed information can be found in the revised manuscript.

Table 6 Elasticity Estimates for the Model 1. Variable

Elasticity Fatal crashes

Hand-held cell phone ban (for all drivers) Text messaging ban (for all drivers) Learner stage (younger than 16 years old) Full privilege stage (younger than 18 years old) Motorcycle helmets (universal helmet law) Special provisions for mature drivers Highest speed limits higher than 70 mph Permitting the use of red light cameras Fines for drunk driving Fines for speeding Population Median family income Annual vehicle miles traveled Public road length of IRI > 220

Injury crashes

PDO crashes

−24.44

−19.48

−27.00 26.54

−21.62 15.90

−23.37 26.18

16.55

10.85

18.13

−11.97

−17.35

−15.63

21.35

13.23 13.06

−13.28 1.77 −2.80 7.99 0.63

−19.82 −10.40 0.91 −1.46 3.98 0.32

−14.90 −11.18 2.09 −2.54 7.97 0.71

motorcycle crashes. For those states that repealed the all-rider helmet laws, the reinstating is recommended. Since elder drivers have a higher crash risk than middle aged drivers, many states have enacted laws that contain specific licensing requirements for elder drivers. There are two aspects of license renewal that vary significantly: the length of time between renewals and the additional requirements that impose on elder drivers. The requirements include renewing in person rather than electronically and testing (vision and/or road tests) that is not routinely required by other drivers. Such additional requirements exist in 33 states. The results show that the variable of special provisions for mature drivers is significantly associated with the reduction of injury and PDO crashes. The majority of elder drivers drive safely because they have a lot of experience. However, the driving ability of the elder drivers often is declined. Stricter state laws for the renewal of elder drivers’ licenses, which evaluate the driver’s vision, hearing, and other abilities, as well as certain health conditions and medications, might contribute to the frequency reduction of elder drivers involved crashes. The highest speed limits that are higher than 70 mph are significantly associated with the increase of fatal and injury crashes. The findings indicate that with higher posted speed limits, especially higher than 70 mph, the most severe injuries could occur in traffic crashes where the vehicles are probably driven over the speed limit. The findings related to the use of red light cameras are expected, which indicate that the states that allow the use of red light cameras are associated with higher PDO crashes. Though the use of red light cameras might have positive effects on traffic safety, especially on reducing the occurrences of fatal crashes, the findings show that the use of red light cameras can increase the frequencies of PDO crashes. The findings are consistent with several studies (Llau et al., 2015; Hallmark et al., 2010; Shin and Washington, 2007), which showed the implementation of red-light cameras increase the number of rear-end collisions. To prevent red-light running and promote the implementation of red-light cameras, the red light camera system should be installed cautiously on selected sites based on accurate crash and red-light violation data. In addition, appropriate and sufficient warning signs, which warn the drivers that the red light cameras are used, should be posted as part of driver awareness and education. Regarding the variables of penalty factors, fines for drunk driving are found to be significantly associated with injury and PDO crash

6. Conclusions State highway safety laws are enacted to improve driving behaviors, drivers’ attitudes, and reduce traffic crashes. By analyzing and understanding the performances of these key highway safety laws, the results reveal new insights that could influence policy making and more lives could be saved. In this study, the MVDT models are proposed to assess the effectiveness of highway safety laws on crash-reducing. The estimated results show that, compared to the MVST models and MVDT models with lagged random variables, the MVDT models with lagged observed variables provide superior goodness-of-fit. The predictions from MVDT models with lagged observed variables are closer to the observed values and can capture the changing trend of the observed values, since the lagged observed variables can better account for the temporal correlation issues in crash counts. The modeling results show that: 1 Four state highway safety law related factors, text messaging ban (for all drivers), learner stage (younger than 16 years old), full privilege stage (younger than 18 years old), and fines for speeding 300

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are found to have consistent significant effects on crash counts across severities. The variables of the text messaging ban (for all drivers) and fines for speeding have significant effects on reducing crash frequencies for fatal, injury, and PDO crashes. The other two variables are significantly associated with the increase of crash frequencies regardless of crash types. 2 Six state highway safety law related factors, hand-held cell phone ban (for all drivers), motorcycle helmets (universal helmet law), special provisions for mature drivers, highest speed limits higher than 70 mph, permitting the use of red light cameras, and fines for drunk driving are found to have different effects on crash counts across severities. The variables of hand-held cell phone ban (for all drivers), special provisions for mature drivers, and fines for drunk driving are found to have significant effects on reducing injury and PDO crashes. The variable of highest speed limits higher than 70 mph is found to be significantly associated with the increase of fatal and injury crashes. The variable of motorcycle helmets (universal helmet law) is found to have significant effects on reducing fatal crashes and the variables of permitting the use of red light cameras is found to be significantly associated with the increasing of PDO crashes. 3 All the significant control variables have consistent effects on crash counts across severities. The variable of median family income is found to be significantly associated with crash reduction for fatal, injury, and PDO crashes. The variables of population, annual vehicle miles traveled, and public road length of IRI > 220 are found to associate with the increase of crash frequencies regardless of crash types. 4 Two lagged observed variables are found to have significant effects on crash count prediction. The findings show that the more adjacent observed variable has stronger impacts on crash count prediction.

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Limited by the dataset, only two lagged observed variables are examined in the proposed models. In further studies, more observed variables should be included in the models and their significance for the prediction should be investigated. We would like to do a comparative and comprehensive study using the proposed MVDT model to analyze the crash counts at state level and roadway segment level, respectively. We are also interested in incorporating Kalman filter methods in the proposed models to improve the model performances. In addition, we would like to incorporate the factors related to the citation characteristics, such as the citation rates of speeding into the study Acknowledgements The authors gratefully acknowledge funding provided by the Southeastern Transportation Center, a Regional UTC funded by the USDOT, Office of the Assistant Secretary for Research and Technology through agreement number DTRT13-G-UTC34. Additional funding was provided by the Natural Science Foundation of China (Grant No. 71401012). References Advocates for Highway & Auto Safety, 2016. 13th Annual Roadmap of State Highway Safety Laws. http://saferoads.org/roadmaps/. Anastasopoulos, P.Ch., Shankar, V.N., Haddock, J.E., Mannering, F.L., 2012. A multivariate Tobit analysis of highway accident-injury-severity rates. Accid. Anal. Prev. 45, 110–119. Arbogast, K.B., Durbin, D.R., Cornejo, R.A., Kallan, M.J., Winston, F.K., 2004. An evaluation of the effectiveness of forward facing child restraint systems. Accid. Anal. Prev. 36 (4), 585–589. Atchley, P., Atwood, S., Boulton, A., 2011. The choice to text and drive in younger drivers: behavior may shape attitude. Accid. Anal. Prev. 43 (1), 134–142. Branas, C.C., Knudson, M.M., 2001. Helmet laws and motorcycle rider death rates. Accid. Anal. Prev. 33 (5), 641–648. Brown, C.V.R., Hejl, K., Bui, E., Tips, G., Coopwood, B., 2009. Risk factors for riding and crashing a motorcycle unhelmeted. J. Emerg. Med. 41 (4), 441–446. Chang, S., 2011. Simulation estimation of two-tiered dynamic panel Tobit models with an

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