Approach. A thesis presented to. the faculty of. In partial fulfillment. of the requirements for the degree. Master of Science.

Transcription

1 Road Safety Assessment of U.S. States: A Joint Frontier and Neural Network Modeling Approach A thesis presented to the faculty of the Russ College of Engineering and Technology of Ohio University In partial fulfillment of the requirements for the degree Master of Science Gokhan Egilmez August Gokhan Egilmez. All Rights Reserved.

2 2 This thesis titled Road Safety Assessment of U.S. States: A Joint Frontier and Neural Network Modeling Approach by GOKHAN EGILMEZ has been approved for the Department of Civil Engineering and the Russ College of Engineering and Technology by Deborah S. McAvoy Associate Professor of Civil Engineering Dennis Irwin Dean, Russ College of Engineering and Technology

3 3 ABSTRACT 1 EGILMEZ, GOKHAN, M.S., August 2013, Civil Engineering Road Safety Assessment of U.S. States: A Joint Frontier and Neural Network Modeling Approach. Director of Thesis: Deborah S. McAvoy In this thesis, road safety assessment and prediction modeling for U.S. states fatal crashes are addressed. In the first part, a DEA-based Malmquist Index model was developed to assess the relative efficiency and productivity of U.S. states in decreasing the number of road fatalities. Even though the national trend in fatal crashes has reached to the lowest level since 1949 (Traffic Safety Annual Assessment Highlights, 2010), a state-by-state analysis and comparison has not been studied considering other characteristics of the holistic national road safety assessment problem in any work in the literature or organizational reports. The single output, fatal crashes, and five inputs were aggregated into single road safety score and utilized in the DEA-based Malmquist Index mathematical model. The period of was considered due to data availability for the inputs and the output considered. According to the results, there is a slight negative productivity (an average of -0.2 percent productivity) observed in the U.S. on minimizing the number of fatal crashes along with an average of 2.1 percent efficiency decline and 1.8 percent technological improvement. The productivity in reducing the fatal crashes can only be attributed to the technological growth since there is a negative efficiency growth is occurred. It can be concluded that even though there is a declining trend observed in 1 This chapter contains adapted writing directly from following publication: Egilmez, G., & McAvoy, D. (2013). Benchmarking road safety of U.S. states: A DEA-based Malmquist productivity index approach. Accident Analysis and Prevention, 53(1), doi: /j.aap

4 4 the fatality rates, the efficiency of states in utilizing societal and economical resources towards the goal of zero fatality is not still efficient. In the second part, a nonparametric prediction model, Artificial Neural Network, was developed to assist policy makers in minimizing fatal crashes across the United States. Seven input variables from four safety performance input domains while fatal crashes was utilized as the single output variable for the scope of the research. Artificial Neural Networks (ANN) was utilized and the best neural network model was developed out of 1000 networks. The proposed neural network model predicted data with 84 percent coefficient of determination. In addition, developed ANN model was benchmarked with a multiple linear regression model and outperformed in all performance metrics including r, R 2 and the standard error of estimate. A sensitivity analysis was also conducted and the results indicated that road length, vehicle miles traveled, and safety expenditures were the top three input variables on fatal crashes. In conclusion, more effective policy making towards increasing safety belt usage and better utilization of safety expenditures to improve road condition are derived as the key areas to focus on for state highway safety agencies from the scope of current research. This research also reveals the significance of the relationship between the four input domains and fatal crashes for the United States from a holistic perspective and offers a robust nonparametric model to policy makers for the prediction of fatal crashes.

5 5 ACKNOWLEDGEMENTS Firstly, I am thankful to Allah (God) for reaching this goal and realizing this thesis with a believing heart. Next, I would like to express my deepest and sincere gratitude to my dear adviser Dr. Deb McAvoy for her support in starting a master education in transportation engineering during my final year of PhD, for her advisory and trust, and providing me the flexibility while making this thesis real. I was so fortunate to work on a topic of my interest with her and publish a research article, entitled Benchmarking road safety of U.S. states: A DEA-based Malmquist productivity index approach in the journal of Accident Analysis and Prevention prior to my graduation. In this regard, I wish her the best of luck in her new position at Ohio University. I would also like to take this opportunity to thank my committee members for their contribution. Last but not least, I also would like to thank my dad, Mr. Muammer Egilmez, my mom, Ms. Munevver Egilmez and my sister Mrs. Umran Egilmez for their prayers, support and encouragement thru good and bad days.

6 6 DEDICATION to Cimcime...

7 7 Table of Contents Page Abstract... 3 Acknowledgements... 5 Dedication... 6 List of Tables... 9 List of Figures Introduction Research Objectives and Organization Comparative Road Safety Assessment of U.S. States Introduction Data Envelopment Analysis (DEA), Productivity and Malmquist Index Research Aims Data Identification of Safety Performance Indicators Data Collection Data Preparation and Normalization Methodology DEA Model... 31

8 Malmquist Index Formulation Results Non-Parametric Predictive Modeling for U.S. States Fatal Crashes Introduction Artificial Neural Networks (ANN) Justification and the Organization of Research Data Predicting Road Fatalities with Multiple Linear Regression (C) The Proposed Prediction Approach: Artificial Neural Networks (ANN) Benchmarking ANN with MLR Sensitivity Analysis Conclusions and Future Work References Appendix: Data Used... 71

9 9 LIST OF TABLES Table 1: Descriptive Statistics Table 2: Road Condition Score Calculation Example Table 3: Correlation Analysis of SPI-2 Domain Input Variables Table 4: Summary of Data Preparation Table 5: Results of Experimentation Table 6: The Overall Analysis Table 7: Normality Tests Table 8: Summary of MLR Model Table 9: Coefficients of the Best MLR Model (Model 4) Table 10: Results of Experimentation (Top 5 out of NNs) Table 11: Connections and Weights of the Best Neural Network Table 12: Connections and Weights of the Best Neural Network Cont d Table 13: The overall comparison of ANN vs. MLR... 59

10 10 LIST OF FIGURES Figure 1. US Road Fatality Trend ( ) Figure 2. Research Aims and Organization Figure 3. Summary of Selected SPIs and Outputs Figure 4. Average Road Safety Efficiency Growth of U.S. States ( ) Figure 5. Trend Analysis Figure 6. Sensitivity Analysis Figure 7. A Simple Neural Network Figure 8. The Architecture of the Best Performing ANN Model Figure 9. Predicted vs. Actual Fatal Crashes for Test, Train and Validation Data Figure 10. Predicted vs. Actual Fatal Crashes for Test, Train and Validation Data Figure 11. Predicted vs. Actual Values of ANN (Test Data) Figure 12. Results of Sensitivity Analysis... 61

11 11 1. INTRODUCTION 2 In the United States, federal and state governments utilize individual policydriven procedures and strategies to reduce crash frequency and societal cost. However, the number of crashes has not fallen below 30,000 in the last 50 years, even though a substantial effort toward improving highway safety through the reduction of transportation-related fatalities has been undertaken by agencies and government organizations. The vast majority of the funding is available through the authorization of the federal surface transportation program; currently SAFETEA-LU (the Safe, Accountable, Flexible and Efficient Transportation Equity Act: A Legacy for Users). In return, State Highway Safety Offices administer a variety of highway safety grant programs designated in the federal transportation authorization. An example of the programs and the federal funding available includes, but is not limited to, the following: State Highway Safety Grant Programs, $234.8 million; Occupant Protection Incentive, $25 million; Child Safety and Child Booster Seat Incentive, $7 million. As a result, considerable amount of resources is being utilized to improve the safety of commuters. However, it is important to compare U.S. states road safety performance considering the recent trends and develop decision support tools to envision the future trend. 2 This chapter contains adapted writing directly from following publication: Egilmez, G., & McAvoy, D. (2013). Benchmarking road safety of U.S. states: A DEA-based Malmquist productivity index approach. Accident; analysis and prevention, 53(1), doi: /j.aap

12 12 2. RESEARCH OBJECTIVES AND ORGANIZATION 3 Even though significant amount of effort, time and money is being invested in the United States, we still lose at least 30,000 people to road crashes annually (See Figure 1). Since, each state has its own organizational structure, it is important to compare road safety performance state-by-state to have an overall understanding about the road safety performance in the United States. On the other hand, a holistic predictive modeling approach can also offer vital guidance to stakeholders to visualize the fatal crash trend in the mid and long run quantitatively. Therefore, this research is intended to first compare state by state road safety performance assessment between 2002 and 2008 then implement a nonparametric predictive modeling approach as a decision support tool for practitioners use. Figure 1. US Road Fatality Trend ( ) 3 This chapter contains adapted writing directly from following publication: Egilmez, G., & McAvoy, D. (2013). Benchmarking road safety of U.S. states: A DEA-based Malmquist productivity index approach. Accident Analysis and Prevention, 53(1), doi: /j.aap

13 13 The hierarchical structure of the research aims are illustrated in Figure 2. In benchmarking phase, safety performance indicators that affect the fatal crash trend are identified. Next, the proposed methodology (Data Envelopment Analysis) is utilized to analyze the annual road safety performance. In the final part of the benchmarking phase, sensitivity of safety performance indicators are analyzed (See Figure 2). In the second phase, predictive modeling approaches are aimed to utilize to collected data. Both parametric (Multiple Linear Regression) and nonparametric (Artificial Neural Networks) models are aimed to be utilized, validated and compared to identify the best model. The second phase is finished with sensitivity analysis of safety performance indicators. Benchmarking Identifying road safety performance indicators Benchmarking U.S. states road safety Sensitivity analysis of safety performance indicators Predictive Modeling Parametric predictive modeling Nonparametric predictive modeling Validation and comparison Sensitivity analysis Figure 2. Research Aims and Organization

14 14 The next two chapters present the benchmarking and predictive modeling phases of this thesis, respectively. The organization of thesis is planned as two distinct sections since each decision support approach provide different insight about the problem studied. Therefore, in each section, a detailed introduction, literature review, problem statement, method and results sub-sections are provided separately to enhance the overall understanding about the benchmarking and predictive modeling phases. In fact, benchmarking phase evaluates the road safety performance of U.S. states by comparing each state with the remaining states over a time period. Then, a holistic predictive modeling approach is coupled to provide more insight about the forecasting fatal crashes.

15 15 3. COMPARATIVE ROAD SAFETY ASSESSMENT OF U.S. STATES Introduction Contributing to the significant number of crashes are rising travel demand, annual vehicle miles of travel, inexperienced or young drivers along the road network and older drivers with slower reaction times. Several methods have been employed to assess highway safety and assist policy makers in their decision making processes. Data Envelopment Analysis (DEA) is one of the methods that has recently been used to analyze highway safety efficiency (Elke Hermans, Van den Bossche, & Wets, 2008). DEA is a very robust tool which compares similar elements based upon various input(s) and produces a desired output(s). The robustness of DEA comes from its wide applicability to various problems. DEA has been widely applied to several problems from various fields such as economics (Zhang, Bi, Fan, Yuan, & Ge, 2008), (Filippetti & Peyrache, 2011), sustainability (Lee & Farzipoor Saen, 2012), finance (Kirikal & Tehnikaülikool, 2005), healthcare (Feng & Yuan-Biao, 2010), construction (Xue, Shen, Wang, & Lu, 2008), transportation (Ozbek, Garza, & Triantis, 2009) (Cooper, Seiford, & Zhu, 2011), etc. With regard to highway safety, Odeck (2001) analyzed the efficiency of the Norwegian road network using two competing methods: a data envelopment analysis and a deterministic frontier analysis. In another study, the efficiency of targeted operational achievements of the Norwegian Public Roads Administration was investigated with DEA and Malmquist Indices (Odeck, 2006). A bootstrapping method was also utilized to 4 This chapter contains adapted writing directly from following publication: Egilmez, G., & McAvoy, D. (2013). Benchmarking road safety of U.S. states: A DEA-based Malmquist productivity index approach. Accident Analysis and Prevention, 53(1), doi: /j.aap

16 16 determine confidence intervals for efficiency scores and test hypotheses regarding productivity growth. To provide a better indication of highway safety in different regions or countries, a comparison was made with respect to safety performance indicators (SPIs). The properties of SPIs were studied in terms of their relationship to the outcome of highway crash fatalities (Tingvall et al., 2010). The assumption of linearity between SPIs and a final outcome was partly rejected in these studies. In addition, the availability of data largely limited the scope of the comparison. While evaluating highway safety, there are several indicators, including, but not limited to, infrastructure characteristics, vehicle miles traveled, alcohol involvement and safety belt usage, which need to be considered. To enable an overall comparison of different countries or regions, a single highway safety index is required (Elke Hermans, Brijs, Wets, & Vanhoof, 2009). To be able to have single highway safety index, the creation of a combination of relevant highway safety indicators is then required. Prior to defining the index variable, a weighting strategy must be employed to appropriately reflect the relative importance of such safety indicators. Even though several studies have been conducted, there is neither a widely-accepted nor a reasonable method for the assignment of weights (Tatari & Kurmapu, 2011). For these reasons, the DEA methodology provides an acceptable alternative solution for highway safety efficiency determination. DEA provides a theoretical framework, does not require a weighting procedure, and rates the highest among five multi-criteria evaluation methods (Elke Hermans et al., 2008). In a latter work, Hermans et al. (2009) compared roadway safety of 25 European countries (Elke Hermans et al., 2009). Several SPIs were considered

17 17 such as alcohol and drug use, vehicle protective systems, vehicle characteristics, infrastructure quality, and trauma management. The comparison was completed by using a non-bias weighting procedure incorporated into a linear programming optimizationbased efficiency analysis model, so called single-period output-oriented DEA. Even though, road safety performance assessment is a crucial concept and significant research has been conducted for European countries from a holistic perspective, to the best knowledge of authors U.S. states road safety assessment has not been addressed in literature. The overarching goal of this study is to develop an analytical tool that can be used to analyze and compare the road safety performance of the U.S. states. To assess and benchmark U.S. states road safety, a well-known linear programming-based method, Data Envelopment Analysis (DEA), is utilized Data Envelopment Analysis (DEA), Productivity and Malmquist Index Data envelopment analysis is a linear programming and production theory-based mathematical approach developed by Charnes Cooper and Rhodes (CCR) in 1978 (Charnes, Cooper, & Rhodes, 1978). In a typical DEA model, the objective is to compare similar element types based on predetermined inputs and outputs. Charnes et al. explained that the comparison should be made based on decision making efficiency. Therefore, a decision making unit (DMU) is considered the element subject to comparison. Schools, manufacturing plants, countries, hospitals, states can be identified as some examples of DMUs. DEA aims to measure how efficiently selected DMUs generate the selected outputs by using selected inputs as the scope of comparison. According to Ramanathan s definition, the efficiency or performance of a DMU is the

18 18 ratio of total outputs to total inputs, which was inspired from the productivity equation (Ramanathan, 2003). While the productivity for a profit organization can easily be calculated by looking at profit and market share, it might be difficult to calculate the productivity of non-profit organizations which have different inputs and outputs with varying scales. In this case, DEA provides the flexibility to model such productivity and provide an evaluation for any type of organization. The motivation behind DEA is to assess the efficiency from either an output maximization or input minimization point of views by using linear programming based optimization. The main advantage of DEA is that it does not require any subjective weighting procedure while benchmarking similar units and an overall performance score for a DMU can be derived as efficiency, a measure of how well the inputs are utilized towards producing the outputs for the preliminary defined scope (Egilmez, Kucukvar, & Tatari, 2013). In this regard, DEA enables to define a single road safety performance score which has been successfully utilized in various works including Hermans et al. (2008). In a perfect world, all DMUs can be 100 percent efficient if they all provide a similar level of productivity; however, in reality inefficiency exists allowing DEA to be utilized as a robust efficiency evaluation and a target projection tool. The DMUs with 100 percent efficiency are interpreted as the most productive and potentially the benchmark for other DMUs. In addition, the inefficiency of the other DMUs is relative to the 100 percent efficient DMU(s). In a simple problem such as single or double-input and single-output, productivity can be evaluated by calculation and graphical frontier evaluation methods. However, in reality, most of the DMUs have multiple inputs and

19 19 outputs. To deal with such cases, the mathematical model version of DEA (developed by CCR after 20 years when Farrel (1957) first introduced the concept) has been used in the majority of the literature (Farrell, 1957). Following is the general output maximization form of the CCR DEA model; Indices and parameters: i: Inputs (i=1 I) j: Outputs (j=1 J) m: Decision making units (DMUs) x im : i th input of m th DMU (n =1..m,..N) u im : Weight of i th input of m th DMU y jm : j th output of m th DMU (n =1...m,..N) v jm : Weight of j th output of m th DMU x im : i th input of n th DMU (n =1..n,..N) y jm : J th output of n th DMU(n =1..n,..N) ε: The minimum desired weight Objective function: Subject to:

20 20 The objective is to maximize the total weighted output (Equation 1). Equation 2 guarantees that the total weighted sum of inputs does not exceed 1. Equation 3 guarantees that the relative efficiency of a DMU falls between 0 and 1. The variables and indices are represented in Equation 4. Ramanathan (2003) provides a comprehensive explanation of CRR models. The term productivity is generally used as a metric to evaluate a company s performance over a period. It is also defined as the ratio of the generated outputs to the inputs used. The evaluation can be named depending on the type of output used (e.g. productivity of capital, investment). Since it is a relative concept (Kirikal & Tehnikaülikool, 2005), DEA is used as a comparison tool. Even though the general usage of productivity is a component of the monitoring, analysis and supervision of a company s performance, it is also applicable to any DEA problem studied, due to the similarity associated with the usage of a relative efficiency concept. In any profit or non-profit organization, the productivity of the overall system or certain sub-system is constantly evaluated for improvement. As such, companies and government organizations invest millions of dollars to increase their productivity in order to realize objectives, such as maximizing economic growth, profitability and competitiveness, or minimizing costs.

21 21 When measuring productivity, there are two perspectives usually considered; the level of productivity at a time and the trend in the productivity throughout a period (Kirikal & Tehnikaülikool, 2005). While the productivity ratio is used to determine the level of productivity, productivity indices are generally preferred to evaluate the trend. Sten Malmquist (1953) introduced a quantity index for use in a consumption analysis. Later, Caves, Christensen and Diewert (1982) applied Malmquist s approach to a production analysis (Caves, Christensen, & Diewert, 1982) and provided the Malmquist Productivity Index (MI) as shown in Equation 5. The productivity index is calculated by taking the technology in period t as the reference technology. In this case, the Malmquist Productivity Index is a very robust tool since it requires neither cost information for the input(s) and output(s) nor a definite objective such as profit maximization or cost minimization (Kirikal & Tehnikaülikool, 2005). Fare et al. (1992) decomposed Caves et al. s (1982) Malmquist productivity index into two mutually exclusive and exhaustive components: changes in productivity over time (as shown in Equation 6) and shifts in technology over time (as shown in Equation 7) along with a case study regarding the analysis of productivity growth for a sample of Swedish pharmacies (R. Fare, Grosskopf, Lindgren, & Roos, 1992). The productivity index is defined as the geometric mean of the two Malmquist Productivity Indices as shown in Equation 8, where x indicates the input(s), y indicates the output(s) and t is the time index.

22 22 According to the Equation 8, D represents the distance function which characterizes the production technology based on normalized data (Shephad, 1970). A DMU is assumed to be technically efficient if the distance function equals one. MI represents the Malmquist Productivity Index between time periods t and (t+1). A value of MI greater than 1 denotes productivity growth while a value of less than 1 represents productivity decline. An MI equal to 1 indicates no change in productivity over the period. The model described in the Equations 6, 7 and 8 is based on Constant Returns to Scale (CRS) and known as FLGR (Fare, Grosskopf, Lindgren and Roos). In this case, returns to scale means an increasing, constant or decreasing efficiency based on the size of DMU. CRS assumes that an output will change by the same proportion as the inputs are changed (e.g. doubling of all inputs will double the output). Since this assumption does not reflect the actual case in all situations, Fare et al. (1994) proposed the DEA Malmquist Index model with Variable Returns to Scale (VRS), which is also known as FGNZ&FLGR model (Rolf Fare, Grosskopf, Norris, & Zhang, 1994). VRS considers both increases and decreases in production technology over time which links it to the

23 23 efficiency evaluation. VRS is a more comprehensive and robust approach in comparison to CRS. In the FGNZ&FLGR model, the efficiency change includes two entities known as Pure Efficiency Change (PEC) and Scale Efficiency Change (SEC). The new index model is then introduced as follows: According to Equation 9, C denotes the output distance function for CRS and V is the output distance function for VRS. As shown in Equation 9, the FGNZ&FLGR model consists of three components. The first expression evaluates the PEC, the second component measures the SEC and the third expression measures the technical change (TC). The PEC and SEC components are decompositions of efficiency change. PEC (Pure Efficiency Change) is the efficiency change under variable returns to scale (VRS). The summary of the new index model is shown in Equation Research Aims Traffic fatalities have been a major concern for both federal and state governments represented by several reports published by both government and private organizations. The number of traffic fatalities in the nation has reached to its lowest level since 1949 (Traffic Safety Annual Assessment Highlights, 2010) as shown in Figure 1. Even though this declining trend can be interpreted as a positive sign toward highway safety and in support of recent efforts, there are other characteristics of the highway safety problem that are not considered in the fatality analysis making it difficult to

24 24 interpret the low fatality rate as a success for the nation, whose most recent goal is zero fatalities. While the United States is a federally governed country, each state s transportation department and other supporting organizations have their own organizational strategies and action plans to mitigate the frequency of road fatalities, in addition to the national legislation mandates. In this case, examining the safety problem from systematic perspective (nationwide) may provide significant insights on focusing the state organizations efforts towards the national goal. It is also important to consider the highway safety problem and pattern of behavior related to road fatalities at the state level. The majority of the safety reports published by government organizations consider fatality trends and related driving characteristics trends such as vehicle miles of travel (VMT), and the number of drivers while analyzing the trend. Generally, 1-to-1 relationships between characteristics are analyzed and interpreted. However, there is a dire need to analyze the overall problem simultaneously considering roadway fatalities as well as other characteristics, such as those listed above. Most of the fatality predictor variables are interconnected; however, their level of impact in regards to highway fatalities may not consistent across all states in the nation. This research aims to address the efficiency and productivity impacts of individual states on highway fatalities Data Identification of Safety Performance Indicators According to the European Transportation Safety Council s definition, a Safety Performance Indicator (SPI) is a measurement that is causally related to accidents or

25 25 injuries, used in addition to a count of accidents or injuries in order to indicate a safety performance or understand the process that leads to accidents. In a recent work, Hermans et al. (2009) considered alcohol and drugs, speed, protective systems, vehicle, infrastructure and trauma management as SPIs and studied their relation with the crashes and fatalities as outcomes. In this regard, the data related to several risk domains is available for a country-based comparison (especially for the European Union countries) and provided in well-know databases such as EuroStat. In this study, the same risk domains used in the Hermans et al. s work (2009) were intended to be used as the scope of benchmarking and road safety performance assessment of the U.S. states depending on the data availability. Therefore, four main subject areas were considered as the main SPI domains; 1) the economic investment on system, 2) the usage of the system, 3) the condition of system and 4) personal safety in the system. Economic investment and personal safety was expected to have a decreasing impact on the total number of fatalities. It was expected that the usage of the system would have an increasing impact on the likelihood of a fatality; higher volumes along a roadway increase the crash probability and risk. The condition of system could have increasing or decreasing impact on the fatalities. Moreover, additional sub-indicators were considered as the predictors of the main SPI domains, as follows; 1. The economic investment on system Highway safety expenditures (HSE) 2. The usage of system Registered vehicles (RV)

26 26 Licenced drivers (LD) Vehicle-miles traveled (VMT) 3. The condition of system Total road length (RL) Overall road condition (RC) 4. The personal safety in system Safety belt usage In this study, the number of fatalities was considered as the only outcome due to the severe societal consequences associated with highway fatalities. The summary of the SPIs and outputs is illustrated in Figure 3. SPI-1: The economic investment on system Highway Safety Expenditures SPI-2: The usage of system # Vehicles # Drivers VMT SPI-3: The condition of system Total road length Overall road condition SPI-4: The personal safety in system Safety belt usage rate The number of fatal crashes Figure 3. Summary of selected SPIs and outputs

27 Data Collection The Research and Innovative Technology Administration (RITA) Bureau of Transportation Statistics online database was used to collect data for the input data of 50 states for the period between 2002 and 2008 (RITA, 2010). The District of Columbia was not included due to the lack of data for some of the years considered in the analysis. RITA s database was selected as it provided the most comprehensive and readily available state-based dataset. On the other hand, fatal crash data is obtained from Fatality Analysis Reporting System (FARS) database of the National Highway Traffic Safety Administration (NHTSA). The study period was selected as from 2002 to 2008 based upon the largest period of data that represented all inputs and outputs. The data availability and descriptive statistics of the inputs and outputs are provided in Table 1. Table 1: Descriptive Statistics Variable N Minimum Maximum Mean Std. Deviation Period HS Expenditures ($M) ,425 24,020,000 2,946,510 4,001, Registered Vehicles Licenced Drivers Vehicle-Miles Traveled (VMT) Total Road Length (Miles) 350 4, ,404 79, , Road Condition Safety Belt Usage (%) Fatal Crashes

28 Data Preparation and Normalization Prior to efficiency assessment, the collected input and output data are prepared to be used in the experimentation. In this regard, road condition, fatality rate and VMT, registered vehicles and licensed drivers data are transformed to be used in the experimentation. Firstly, road condition data were transformed from categorical to numerical form. Since the road condition data were originally in categorical form which is based on a scale from very good to poor. In this regard, the transformation was applied to obtain an overall road condition index, based upon a Likert-scale dataset provided by RITA for road condition; very good, good, fair, mediocre and poor and the roadway length. Each state s road network was subdivided into these five categories and each category included the length in miles of road in the corresponding condition. To obtain an overall road condition score, each category was assigned with a weight from one to five (one representing the worst condition and five representing the best condition). The number of miles in the corresponding category was multiplied with the weight assigned resulting in the total weighted-miles of road. Then, the total weighted-miles of road was divided by the total graded road length and the maximum weight (5) resulting in an overall state road condition score between 0 and 1. An example, based upon the data provided in Table 2 for the State of Alabama, is also provided as follows. The total weighted road condition value equaled (5*2, *9, *9, * 1, *728) = 83,929. On the other hand, the total graded road is 23,939 miles. Therefore, the overall road condition score was (83,929 / (23,939x5)) = 0.70.

29 29 Table 2: Road Condition Score Calculation Example State Alabama Very good 2,898 miles Good 9,324 miles Fair 9,437 miles Mediocre 1,552 miles Poor 7,28 miles Total Graded Road 23,939 miles Total Weighted Road 83,929 miles Road Condition Score 0.70 Secondly, a correlation analysis is conducted for the input variables of SPI-2 domain (VMT, registered vehicles and licensed drivers) and results are provided in Table 3. Results indicated a positive, strong and significant correlation among all three variables. Therefore, the three variables are combined as a single input variable to be used in the experimentation. The new variable is named as VMT Intensity and calculated with Equation 11. Table 3: Correlation Analysis of SPI-2 Domain Input Variables Vehicle Driver VMT Vehicle Pearson Correlation **.980 ** Sig. (2-tailed) Driver Pearson Correlation.986 ** ** Sig. (2-tailed) VMT Pearson Correlation.980 **.990 ** 1 Sig. (2-tailed) The effect direction of inputs on the output is also an important aspect that has to be considered prior to experimentation. For the particular highway safety problem

30 30 considered, such variables as highway safety expenditure, safety belt usage, road length and road condition are expected to have a decreasing impact on the number of fatalities. On the other hand, system usage variables (VMT, number of vehicles and number of drivers), thus VMT intensity as an overall system usage parameter, are expected to have an increasing impact on the output considered. Therefore, reciprocal transformation is applied to VMT intensity variable as shown in Equation 12. As a result of reciprocal transformation, the inverse of VMT Intensity is used along with other SPIs since the direction of effect became parallel for all inputs. Fourth, the fatality rate data is transformed into its inverse by using Equation 12 to be able to satisfy the maximization objective of proposed DEA model. The finalized version of data used in the DEA experimentation is shown in Table 4. Table 4: Summary of Data Preparation Variable Transformation Applied? Transformation Method Fatality Rate Yes Total Annual Time / The Fatality Rate VMT Intensity Yes Reciprocal Transformation (1/VMT Intensity) Road Condition Yes Quantification of Categorical Data Highway Safety Expenditure No N/A Road Length No N/A Safety Belt Usage No N/A Finally, the prepared data is normalized by using mean normalization method. Since there is an imbalance in the data magnitude due to multiple units such as million dollars and miles, the mean normalization procedure has been applied for all of the inputs

31 31 and the output. This normalization method is widely used in previous DEA studies (Talluri and Yoon, 2000). Mean normalization was simply conducted by calculating the mean for each input and output, and dividing each input or output by its respective mean Methodology DEA Model The inputs considered in the model included highway safety expenditure, the number of registered vehicles, the number of registered drivers, total vehicle miles traveled, total roadway length, overall road condition and safety belt usage rate. The output was the number of fatal crashes. To summarize, seven inputs and four outputs were considered. In a typical DEA model, the minimum number of DMUs required is the maximum of sum and product rules, which are shown in Equation 13, where n input is the number of inputs and n output is the number of outputs (Ramanathan, 2003). For the current model, the minimum number of DMUs required is 30 (max {(3*(5+1) =30; 5x1=5}). (The number of inputs is reduced to five and detailed explanation is given in 4.1. Data Preparation and Normalization section). Since the total number of DMUs (50 states) is greater than the minimum number of DMUs required (30), it can be concluded that DEA can be utilized as the benchmarking model for the road safety assessment problem. Since the objective of this research was to evaluate the efficiency of inputs on minimizing the number of fatal crashes, an output-oriented DEA model was considered for the efficiency evaluation. In this circumstance, a transformation method was

32 32 employed in order to minimize the fatality output since an output-oriented DEA model requires an output maximization. The transformed output was then defined as the average time between the occurrences of two fatalities as shown in Equation 14. The total annual time (365x24 = 8760) is defined by T, f it is the number of fatalities for the category i in year t and µit is the average time between two fatalities. Therefore, minimization of the number of fatalities was represented as the maximization of the average time between two fatalities. Such transformation method for undesirable outputs have been utilized in various DEA applications including Seiford & Zhu (2002) Färe & Grosskopf (2004) and Hadi Vencheh et al. (2005). In terms of returns to scale property, variable returns to scale (VRS) was selected since the production capability of inputs was assumed to have non-constant returns to scale, which enabled the model to recognize the possible scale diseconomies between states that are different in size of the inputs (Tatari & Kurmapu, 2011). The DEA VRS linear program used, originally developed by Banker, Charnes and Cooper (1984), is as follows: Notation: o: The DMU being evaluated : Output multiplier : Input multiplier : The number of outputs : The number of inputs

33 33 M: The number of DMUs : The amount of output o produced by DMU j : The amount of input i used by DMU j s: Scale weight Objective function: Subject to: The objective function is the weighted sum of outputs that has to be maximized (Equation 15). Equation 16 limits the total sum of weights assigned to inputs to one. Equation 17 is the normalization constraints for the weights assigned to inputs and outputs for each DMU. Once the linear model was run for the periods t and (t+1) separately, based on the outputs obtained for each period, the total factor productivity growth (TFPG) between the consecutive periods was calculated via the Malmquist Index formulation.

34 Malmquist Index Formulation To be able to capture trend efficiency over a period, the Malmquist Index Productivity Growth was included in the model. The Malmquist Index formulation was explained in detail in the first section of this chapter. Since DEA-VRS model was selected to analyze each period, Fare et al. s (1984) FGNZ&FLGR model was employed to formulate Malmquist Index. The formulation used in this study was as follows: MI is the Malmquist Productivity Index for the period (t, t+1). D o is the output distance function, f is the fatality index and SPI i is the i th safety performance indicator. For ease of representation, k and i are used as fatality category and SPI indices, respectively. However, all of the categories and SPIs were considered simultaneously in experimentation Results The results of the proposed model were calculated by solving the linear programming models and utilizing the Malmquist Productivity Index formulation. The results are shown in Table 5. The values are means of the period between 2002 and There are three components of MI in FGNZ&FLGR model, namely: PEC, SEC and TC. As previously stated, PEC (Pure Efficiency Change) is the efficiency change of the DMU s under variable returns to scale. On the other hand, the multiplication of PEC and

35 35 SEC provide the efficiency under constant returns to scale (CRS) (Fare et al., 1984). Therefore, PEC results are taken into consideration to interpret the road safety performance of U.S. states. For a DMU, if the PEC is greater than one, this indicates a positive efficiency growth. If there is unity in PEC (PEC=1), this indicates a constant efficiency. On the other hand, DMUs with PEC values that are less than one indicate a negative efficiency growth in road safety performance. Moreover, TC represents technological growth, which represents the change in the production capability of inputs throughout the period since it was originated from economy field the termination is kept the same. TC basically stands for the shift in the input categories (SPIs) in the current work. In terms of PEC, 33 states showed a decreasing performance in efficiency, 7 states have constant efficiency and an increasing efficiency trend was observed in only ten states, namely: Arkansas, Colorado, Massachusetts, Michigan, Minnesota, Nebraska, New Jersey, New Mexico, and Wisconsin. However, the majority of the states (47 out of 50) had an increasing technological efficiency from 2002 to Only three states had with a negative growth in TC (North Dakota, Vermont and Wyoming). The results of TC imply that a positive improvement occurred in resource utilization and technology with the period throughout the country (The average annual negative growth in TC for the seven states is 2.7 percent). In terms of overall productivity index (MI), two-third of states indicated a positive growth in terms of decreasing the roadway fatalities with the resources utilized. 18 states were found to have a negative growth. A national map was also developed to indicate the PEC trend among states and is shown in Figure 4.

36 36 In terms of the overall national performance, a similar trend was also observed. The mean PEC, SEC, TC and MI values of U.S. states are shown in Table 6. The average efficiency growth was -2.1%, the average technological improvement was 1.8% and the average productivity growth was -0.2%. The minimum efficiency growth was -49 percent (New Jersey) and the maximum efficiency growth was observed in with 46.4 percent (California). In terms of productivity, New Jersey had the highest (6.5 percent) and North Dakota had the lowest (-6.2 percent) productivity growth. The range of productivity was observed as 12.7 percent whereas a significantly greater range in efficiency was observed with 95.4 percent among all states. In conclusion, overall results indicate that the productivity increase (the decline in fatality rates) was more attributable to the technological improvements rather than efficiency. The majority of the states experienced either a negative (24 states) or constant (20 states) efficiency growth in utilizing the resources to reduce fatalities.

37 37 Table 5: Results of Experimentation State PEC SEC TC MI State PEC SEC TC MI Alabama Montana Alaska Nebraska Arizona Nevada Arkansas New Hampshire California New Jersey Colorado New Mexico Connecticut New York Delaware North Carolina Florida North Dakota Georgia Ohio Hawaii Oklahoma Idaho Oregon Illinois Pennsylvania Indiana Rhode Island Iowa South Carolina Kansas South Dakota Kentucky Tennessee Louisiana Texas Maine Utah Maryland Vermont Massachusetts Virginia Michigan Washington Minnesota West Virginia Mississippi Wisconsin Missouri Wyoming (Dark green indicates a positive growth, light green indicates constant efficiency and red indicates a negative efficiency growth) Figure 4. Average Road Safety Efficiency Growth of U.S. States ( )

38 U.S. States Average Road Safety Performance 38 Table 6: The Overall Analysis Type of Result PEC SEC TC MI US_Max US_Mean US_Min %Growth -2.1% 0.2% 1.8% -0.2% The trends of pure efficiency, technological change and Malmquist productivity index for the analysis period between 2002 and 2008 are also illustrated in Figure 5. In all of the metrics (PEC, MI and TC), the results fluctuate over the time, which indicates a non-stable performance for the U.S. states for the analysis period U.S. States Average Road Safety Performance TC MI PEC TC MI PEC Figure 5. Trend Analysis

39 39 For example, technological change indicated a positive growth (1% to 13%) in 4 out of 6 periods ( , and ) and a negative growth (1% and 10% in and , respectively). On the other hand, in terms of road safety efficiency, the direction of growth is negative in all periods except two periods as with 12% and with 2% positive growth. Finally, productivity growth, which is calculated by multiplication of PEC, SEC and TC values, also showed a non-stable performance throughout the analysis period. Productivity growth is observed as negative in three periods with a range between 1% and 3%, whereas a slight positive growth is also indicated in years between and with a range between 1% and 2%. All in all, the only slight positive productivity is attributed to efficiency growth in period. In contrast, in all other periods, the technological change is observed as the driver of the productivity growth. In ideal case, the efficiency growth is expected to have more or equal increasing impact on the productivity compared to technological change. However, on the average U.S. states, productivity growth performance in decreasing fatal crashes is due to solely the improvement in the inputs. When the technological change impact is not considered, the efficiency growth unfortunately has a decreasing impact on the productivity goal and U.S. states efficiency growth map (Fig. 3) also represents this conclusion. Figure 6 presents the average sensitivity of each input category on the efficiency of U.S. states for each period. The sensitivity results enable us to understand the magnitude of change in the average efficiency of a state, which is explained by the

40 40 variation in specific safety performance indicator (input category). To conduct sensitivity analysis, Zhou s (2001) sensitivity analysis model is run for each period considering variable returns to scale (VRS). 80.3% 17.2% Average 81.0% 28.6% 26.5% 84.4% 11.6% % 23.3% 22.5% 82.9% 15.3% % 32.0% 26.7% 81.2% 13.3% % 24.6% 25.3% 80.6% 14.8% % 33.5% 27.5% 80.8% 19.6% % 32.5% 28.2% 74.0% 20.0% % 27.8% 26.5% 78.2% 25.6% % 26.6% 28.5% 0.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0% 90.0% Safety Belt Usage Road Length Road Condition VMT Intensity Expenditure Figure 6. Sensitivity Analysis According to the Figure 6, it is found that safety belt usage and road condition are the top two inputs that road safety efficiency has showed the highest sensitivity with. For these two SPIs, the average variation in efficiency is between 80% for the entire period.

41 41 Additionally, VMT intensity and highway safety expenditures have relatively less impact on the variation in road safety efficiency and the sensitivity results were obtained as 28.6% and 26.5%, respectively. Moreover, the sensitivity results of each SPI do not fluctuate significantly over the time. Therefore, it can be concluded that the road condition and safety belt usage are found to be the most significant SPIs out of the selected five input categories.

42 42 4. NON-PARAMETRIC PREDICTIVE MODELING FOR U.S. STATES FATAL CRASHES 4.1. Introduction Road safety is becoming an indispensable element of socio-economic development since transportation of people and goods account for a significant part of daily activities. Therefore, stakeholders have to develop successful road safety policies and projects to reduce the road fatalities thus improving road safety. In this regard, utilizing scientific modeling techniques is crucial to describe, explain and/or predict a certain phenomenon. Additionally, incorporation of policy variables can make such models more effective in quantifying suggested policies and proposing future projections. Prediction models are one of the most widely used techniques to support decision making initiatives towards successful and effective policy making. In a typical prediction model, one or more dependent variables are connected to a number of independent variables such that a linear or nonlinear mathematical relationship is built, which enables the modeler to understand the pattern of dependent variables behavior over time period with independent variables. Crash prediction models can also be used to identify significant contributing factors and establish quantifiable relationships between crashes and explanatory variables in order to develop successful policies towards reducing crashes, particularly fatalities. With regard to road safety, literature is abundant with predictive models. In terms of parametric models, several types of regression models have been utilized including Bayesian Multivariate Poisson Regression (Ma & Kockelman, 2006), Negative Binomial

43 43 (de Guevara, Washington, & Oh, 2004), Stepwise-forward Regression (Montella, Colantuoni, & Lamberti, 2008), Support Vector Machine (Li, Carriquiry, Pawlovich, & Welch, 2008), combination of negative binomial and logarithmic link function(t. Johnson, Ivan, & Zhang, 2007) and Calibration Model for Regression (Tarko, 2006) and comparison of different techniques (El-Basyouny & Sayed, 2006). Time series modeling is also important in road safety. Several time series analysis models including DRAG models, univariate dynamic models (e.g. ARIMA, structural), and state-space models have been successfully implemented. For example, Harvey and Durbin (Harvey & Durbin, 1986) developed a structural model to understand and model the pattern of behavior associated road crashes using the impact of seat belt legislation as causality. In another work, Hermans et al. (E. Hermans, Wets, & Bossche, 2006) worked on a time series analysis of Belgian road traffic crashes considering the frequency and severity aspects. The monthly data collected from 1974 to 1999 was used to develop a state-space model which includes variables such as safety belt usage, weather condition, etc. Nonparametric prediction methods have been also utilized in research. The majority of the prediction models used a dataset collected from a specific section of a road network. For example, Moghaddam et al. (2010) developed a series of artificial neural network-based prediction models to estimate crash severity and to identify significant crash-related factors in urban highways of Milan, Italy. Riviere et al. (2006) evaluated the deformation energy absorbed by a vehicle during a collision and utilized an ANN to estimate the energy absorbed as a function of speed (energy equivalent speed EES). Xie et al. (2007) used backpropagation and Bayesian neural networks modeling

44 44 using data collected on rural frontage roads in Texas. In another work, Abdelwahhab and Abdel-Aty (2002) utilized ANN to evaluate the traffic safety of toll plazas and the impact of electronic toll collection (ETC) systems on highway safety along the Central Florida expressway system. Chang (2005)compared ANN and negative binomial regression models on the crash frequency collected from the National Freeway 1 in Taiwan for the period between 1997 and Results indicated that ANN is a consistent alternative method for analyzing freeway crash frequency. Recently, Lord and Mannering (2010) provided a comprehensive review of statistical models on crash frequency data. The review classified models proposed in literature into 15 categories based on the type of model used. As a nonparametric method, ANN has significant advantages over other models, such as not requiring assumptions about distribution of data (e.g. normality, equal variance tests) and providing a better statistical fit than traditional parametric models (Lord & Mannering, 2010). Especially when dealing with non-normal data, ANN is widely applied to road safety problems around the world Artificial Neural Networks (ANN) An artificial neural network is an information-processing system inspired from the structural or functional aspects of biological neural networks. A typical neural network consists of three elements: 1) architecture, 2) training or learning algorithm and 3) activation function. ANN architecture can be defined as the pattern of connections between the neurons. On the other hand, determining the weights on the connections of neurons in the architecture is referred as training. Activation function is the information processing function defined for each connection point, or node. Activation function

45 typically determines the output based on the sum of weighted input signals received. An illustration of a very simple neural network is provided in Figure I 1 w 1 I 2 w 2 HU w 4 O w 3 I 3 Figure 7. A Simple Neural Network In the neural network architecture given in Figure 7, there are three inputs (I 1, I 2, I 3 ), one output (O) and one hidden unit (HU), which is a nonlinear activation function used to model the information process between inputs and output. According to Figure 7, the output neuron (O) receives activated information from input neurons through the hidden layer unit (HL), which is a nonlinearly activating node. ANN has been used in various areas including signal processing, medicine, pattern recognition, prediction and classification, which was originally motivated by a desire to emulate and understand the human brain and its strengths. Since the simplest artificial neural network was developed by McCulloch-Pitts in 1943, the neural network research and algorithms have evolved significantly (e.g. backpropagation by Parker, 1985; Hopfield nets, 1987) and have

46 46 become a robust modeling tool today in various research areas including roadway safety assessment Justification and the Organization of Research The majority of prediction models in literature deal with a certain segment of a roadway or a regional area. This scale-wise limitation improves the models performance on the selected scale of modeling. On the other hand, such models are not generalizable. In fact, there is a direct need to assess the road safety of the U.S. as a whole to be able to understand the overall trend in the short and long-term. While it is crucial to analyze individual areas, segments and parts of national road network, the authors believe that a more holistic view also needs to be proposed to support the strategic decision making for the implementation in the larger scope and long-term. Therefore, the nation s fatality trend was modeled with a non-parametric modeling technique, Automated Artificial Neural Networks (AANN), considering macro-economic and aggregated variables. The objective of research was to model nationwide fatality trend over a period based on macro-scale predictors Data Since same data structure is used for this part of thesis as well, please refer to the section 3.4 for more information Predicting Road Fatalities with Multiple Linear Regression (MLR) Multiple (Multivariate) Linear Regression is one of the most common predictive modeling approaches, which attempts to model the relationship between a response variable and two or more explanatory variables. The relationship is set quantitatively by

47 47 fitting a linear equation to the observed data. As a parametric statistical modeling method, MLR is a very robust statistical modeling tool which has been used in various research fields including crash prediction. Following is a general form of MLR: where β is the intercept term, c i (for i=1 n) are the regression coefficients, y is the response variable, x i (for i=1 n) are the independent predictor variables and is the residual error. In this study, a multivariate linear regression model was developed for the fatal crash prediction of the United States highway network. Prior to modeling, a normality test was conducted for all data since MLR requires data to be normal (R. A. Johnson & Wichern, 2007). The results of normality check are shown in Table 7. According to the normality test results, none of the data for the predictor and response variables were normal (all p values are less than 0.05). Therefore, data transformation methods were applied to be able to have normal data. Three well-known transformation methods were used, namely: logarithmic (Bartlett & Kendall, 1946), square root and reciprocal transformation (R. A. Johnson & Wichern, 2007). The results of normality tests to the transformed data are also provided in Table 7. Even though aforementioned transformations were applied to the predictor and response variables, results indicate that majority of the variables in both original and transformed datasets do not meet the normality assumption of linear regression. This situation makes the utilization of a nonparametric method inevitable. In this part of thesis, automated artificial neural network (AANN) was utilized as the nonparametric method to model the relationship between fatal crashes and selected safety performance indicators.

48 48 Table 7: Normality Tests Original Data Modified Data with Lognormal Transformation Kolmogorov-Smirnov a Shapiro-Wilk Kolmogorov-Smirnov a Shapiro-Wilk Statistic Sig. Statistic Sig. Statistic Sig. Statistic Sig. State ID Fatal Crashes Year Expenditure Road Length Road Condition Safety Belt Usage VMT Intensity Modified Data with Square Root Transformation Modified Data with Reciprocal Transformation Kolmogorov-Smirnov a Shapiro-Wilk Kolmogorov-Smirnov a Shapiro-Wilk Statistic Sig. Statistic Sig. Statistic Sig. Statistic Sig. State ID Fatal Crashes Year Expenditure Road Length Road Condition Safety Belt Usage VMT Intensity

49 49 However, the original data was also modeled with multivariate linear regression in order to be used as benchmark for the proposed approach. The summary of the stepwise multivariate linear regression results are given in Table 8. Table 8: Summary of MLR Model Model R R Square Adjusted R Square Std. Error of the Estimate a b c d e f a. Predictors: (Constant), Road Length b. Predictors: (Constant), Road Length, Expenditure c. Predictors: (Constant), Road Length, Expenditure, Road Condition d. Predictors: (Constant), Road Length, Expenditure, Road Condition, Year e. Predictors: (Constant), Road Length, Expenditure, Road Condition, Year, State ID VMT Intensity g. Dependent Variable: Fatalities Results indicated that Stepwise Regression model provided four regression models with one, two, three and four independent variables, respectively (See Table 8). As more variables were included in model structure, the coefficient of determination (Rsquare) increased. The best fit was found with the sixth model since the least standard error of the estimate (433.2) and the greatest R-square (73.2 percent) were obtained. More detailed information about the sixth model is given in Table 9.

50 50 Table 9: Coefficients of the Best MLR Model (Model 4) Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 6 (Constant) Road Length Expenditure 8.110E Road Condition Year State ID VMT Intensity The Proposed Prediction Approach: Artificial Neural Networks (ANN) A total of seven input variables with fatal crashes as the output variable were used in the modeling. Seventy percent of the data was used for training and the remaining 30 percent was equally shared as validation (15 percent) and test (15 percent) data. Test, validation and training data were randomly selected. In this regard, the training data were used to train the network and adjust the weights on the neural network; the validation data were used to minimize over-fitting and the test data was used only for testing the final solution in order to confirm the actual predictive power of the network. Automated Network Search (ANS) mode of STATISTICA was used for the experimentation. This experimentation mode was used to determine the best performing neural network out of several network structures with different number of nodes and activation functions in the hidden layers. In this context, 1000 ANN models were developed using combinations of back-propagation multilayer perceptron and radial basis function architectures and five activation functions (logistic sigmoid, hyperbolic, tangent, negative exponential and identity). The most significant advantageous side of ANN was that such nonlinear activation functions and various network architectures were utilized to improve the fitting of prediction model. As a result of the experimentation, the top five networks were determined and related performance metrics are provided in Table 10.

51 51 The best network (ANN-1, see Table 10) consists of 7 input neurons, 16 hidden neurons in a single hidden layer and one output neuron. Hyperbolic tangent function (See Eq. 21) was determined as the activation function for the sixteen hidden neurons. In terms of output activation function, negative exponential function (See Eq. 22) was determined. The network architecture of the best ANN is shown in Figure 8. Table 10: Results of Experimentation (Top 5 out of NNs) Top 5 Neural Networks ANN-1 ANN-2 ANN-3 ANN-4 ANN-5 Network name MLP MLP MLP MLP MLP Training R-square Test R-square Validation R-square Training SEE Test SEE Validation SEE Training algorithm BFGS 12 BFGS 62 BFGS 28 BFGS 8 BFGS 29 Error function SOS SOS SOS SOS SOS Hidden activation Tanh Exponential Sine Exponential Sine Output activation Exponential Sine Exponential Sine Exponential According to Eq. (3), X i is the input variable value, w ij is the weight value between the input neuron i and hidden neuron j and X j is the value of hidden neuron j. Similarly, the output value is calculated via the negative binomial function given in Eq. (4), where X j is the value of hidden neuron, w jk is the weight value and is the bias term between

52 52 the hidden neuron j and the output neuron k. According to Table 10, the best ANN the coefficient of determination (R-square) values are 85.2 percent for training, 81.1 percent for validation and 83.5 percent for the testing data. Since the coefficient of determination value was greater than 0.7 (generally accepted R 2 value, Tatari & Kucukvar, 2011), the developed ANN model s prediction performance is satisfactory. Moreover, the connections and the weight values between input, hidden layer and output neurons are provided in Table 11 and 12. The prediction power of the best ANN was obtained as 83.5 percent. To visualize the prediction performance, as one of the widely used graphs, scatter plot of predicted and actual data for the best performing network was shown in Figure 8.

53 53 Hidden Bias Hidden Neuron 1 Hidden Neuron 2 Hidden Neuron 3 Input Bias State ID Year Expenditure Road Length Road Cond. Safety Belt Usage VMT Intensity Hidden Neuron 4 Hidden Neuron 5 Hidden Neuron 6 Hidden Neuron 7 Hidden Neuron 8 Hidden Neuron 9 Hidden Neuron 10 Hidden Neuron 11 Hidden Neuron 12 Fatal Crashes Hidden Neuron 13 Hidden Neuron 14 Hidden Neuron 15 Hidden Neuron 16 Figure 8. The Architecture of the Best Performing ANN Model

54 54 Table 11: Connections and Weights of the Best Neural Network No Connections Weights No Connections Weights 1 State ID --> hidden neuron Road Length --> hidden neuron Year --> hidden neuron Road Condition --> hidden neuron Expenditure --> hidden neuron SBU --> hidden neuron Road Length --> hidden neuron VMT Intensity --> hidden neuron Road Condition --> hidden neuron State ID --> hidden neuron SBU --> hidden neuron Year --> hidden neuron VMT Intensity --> hidden neuron Expenditure --> hidden neuron State ID --> hidden neuron Road Length --> hidden neuron Year --> hidden neuron Road Condition --> hidden neuron Expenditure --> hidden neuron SBU --> hidden neuron Road Length --> hidden neuron VMT Intensity --> hidden neuron Road Condition --> hidden neuron State ID --> hidden neuron SBU --> hidden neuron Year --> hidden neuron VMT Intensity --> hidden neuron Expenditure --> hidden neuron State ID --> hidden neuron Road Length --> hidden neuron Year --> hidden neuron Road Condition --> hidden neuron Expenditure --> hidden neuron SBU --> hidden neuron Road Length --> hidden neuron VMT Intensity --> hidden neuron Road Condition --> hidden neuron State ID --> hidden neuron SBU --> hidden neuron Year --> hidden neuron VMT Intensity --> hidden neuron Expenditure --> hidden neuron State ID --> hidden neuron Road Length --> hidden neuron Year --> hidden neuron Road Condition --> hidden neuron Expenditure --> hidden neuron SBU --> hidden neuron Road Length --> hidden neuron VMT Intensity --> hidden neuron Road Condition --> hidden neuron State ID --> hidden neuron SBU --> hidden neuron Year --> hidden neuron VMT Intensity --> hidden neuron Expenditure --> hidden neuron State ID --> hidden neuron Road Length --> hidden neuron Year --> hidden neuron Road Condition --> hidden neuron Expenditure --> hidden neuron SBU --> hidden neuron Road Length --> hidden neuron VMT Intensity --> hidden neuron Road Condition --> hidden neuron State ID --> hidden neuron SBU --> hidden neuron Year --> hidden neuron VMT Intensity --> hidden neuron Expenditure --> hidden neuron State ID --> hidden neuron Road Length --> hidden neuron Year --> hidden neuron Road Condition --> hidden neuron Expenditure --> hidden neuron SBU --> hidden neuron Road Length --> hidden neuron VMT Intensity --> hidden neuron Road Condition --> hidden neuron input bias --> hidden neuron

55 55 Table 12: Connections and Weights of the Best Neural Network Cont d. No Connections Weights No Connections Weights 41 SBU --> hidden neuron input bias --> hidden neuron VMT Intensity --> hidden neuron input bias --> hidden neuron State ID --> hidden neuron input bias --> hidden neuron Year --> hidden neuron input bias --> hidden neuron Expenditure --> hidden neuron input bias --> hidden neuron Road Length --> hidden neuron input bias --> hidden neuron Road Condition --> hidden neuron input bias --> hidden neuron SBU --> hidden neuron input bias --> hidden neuron VMT Intensity --> hidden neuron input bias --> hidden neuron State ID --> hidden neuron input bias --> hidden neuron Year --> hidden neuron input bias --> hidden neuron Expenditure --> hidden neuron input bias --> hidden neuron Road Length --> hidden neuron input bias --> hidden neuron Road Condition --> hidden neuron input bias --> hidden neuron SBU --> hidden neuron input bias --> hidden neuron VMT Intensity --> hidden neuron hidden neuron 1 --> Fatality Rate State ID --> hidden neuron hidden neuron 2 --> Fatality Rate Year --> hidden neuron hidden neuron 3 --> Fatality Rate Expenditure --> hidden neuron hidden neuron 4 --> Fatality Rate Road Length --> hidden neuron hidden neuron 5 --> Fatality Rate Road Condition --> hidden neuron hidden neuron 6 --> Fatality Rate SBU --> hidden neuron hidden neuron 7 --> Fatality Rate VMT Intensity --> hidden neuron hidden neuron 8 --> Fatality Rate State ID --> hidden neuron hidden neuron 9 --> Fatality Rate Year --> hidden neuron hidden neuron 10 --> Fatality Rate Expenditure --> hidden neuron hidden neuron 11 --> Fatality Rate Road Length --> hidden neuron hidden neuron 12 --> Fatality Rate Road Condition --> hidden neuron hidden neuron 13 --> Fatality Rate SBU --> hidden neuron hidden neuron 14 --> Fatality Rate VMT Intensity --> hidden neuron hidden neuron 15 --> Fatality Rate State ID --> hidden neuron hidden neuron 16 --> Fatality Rate Year --> hidden neuron hidden bias --> Fatality Rate Expenditure --> hidden neuron The actual fatal crash data is represented on the X axis and the predicted values are represented on the Y axis (See Fig. 9). According to Figure 9, majority of the values are scattered between 0 and Even though there are some outliers in data, all of the

56 predicted values are greater than zero and majority of the predicted and actual values are scattered close to the diagonal line, which is parallel to the R-square value (83.5 percent) Scatter Plot: Artificial Neural Network Model (Train, Test and Validation) Prediction-ANN FatalityRate Figure 9. Predicted versus Actual Fatal Crashes for Test, Train and Validation Data 4.7. Benchmarking ANN with MLR In this section, the results of ANN and MLR models are compared. For a fair comparison, ANN s test data was used to find the predicted values of MLR. Both ANN and MLR models predicted and actual values are graphed using the test data as shown in Figures 5 and 6, respectively. The visual comparison of ANN and MLR models were performed with the scatter plots given in Figures 10 and 11. According to Figure 10, the actual and predicted values were spread around the diagonal line. In other words, since the distances of data points from the diagonal line (residuals) are significant for the majority of data points, the prediction performance of MLR was not observed as satisfactory. Indeed, some of the predictions were observed as

57 57 negative. On the other hand, the pattern of behavior between the actual and predicted values of ANN model was observed as superior to the one obtained with MLR model. None of the predictions were observed as negative and the residuals were significantly lower than the ones observed with MLR. While the majority of the residuals ranged between 0 and 1000 for MLR model, most of the residuals of ANN model ranged up to 500 (See Fig. 11). Another comparison between the two prediction models, ANN and MLR, was made based on three factors: coefficient of correlation (r), coefficient of determination (R 2 ) and standard error of estimate (SEE). In this context, the coefficient of correlation expresses the strength of linear relationship between actual and predicted fatal crashes. The coefficient of determination provides an overall understanding about the proportion of variability in a data set that is accounted for by the statistical model (See Equation 23). where is the actual value, is the predicted value and is the mean value of the data for data point i. Additionally, the standard error of estimate (SEE) is another factor used to compare the prediction performance of the proposed nonparametric approach (ANN) and the conventional linear approach (MLR). SEE is also often used in statistical modeling as a measure of the accuracy of the predictions as shown in Equation 24, where n is the number of data points and k is the number of predictor variables.

58 Scatter Plot: Observ ed v s MLR (Test) MLR Observ ed Figure 10. Predicted versus Actual Fatal Crashes for Test, Train and Validation Data 4000 Scatter Plot: Observed vs ANN (Test) ANN Observed Figure 11. Predicted vs. Actual Values of ANN (Test Data)

59 59 The results of comparison are shown in Table 12. To make a fair comparison, the test, training and validation parts of the dataset were separately compared with the MLR model and the overall comparison was also made considering the entire dataset. Table 13: The overall comparison of ANN vs. MLR ANN (Test) MLR (Test) ANN (Train ) MLR (Train ) ANN (Validation ) MLR (Validation ) ANN (Overall ) MLR (Overall ) r R SE E Results indicated that, the proposed nonparametric approach outperformed the MLR in all factors. In this context, the proposed neural network model provided greater coefficient of determination in all cases including test, train and validation data and resulted in a an 84 percent R 2 and standard error of estimate of Since, the data was originally not normal and the transformation methods were not able to provide a normal dataset, the MLR approach was not an appropriate model and a more comprehensive model was needed to accommodate the non-normal data. In this regard, ANN successfully provided a more valid and better prediction model which accounted for the majority of the variability (84 percent) and provided lesser SEE Sensitivity Analysis In this section, the results of sensitivity analysis are provided (See Fig. 10). A sensitivity analysis indicates which input variables were considered most important by the particular neural network (Statsoft, 2012). With the guidance of the sensitivity

60 60 analysis, significant insights can be drawn from the results of neural network model about the usefulness of individual input variables. To perform the sensitivity analysis, a global sensitivity analysis model of ANS approach was used. The global sensitivity analysis approach utilized the missing value substitution procedure, in which each input variable was taken out of the network to capture the relative contribution that was obtained by comparing the cases before and after excluding the corresponding input variable. To calculate the sensitivity of a particular input variable, the test data was run with the network and the network error was determined. Then, the observed values of variable were replaced with the values estimated by the missing value procedure and the network error was calculated again. Then, the sensitivity was determined by calculating the ratio of the error with missing value substitution to the original error. The sensitivity values of input variables are provided in Figure 10. While the least sensitive input was found to be road condition, road length was determined as the most sensitive input and the sensitivity values ranged between 1 and 3. Road length, VMT intensity, expenditure and state ID input variables were found more sensitive than year, road condition and safety belt usage. In this case, the coefficient of variation is also important while interpreting the sensitivity of input variables since the frequency of fatal crashes vary among different states. The road length, VMT intensity, expenditure and state ID variables coefficient of variance values were found as greater than year, safety belt usage and road condition. Therefore, it was not surprising that such variables have greater sensitivity than road condition and safety belt usage. In other words, the United States road condition and safety belt usage do not vary as much as other macro-variables

61 61 including expenditure, VMT intensity and road length. Therefore, when making policies at the state level, the magnitude of such input variables affect the fatal crashes more than safety belt usage and road condition as expected. However, road condition and safety belt usage were still important aspects of the problem studied even though the relative sensitivity values are smaller due to smaller coefficient of variance values. RoadCondition Safety Belt Usage Year StateID Expenditure VMT Intensity RoadLength Coefficient of Variation Sensitivity Figure 12. Results of Sensitivity Analysis

62 62 5. CONCLUSIONS AND FUTURE WORK 5 In this thesis, road safety assessment and prediction modeling of U.S. states are addressed. A two-phase methodology is implemented for benchmarking and prediction modeling of U.S. states road fatalities. In the first part of the thesis, the nations highway safety efficiency growth was analyzed. Recent annual highway safety reports indicate that there is a declining trend in the fatality rates in the nation. Every year, millions of dollars are invested on maintenance, construction, education, research and various other areas to reduce fatality rates. While the Federal Government provides guidance to the states, each state creates individualized strategic plans, and implements projects in the aim of reducing fatal crashes along roadways. In this regard, it is important to assess U.S. states road safety performance considering several characteristics that impact the fatal crash trend such as vehicles, drivers, road condition, and road safety expenditures vary among the states. To do so, a DEA-based Malmquist Production Indexing approach was utilized to evaluate the road safety performance of the fifty U.S. states. Four main areas were considered as the risk domains that affect the fatality rates including the economic investment on system, the usage of system, the condition of system and personal safety. On the other hand, the main output was considered as the number of fatal crashes. The risk domains were then subdivided into seven safety performance indicators (SPIs); 1) safety expenditures, 2) the number of registered vehicles, 3) the number of registered drivers, 4) VMT, 5) safety belt usage, 6) total road length and 7) road condition score. The number of fatal crashes was considered as the output. The experimentation was 5 This chapter contains adapted writing directly from following publication: Egilmez, G., & McAvoy, D. (2013). Benchmarking road safety of U.S. states: A DEA-based Malmquist productivity index approach. Accident Analysis and Prevention, 53(1), doi: /j.aap

63 63 performed for the period between 2002 and 2008, in which the data for all inputs and outputs were available. The analysis of DEA results could be very helpful to state highway agencies to compare the relative efficiency in terms of road safety performance. Results indicate that there was a slight negative productivity (an average of -0.2 percent) observed on minimizing the number of fatal crashes along with an average of 2.1 percent efficiency decline and 1.8 percent technological improvement. The results of period by period analysis indicate that majority of productivity results are attributed to the growth in technological change rather than the efficiency growth. Parallel to period by period analysis, the overall analysis of U.S. states indicates that the reduction in fatal crash frequency is attributed to only the improvement in the selected SPIs which was represented with technological change (TC). However, the efficiency scores indicate a negative growth on the average which raises the major concern about the utilization of inputs. In this regard, the main lesson learned from the study is that, when the reduction in fatal crash frequency and the improvement in SPIs considered together, the improvement in SPIs is greater than the reduction in fatal crash frequency which resulted in overall negative efficiency. Therefore, the controllable SPIs such as expenditure, safety belt usage and road condition have to be improved in a more effective and efficient manner towards reducing the fatal crash frequency. In this regard, since sensitivity results indicate that road condition and safety belt usage are the most sensitive inputs to the road safety score; more effective policy making towards increasing safety belt usage and better

64 64 utilization of safety expenditures to improve road condition are found as the key areas to focus on for state highway safety agencies. Current work is the first attempt to assess state-wide road safety performance assessment problem. There is still more work to do as future direction of current research. First of all, important characteristics of fatal crashes such as alcohol involvement, the vehicle type (e.g. truck, passenger car) should be considered as outputs along with the potential indicators as inputs. Further analysis in terms of target setting and performance improvement for inefficient states could also be an important future direction of current research. Finally, other transportation nodes such as rail, air, etc and the societal costs of fatal and non-fatal crashes are also planned to be incorporated in further models. In terms of the second part of the thesis, significant conclusions can be made as well. In the second part of the thesis, predicting fatal crashes of the United States was studied. A nonparametric prediction approach, Artificial Neural Network (ANN), was utilized and compared with traditional parametric prediction modeling approach, Multiple Linear Regression (MLR). The justification of utilizing ANN as nonparametric approach was due to non-normality observed on the original data and its transformed forms which was acquired with three transformation methods as reciprocal, lognormal and square-root. Later, the proposed neural network approach and MLR model were compared based on visual and quantitative performance metrics. Automated Neural Search module of STATISTICA was selected to develop the ANN model. The best neural network was determined considering the performance metrics as a result of ANN experimentation with 1000 neural networks. The 1000 candidate networks were developed considering

65 65 combinations of a set of hidden neurons, linear and nonlinear activation functions and network architectures. After validation of best network, the proposed approach and MLR model were compared. Scatter plots were utilized to for the purpose of visual comparison, whereas r, R 2 and standard error of estimate were utilized to compare the models prediction performance quantitatively. Based on the scatter plots and all performance metrics, the proposed neural network model outperformed the MLR model and was found to be satisfactory due to a better overall fit (R2=0.84 >0.7) and less standard error of estimate. In the final step of experimentation, a neural network-based sensitivity analysis was conducted to analyze relative sensitivity of input variables to the fatal crashes. Results of sensitivity analysis indicated that road length was found to be the most sensitive input variable and road length, VMT intensity, expenditure and state ID were found as more sensitive than year, safety belt usage and road condition input variables. This research has been conducted with the input variables that affect the road crashes and currently available on RITA s database. However, inclusion of other input variables can provide more insights and increase the prediction performance of ANN. Therefore, for better generalized modeling, more emphasis has to be given on increasing the state-based data availability in terms of other variables such as alcohol usage. Furthermore, other alternative nonparametric prediction methods such as random forest and boosted trees can be utilized to improve the prediction performance.

66 66 REFERENCES Abdelwahab, A., & Abdel-aty, M. (2002). Artificial Neural Networks and Logit Models for Traffic Safety Analysis of Toll Plazas. Transportation Research Record: Journal of the Transportation Research Board, 1784, Bartlett, M. S., & Kendall, D. G. (1946). The Statistical Analysis of Variance- Heterogeneity and the Logarithmic Transformation. Supplement to the Journal of the Royal Statistical Society, 8(1), Caves, D. W., Christensen, L. R., & Diewert, E. W. (1982). The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity. Econometrica, 50, Chang, L.-Y. (2005). Analysis of freeway accident frequencies: Negative binomial regression versus artificial neural network. Safety Science, 43(8), Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decisionmaking units. European Journal of Operational Research, 3(4), Cooper, W. W., Seiford, L. M., & Zhu, J. (2011). Handbook on Data Envelopment Analysis. (W. W. Cooper, L. M. Seiford, & J. Zhu, Eds.) (Vol. 164, pp. 1 39). Boston, MA: Springer US. De Guevara, F. L., Washington, S. P., & Oh, J. (2004). Forecasting Crashes at the Planning Level: Simultaneous Negative Binomial Crash Model Applied in Tucson, Arizona. Transportation Research Record: Journal of the Transportation Research Board, 1897, Egilmez, G., Kucukvar, M., & Tatari, O. (2013). Sustainability Assessment of U.S. Manufacturing Sectors: An Economic Input Output-based Frontier Approach. Journal of Cleaner Production, 53, El-Basyouny, K., & Sayed, T. A. (2006). Comparison of Two Negative Binomial Regression Techniques in Developing Accident Prediction Models. Transportation Research Record: Journal of the Transportation Research Board, (1950), Färe, R., & Grosskopf, S. (2004). Modeling undesirable factors in efficiency evaluation: Comment. European Journal of Operational Research, 157(1), Fare, R., Grosskopf, S., Lindgren, B., & Roos, P. (1992). Productivity changes in Swedish pharamacies : A non-parametric Malmquist approach. Journal of Productivity Analysis, 3(1-2),

67 Fare, Rolf, Grosskopf, S., Norris, M., & Zhang, Z. (1994). Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries. American Economic Review, 84(1), Farrell, M. J. (1957). The Measurement of Productive Efficiency. Journal of Royal Statistical Society, 120(A), Feng, Z., & Yuan-Biao, Z. (2010). Relative efficiency evaluation of Chinese health care system based on data envelopment analysis (DEA) model. In 2010 International Conference on Computer and Communication Technologies in Agriculture Engineering (pp ). IEEE. Filippetti, A., & Peyrache, A. (2011). The Patterns of Technological Capabilities of Countries: A Dual Approach using Composite Indicators and Data Envelopment Analysis. World Development, 39(7), Hadi Vencheh, A., Kazemi Matin, R., & Tavassoli Kajani, M. (2005). Undesirable factors in efficiency measurement. Applied Mathematics and Computation, 163(2), Harvey, A. C., & Durbin, J. (1986). The Effects of Seat Belt Legislation on British Road Casualties: A Case Study in Structural Time Series Modelling. Journal of the Royal Statistical Society, 149(3), Hermans, E., Wets, G., & Bossche, F. Van den. (2006). Frequency and Severity of Belgian Road Traffic Accidents Studied by State-Space Methods. Journal of Transportation and Statistics, 9(1). Hermans, Elke, Brijs, T., Wets, G., & Vanhoof, K. (2009). Benchmarking road safety: lessons to learn from a data envelopment analysis. Accident; analysis and prevention, 41(1), Hermans, Elke, Van den Bossche, F., & Wets, G. (2008). Combining road safety information in a performance index. Accident; analysis and prevention, 40(4), Johnson, R. A., & Wichern, D. W. (2007). Applied Multivariate Statistical Analysis (6th Editio., p. 800). Pearson. Johnson, T., Ivan, J. N., & Zhang, C. (2007). Crash Prediction Models for Intersections on Rural Multilane Highways: Differences by Collision Type. Transportation Research Record: Journal of the Transportation Research Board, (2019),

68 Kirikal, L., & Tehnikaülikool, T. (2005). Productivity, the Malmquist index and the empirical study of banks in Estonia. Tallinn Technical University Press. Lee, K.-H., & Farzipoor Saen, R. (2012). Measuring corporate sustainability management: A data envelopment analysis approach. International Journal of Production Economics, 40(1), Li, W., Carriquiry, A., Pawlovich, M., & Welch, T. (2008). The choice of statistical models in road safety countermeasure effectiveness studies in Iowa. Accident; analysis and prevention, 40(4), Lord, D., & Mannering, F. (2010). The statistical analysis of crash-frequency data: A review and assessment of methodological alternatives. Transportation Research Part A: Policy and Practice, 44(5), Ma, J., & Kockelman, M. K. (2006). Bayesian Multivariate Poisson Regression for Models of Injury Count, by Severity. Transportation Research Record: Journal of the Transportation Research Board, (1950), 24. Moghaddam, F. R., Afandizadeh, S., & Ziyadi, M. (2010). Prediction of accident severity using artificial neural networks. International Journal of Civil Engineering, 9(1), Montella, A., Colantuoni, L., & Lamberti, R. (2008). Crash Prediction Models for Rural Motorways. TRR Journal of Transportation Research Board, 2083( ). Odeck, J. (2006). Identifying traffic safety best practice: an application of DEA and Malmquist indices. Omega, 34(1), Ozbek, M. E., Garza, J. M. D., & Triantis, K. (2009). Data Envelopment Analysis as a Decision-Making Tool for Transportation Professionals. Journal of Transportation Engineering, 135(11), Parker, D. (1985). Learning Logic - Technical Report. Ramanathan, R. (2003). An introduction to data envelopment analysis (p. 203). New Delhi: Sage. RITA. (2010). State Transportation Statistics. State Transportation Statistics. Retrieved from on_statistics/state_transportation_statistics_2010/index.html 68

69 Riviere, C., Lauret, P., Ramsamy, J. F. M., & Page, Y. (2006). A Bayesian Neural Network approach to estimating the Energy Equivalent Speed. Accident; analysis and prevention, 38(2), Seiford, L. M., & Zhu, J. (2002). Modeling undesirable factors in efficiency evaluation. European Journal of Operational Research, 142(1), Shephad, R. (1970). Theory of cost and production functions (p. 308). New Jersey: Princeton University Press. Statsoft. (2012). STATISTICA Help. Retrieved from Talluri, S., & Paul Yoon, K. (2000). A cone-ratio DEA approach for AMT justification. IJPE, 66(2), Tank, D. W., & Hopfield, J. J. (1987). Collective Computation in Neuronlike Circuits. Scientific American, 257(6), Tarko, A. P. (2006). Calibration of Safety Prediction Models for Planning Transportation Networks. Transportation Research Record: Journal of the Transportation Research Board, (1950), Tatari, O., & Kucukvar, M. (2011). Cost premium prediction of certified green buildings: A neural network approach. Building and Environment, 46(5), Tatari, O., & Kurmapu, D. (2011). Sustainability assessment of highways: A Malmquist index of US states. In Sustainable Systems and Technology (ISSST), 2011 IEEE International Symposium on (pp. 1 6). Chicago, IL: IEEE. Tingvall, C., Stigson, H., Eriksson, L., Johansson, R., Krafft, M., & Lie, A. (2010). The properties of Safety Performance Indicators in target setting, projections and safety design of the road transport system. Accident analysis and prevention, 42(2), Traffic Safety Annual Assessment Highlights. (2010). Statistics (Vol. 2007). Washington, DC Retrieved from Xie, Y., Lord, D., & Zhang, Y. (2007). Predicting motor vehicle collisions using Bayesian neural network models: an empirical analysis. Accident; analysis and prevention, 39(5), Xue, X., Shen, Q., Wang, Y., & Lu, J. (2008). Measuring the productivity of the construction industry in China by using DEA-based Malmquist productivity indices. Journal of Construction engineering and Management, 134(January),

70 Zhang, B., Bi, J., Fan, Z., Yuan, Z., & Ge, J. (2008). Eco-efficiency analysis of industrial system in China: A data envelopment analysis approach. Ecological Economics, 68(1-2), Zhu, J. (2001). Super-efficiency and DEA sensitivity analysis. European Journal of Operational Research, 129(2),

71 71 APPENDIX: DATA USED State ID Year Fatalities Expenditure Road Length Road Condition Safety Belt Usage VMT Intensity ,242 94, ,738 14, ,291,915 57, ,408 98, ,654 5,145, , ,105,653 86, ,009,955 21, ,620 5, ,810 4,870, , ,362 1,837, , ,303 4, ,594 46, ,273 3,195, , ,399,803 94, , , , , ,693,835 78, ,045,143 60, ,910 22, ,760,003 30, ,304,296 35, ,173 1,310, , ,310, , ,805 73, ,082 1,568, , ,774 69, ,869 93, ,196 34, ,502 15, ,607,526 36, ,025 61, ,411 10,317, , ,427 2,599, , ,143 86, ,285 2,283, , ,020, , ,288 66, ,462 4,645, , ,759 6, ,266,821 66, ,322 83, ,058 1,232,473 88, ,348 5,153, , ,961 42, ,751 14, ,326,726 70, ,362,522 82, ,038 36, ,260, , ,787 27,

72 State ID Year Fatalities Expenditure Road Length Road Condition Safety Belt Usage VMT Intensity , ,242 94, ,738 14, ,118 1,291,915 57, ,408 98, ,224 5,145, , ,105,653 86, ,009,955 21, ,620 5, ,169 4,870, , ,603 1,837, , ,303 4, ,594 46, ,454 3,195, , ,399,803 94, , , , , ,693,835 77, ,045,143 60, ,910 22, ,760,003 30, ,304,296 35, ,283 1,310, , ,310, , ,805 74, ,232 1,568, , ,774 69, ,869 93, ,196 33, ,502 15, ,607,526 38, ,025 63, ,493 10,317, , ,553 2,599, , ,143 86, ,274 2,283, , ,020, , ,288 65, ,577 4,645, , ,759 6, ,266,821 66, ,322 83, ,193 1,232,473 88, ,821 5,153, , ,961 42, ,751 14, ,326,726 71, ,362,522 82, ,038 36, ,260, , ,787 27,

73 State ID Year Fatalities Expenditure Road Length Road Condition Safety Belt Usage VMT Intensity ,154 1,399,968 95, ,021,393 14, ,151 1,878,433 58, ,046,575 98, ,120 12,488, , ,950,945 87, ,311,430 21, ,982 6, ,244 7,179, , ,634 2,220, , ,174 4, ,073 47, ,355 6,045, , ,936,466 94, ,417, , ,323, , ,718,661 77, ,520,059 60, ,552 22, ,384,537 30, ,281,112 35, ,159 2,812, , ,198, , ,063,891 74, ,130 2,241, , ,476 69, ,109 93, ,188,981 33, ,498 15, ,078,096 38, ,100 64, ,495 16,371, , ,573 3,342, , ,919 86, ,286 3,679, , ,225, , ,423,132 65, ,490 6,147, , ,561 6, ,046 1,486,655 66, ,528 83, ,339 1,649,528 88, ,699 8,237, , ,056 42, ,002 14, ,831,342 71, ,041,540 81, ,035,048 37, ,323, , ,167 27,

74 State ID Year Fatalities Expenditure Road Length Road Condition Safety Belt Usage VMT Intensity ,148 1,828,693 96, ,241,047 14, ,179 2,464,950 59, ,152,741 98, ,333 19,830, , ,796,236 87, ,612,904 21, ,343 6, ,518 9,488, , ,729 2,603, , ,044 4, ,551 47, ,363 8,896, , ,473,129 95, ,878, , ,717, , ,743,487 78, ,994,975 60, ,193 22, ,009,070 30, ,257,927 35, ,129 4,313, , ,086, , ,327,976 74, ,257 2,913, , ,178 69, ,060,348 93, ,737,765 34, ,493 15, ,548,666 38, ,059,174 63, ,434 22,424, , ,547 4,084, , ,695 86, ,321 5,074, , ,430, , ,158,975 64, ,616 7,648, , ,363 6, ,094 1,706,488 66, ,734 83, ,270 2,066,582 90, ,536 11,320, , ,124,151 43, ,253 14, ,335,957 71, ,720,558 83, ,101,057 37, ,387, , ,546 27,

75 State ID Year Fatalities Expenditure Road Length Road Condition Safety Belt Usage VMT Intensity ,207 2,012,649 96, ,348,861 14, ,293 3,175,316 60, ,155,025 99, ,240 23,297, , ,735,340 88, ,658,976 21, ,180 6, ,357 10,294, , ,693 3,401, , ,979 4, ,750 47, ,254 8,903, , ,569,315 96, ,952, , ,813, , ,984,177 78, ,277,253 60, ,401 22, ,239,445 31, ,100,739 35, ,086 4,270, , ,312, , ,735,520 74, ,096 3,267, , ,047 73, ,131,864 93, ,620,193 33, ,025 15, ,968,887 38, ,255,322 63, ,454 22,968, , ,554 3,996, , ,330 86, ,238 5,348, , ,601, , ,325,707 64, ,525 8,769, , ,789 6, ,045 1,762,335 66, ,695 84, ,284 2,372,232 91, ,531 12,512, , ,367,188 43, ,915 14, ,366,189 72, ,553,687 83, ,152,909 37, ,632, , ,065 27,

76 State ID Year Fatalities Expenditure Road Length Road Condition Safety Belt Usage VMT Intensity ,110 2,041,731 97, ,454,638 14, ,071 3,556,588 60, ,189,476 99, ,995 22,187, , ,841,408 88, ,642,664 21, ,700 6, ,213 11,489, , ,641 7,155, , ,926 4, ,194 48, ,248 10,331, , ,594,440 95, ,959, , ,697, , ,569,609 78, ,368,376 61, ,123 22, ,540,728 31, ,292,386 36, ,087 4,399, , ,477, , ,890,791 74, ,313, , ,495 73, ,055,982 93, ,034,248 33, ,259 15, ,645,836 38, ,411,553 68, ,332 22,957, , ,676 4,014, , ,862 86, ,255 5,463, , ,854, , ,584,051 59, ,491 9,149, , ,245 6, ,077 1,471,965 66, ,519 83, ,211 2,464,666 91, ,466 13,412, , ,571,472 44, ,186 14, ,027 3,455,431 72, ,325,481 83, ,109,184 38, ,561, , ,813 28,

77 State ID Year Fatalities Expenditure Road Length Road Condition Safety Belt Usage VMT Intensity ,080,012 97, ,581,775 15, ,955,823 60, ,225,478 99, ,434 23,887, , ,989,375 88, ,854,757 21, ,161 6, ,980 12,196, , ,495 4,699, , ,534 4, ,298 47, ,043 10,635, , ,030,610 95, ,930, , ,893, , ,679,318 78, ,113,712 61, ,668 22, ,810,430 31, ,019,456 36, ,375, , ,084, , ,703,244 74, ,241, , ,754 74, ,247,259 93, ,764,651 33, ,877 16, ,619,414 38, ,292,830 68, ,238 24,021, , ,428 4,165, , ,465 86, ,191 5,513, , ,077, , ,741,451 59, ,468 9,792, , ,580 6, ,501,683 66, ,185 82, ,043 2,217,160 92, ,476 16,315, , ,926,879 44, ,949 14, ,169,476 73, ,771,952 83, ,145,635 38, ,867, , ,739 28,

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