DEVELOPMENT OF TIME SERIES MODEL TO
STUDY HISTORICAL TRE ND OF ROAD TRAFFIC
ACCIDENTS IN THE UNI TED STATES AND
INSPECT THE FACTORS AFFECTING THE
TREND

Ashutosh Kedia

M.Tech Project Thesis 2015
DEVELOPMENT OF TIME SERIES MODEL TO
STUDY THE HISTORICAL TREND OF ROAD
TRAFFIC ACCIDENTS IN THE UNITED STATES
AND INSPECT THE FACT ORS AFFECTING THE
TREND

Thesis submitted to the
Indian Institute of Technology, Kharagpur
For award of the degree of Master of Technology by Ashutosh Kedia
Under the guidance of
Prof. Sudeshna Mitra

DEPARTMENT OF CIVIL ENGINEERING
INDIAN INSTITUTE OF TECHNOLOGY KHARAGPUR
MAY 2015
©2015 Ashutosh Kedia. All rights reserved.

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M.Tech Project Thesis 2015
APPROVAL OF THE VIVA-VOCE BOARD

05/05/15
Certified that the thesis entitled DEVELOPMENT OF TIME SERIES MODEL TO
STUDY HISTORICAL TREND OF ROAD TRAFFIC ACCIDENTS IN THE UNITED
STATES AND INSPECT THE FACTORS AFFECTING THE TREND submitted by
ASHUTOSH KEDIA to the Indian Institute of Technology, for the award of the degree,
Master of Technology, has been accepted by the external examiners and that the student has successfully defended the thesis in the viva-voce examination held today.

(External Examiner)

(Chairman)

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(Supervisor)

M.Tech Project Thesis 2015
CERTIFICATE
This is to certify that the thesis entitled “Development of Time Series Model to Study
Historical Trend of Road Traffic Accidents in the United States and Inspect the
Factors Affecting the Trend” submitted by Ashutosh Kedia to Indian Institute of
Technology, Kharagpur, is a record of bona fide research work under my supervision and
I consider it worthy of consideration for the award of the degree of Master of Technology of the Institute.

Date:

____________________________________
Supervisor
Prof. Sudeshna Mitra
Department of Civil Engineering
Indian Institute of Technology Kharagpur

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M.Tech Project Thesis 2015
DECLARATION
I certify that
a. The work contained in the thesis is original and has been done by myself under the general supervision of my supervisor(s).
b. The work has not been submitted to any other Institute for any degree or diploma. c. I have followed the guidelines provided by the Institute in writing the thesis.
d. I have conformed to the norms and guidelines given in the Ethical Code of
Conduct of the Institute.
e. Whenever I have used materials (data, theoretical analysis, and text) from other sources, I have given due credit to them by citing them in the text of the thesis and giving their details in the references.
f. Whenever I have quoted written materials from other sources, I have put them under quotation marks and given due credit to the sources by citing them and giving required details in the references.

___________________
Signature of the Student

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M.Tech Project Thesis 2015
Acknowledgement
I have given enough effort in this thesis. However, it would not have been possible without the kind support and help of many individuals. I would like to extend my sincere thanks to all of them.
I take this opportunity to express my profound gratitude and deep regard to my guide
Prof. Sudeshna Mitra, Professor of Civil Engineering Department, IIT Kharagpur for her exemplary guidance, monitoring and constant encouragement throughout the course of this endeavour. I am highly indebted to her for the guidance and constant supervision as well as for providing necessary information regarding the thesis & also for their support in completing the thesis.
I would also like to extend my deep thankfulness to Prof. Bhargab Maitra, Prof. K.
Sudhakar Reddy, Prof. M.A. Reddy and Prof. K. Prapoorna Biligiri for their constant support, supervision and technical guidance at various stages in my academic front. The blessing, help and guidance given by them shall carry me a long way in the journey of life on which I am about to embark.
Lastly, I thank almighty, my parents, relatives and batch mates for their constant encouragement without which this assignment would not have been possible.

IIT Kharagpur
May 2015

Ashutosh Kedia

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M.Tech Project Thesis 2015
LIST OF ABBREVIATIONS

1. NHTSA – National Highway Traffic Safety Administration
2. FARS – Fatality Analysis Reporting System
3. ARIMA – Auto-Regressive Integrated Moving Average
4. INAR – Integer Valued Auto-Regressive
5. VMT – Vehicle Miles Travelled
6. MVI – Missing Value Imputation
7. AR(i) – ith order Auto-Regressive Term
8. MA(i) – ith order Moving Average Term
9. ANOVA – Analysis of Variance
10. VIF – Variance Inflation Factor
11. DUI – Driving Under Influence

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M.Tech Project Thesis 2015
ABSTRACT
As the road traffic in developing countries like India boosts due to increased demands, growing economy and ease of accessibility to Motor Vehicles, so should the regulatory measures to contain this traffic. The present structure of traffic legislations in India hasn‟t seen much change in the past decade and thus, has become inefficient towards reducing crashes and their severity arising due to the boost in traffic demand. Countries like United
States of America have faced similar issues in their life cycle thus, it is appropriate to take guidance from their mistakes and rectification measures so as to be able to frame effective policies suited for reducing crashes and their severity in India.
In this study, Total Accidents, Total Fatalities, Total Injuries in these Accidents and Total
Non-Injuries in these Accidents have been modelled against demographic, socioeconomic and road traffic related variables associated with these accidents, using
ARIMAX analysis. This helps us in understanding the time trend of these parameters as well as the explanatory variables significantly influencing this trend. Data for these variables were collected from Fatality Analysis Reporting System (FARS), Report of the
United States Department of Transportation on Highway Statistics, US Bureau of
Economic Analysis and US Census Bureau for the period 1975-2012. The model was developed for the United States on a consolidated basis as well as for representative states for various regions in the US. These states were; California, Illinois, New York and
Washington.
Using the analysis, the variables significantly affecting the time trend were identified and a rationale to justify this relationship was established and has been presented in the report.
Also, the trend observed for all the regions have been explained separately using the individual time trend of explanatory variables. Finally, for the consolidated US analysis, extraneous policies that have had an impact on the years with significant fluctuations in the time trend of dependent variables have been studied.

Key Words: Time Series Modeling, ARIMAX, Total Accidents, Total Fatalities, Total
Injuries, Total Non-Injuries, Vehicle Miles Travelled, 85th Percentile Speed

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M.Tech Project Thesis 2015

TABLE OF CONTENTS
LIST OF TABLES………………………………………………………………………………………...…x
LIST OF FIGURES……………………………………………………..……………………...…………..xi
CHAPTER-1
INTRODUCTION.......................................................................................................................................... 1
1.1

GENERAL ............................................................................................. 1

1.2

NEED FOR THIS STUDY ............................................................................... 1

1.3

OBJECTIVE ........................................................................................... 2

1.4

SCOPE OF THE WORK ................................................................................. 2

CHAPTER-2
REVIEW OF LITERATURE ....................................................................................................................... 4
CHAPTER-3
METHODOLOGY ........................................................................................................................................ 8
3.1

FILTERING OF RAW DATA ........................................................................... 9

3.2

MISSING VALUE IMPUTATION .......................................................................... 9

3.3

OUTLIER TREATMENT ................................................................................ 10

3.4

AUTO-CORRELATION ................................................................................. 12

3.5

TIME TREND .......................................................................................... 13

3.6

STATIONARITY ....................................................................................... 13

3.7

BOX-JENKINS METHODOLOGY ....................................................................... 14

3.7.1

AUTO REGRESSIVE (AR) PROCESS ................................................................. 14

3.7.2

MOVING AVERAGE (MA) PROCESS ................................................................ 15

3.7.3

ARIMA PROCESS .................................................................................. 15

3.7.4

AUTO-CORRELOGRAM ............................................................................. 16

3.7.5 PARTIAL AUTO-CORRELOGRAM .................................................................... 16
3.8

MULTICOLLINEARITY ................................................................................ 17

3.9

ARIMAX ............................................................................................. 17

CHAPTER-4
DATA ............................................................................................................................................................ 19

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M.Tech Project Thesis 2015
4.1

DATA DICTIONARY ................................................................................... 20

CHAPTER-5
RESULTS ..................................................................................................................................................... 21
5.1 ANALYSIS FOR USA DATA .............................................................................. 21
5.2 ANALYSIS FOR CALIFORNIA DATA ...................................................................... 32
4.3 ANALYSIS FOR ILLINOIS DATA .......................................................................... 41
4.4 ANALYSIS FOR NEW YORK DATA ....................................................................... 48
4.5 ANALYSIS FOR WASHINGTON DATA .................................................................... 56
CHAPTER-6
SUMMARY .................................................................................................................................................. 64
CHAPTER-7
CONCLUSION ............................................................................................................................................ 65
REFERENCES

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M.Tech Project Thesis 2015
LIST OF TABLES

1. Table 4.1: Data Dictionary for the data used for SAS modeling
2.
3.
4.
5.

Table 5.1: ARIMAX analysis results for Total Fatalities in USA from 1975-1993
Table 5.2: ARIMAX analysis results for Total Fatalities in USA from 1975-2012
Table 5.3: ARIMAX analysis results for Total Injuries in USA from 1975-2012
Table 5.4: ARIMAX analysis results for Total Fatalities in California from 19751993
6. Table 5.5: ARIMAX analysis results for Total Fatalities in California from 19752012
7. Table 5.6: ARIMAX analysis results for Total Injuries in California from 19752012
8. Table 5.7: ARIMAX analysis results for Total Fatalities in Illinois from 19751993
9. Table 5.8: ARIMAX analysis results for Total Fatalities in Illinois from 19752012
10. Table 5.9: ARIMAX analysis results for Total Injuries in Illinois from 1975-2012
11. Table 5.10: ARIMAX analysis results for Total Fatalities in New York from 19751993
12. Table 5.11: ARIMAX analysis results for Total Fatalities in New York from 19752012
13. Table 5.12: ARIMAX analysis results for Total Injuries in New York from 19752012
14. Table 5.13: ARIMAX analysis results for Total Fatalities in Washington from
1975-1993
15. Table 5.14: ARIMAX analysis results for Total Fatalities in Washington from
1975-2012
16. Table 5.15: ARIMAX analysis results for Total Injuries in Washington from
1975-2012

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M.Tech Project Thesis 2015
LIST OF FIGURES

1. Figure 3.1- Flowchart indicating the process of time series modeling
2. Figure 5.1: Time Trend of Total Accidents in the USA
3. Figure 5.2: Time Trend of Total Fatalities in the USA
4. Figure 5.3: Time Trend of Total Injuries in the USA
5. Figure 5.4: Time Trend of Total Non-Injuries in the USA
6. Figure 5.5: Time Trend of Total Registered Vehicles in the USA
7. Figure 5.6: Time Trend of Total Vehicle Miles Travelled in the USA
8. Figure 5.7: Time Trend of 85th Percentile Speed of Vehicles travelling in the USA
9. Figure 5.8: Time Trend of the Percentage of Drivers over the age of 65 in the USA
10. Figure 5.9: Time Trend of Vehicle Miles Travelled on Arterials in the USA
11. Figure 5.10: Time Trend of Total Accidents in California
12. Figure 5.11: Time Trend of Total Fatalities in California
13. Figure 5.12: Time Trend of Total Injuries in California
14. Figure 5.13: Time Trend of Total Non-Injuries in California
15. Figure 5.14: Time Trend of Total Registered Vehicles in California
16. Figure 5.15: Time Trend of Total Drivers in California
17. Figure 5.16: Time Trend of Vehicle Miles Travelled on Arterials in California
18. Figure 5.17: Time Trend of the 85th Percentile Speed in California
19. Figure 5.18: Time Trend of the Percentage of Drivers below the age of 25 in
California
20. Figure 5.19: Time Trend of Vehicle Miles Travelled on Interstate Routes in
California
21. Figure 5.20: Time Trend of Total Vehicle Miles Travelled in California
22. Figure 5.21: Time Trend of Total Accidents in Illinois
23. Figure 5.22: Time Trend of Total Fatalities in Illinois
24. Figure 5.23: Time Trend of Total Injuries in Illinois
25. Figure 5.24: Time Trend of Total Non-Injuries in Illinois
26. Figure 5.25: Time Trend of Total Registered Vehicles in Illinois
27. Figure 5.26: Time Trend of Total Drivers in Illinois
28. Figure 5.27: Time Trend of Vehicle Miles Travelled on Arterials in Illinois
29. Figure 5.28: Time Trend of the 85th Percentile Speed in Illinois
30. Figure 5.29: Time Trend of the Percentage of Drivers below the age of 25 in
Illinois

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M.Tech Project Thesis 2015
31. Figure 5.30: Time Trend of Vehicle Miles Travelled on Interstate Routes in
Illinois
32. Figure 5.31: Time Trend of Total Accidents in New York
33. Figure 5.32: Time Trend of Total Fatalities in New York
34. Figure 5.33: Time Trend of Total Injuries in New York
35. Figure 5.34: Time Trend of Total Non-Injuries in New York
36. Figure 5.35: Time Trend of Total Registered Vehicles in New York
37. Figure 5.36: Time Trend of Total Drivers in New York
38. Figure 5.37: Time Trend of Total Vehicle Miles Travelled in New York
39. Figure 5.38: Time Trend of the 85th Percentile Speed in New York
40. Figure 5.39: Time Trend of the Percentage of Male Drivers in New York
41. Figure 5.40: Time Trend of Vehicle Miles Travelled on Interstate Routes in New
York
42. Figure 5.41: Time Trend of Total Accidents in Washington
43. Figure 5.42: Time Trend of Total Fatalities in Washington
44. Figure 5.43: Time Trend of Total Injuries in Washington
45. Figure 5.44: Time Trend of Total Non-Injuries in Washington
46. Figure 5.45: Time Trend of Total Registered Vehicles in Washington
47. Figure 5.46: Time Trend of Percentage of Male Drivers in Washington
48. Figure 5.47: Time Trend of Vehicle Miles Travelled on Arterials in Washington
49. Figure 5.48: Time Trend of the 85th Percentile Speed in Washington
50. Figure 5.49: Time Trend of the Percentage of Drivers below the age of 25 in
Washington
51. Figure 5.50: Time Trend of Percentage of Driver Over 65 year of Age in
Washington

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M.Tech Project Thesis 2015
CHAPTER-1
INTRODUCTION
1.1

General

In India, more than 250,000 road users died of traffic accidents in 2011 with the total accident toll ranging above 0.5 million. Statistical analysis suggests that in the past decade, India has seen accident numbers rise by a whopping 11% averagely every year.
On the other hand China which used to be at par with India on the overall development front, a decade back, has seen a decreasing trend ever since. While the heterogeneous mix of Indian traffic and drivers‟ recklessness are one of the most important factors contributing to the aforementioned, sadly it can be highly correlated to inefficient policies. The purpose of this project is to study the vehicle crash trend in developed countries to extract meaningful insights for framing traffic policies well suited to tackle this problem in developing countries like India. Countries like United States and United Kingdom have road fatalities per 100,000 inhabitants as 11.6 and 3.5 respectively while in India, it is
19.6. The condition was equally bad in the United States and the United Kingdom but due to effective policy changes, the numbers were reduced significantly. Having faced the problem in their life cycle, it is fairly logical to derive knowledge from their learnings to speed up this process in India. Hence, in this project an attempt has been made to extract this knowledge from the United States road crash data so as to pave a way for efficient policy formulation in India.

1.2

Need for this study

National Highway Traffic Safety Administration (NHTSA) has plenty of data on traffic crashes that have happened since 1975. Ranging from the cause of accident to the time of accident to the geometric and traffic features associated with the accident, NHTSA has complete information on every registered accident that has happened in United States. But the past researches in the area of crash data analysis made use of only a few features out of the ones available in this information. Radun and Summala[1], made use of only

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M.Tech Project Thesis 2015 psychological features of the passengers, Newstead and Elia[2] just use vehicle color and other demographic features, Bossche et al.[3] predicted only the riskiness based on the age and gender category. But much information can be extracted if we make more efficient use of the data. Thus, we can try to find the change in the accident pattern over the years due to the effect of demographic parameters and by involving all the available demographic parameters we can try to determine which parameters will most affect this pattern. Identifying these parameters can enlighten us on the survey routes that can be used during policy formulation for the Indian scenario and as stated previously, can give us a jump start regarding the crash analysis in India.

1.3

Objective

Following are the objectives of the current study:


Studying the trend of road traffic accidents, fatalities, injuries and non-injuries in the United States by performing a time series analysis of the US crash data as well as crash data for the representative states of various regions in the US, for the period 1975-2012.



Modeling Time Trend of the aforementioned variables and identifying the factors significantly affecting the trend



Explaining the effect and significance of these factors on the said trend



Mapping the significant changes in the trend with the changes in the road traffic legislations that were put in place in the United States in the said time period.

1.4

Scope of the work


Extracting crash data from the National Highway Safety Administration‟s data repository, Fatality Analysis Reporting System (FARS) for the years 1975-2012



Extracting data for the explanatory variables from US Department of
Transportation report on Highway Statistics, US Bureau of Economic Analysis and US Census Bureau



Filtering the data based on the relevant variables from in the dataset based on technical judgment

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M.Tech Project Thesis 2015


Re-construction of variables to modify them so that they are suitable for use in the analysis 

Framing data to give a time series data for different panels



Performing Box-Jenkins time series approach to build the time series model for the United States data and for the data of the representative states of California,
Illinois, New York and Washington



Identifying the factors significantly effecting the time trend for each dataset



Explaining the effect and significance of these factors on the said trend



Mapping of significant trend variations with traffic policy changes in the United
States

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M.Tech Project Thesis 2015
CHAPTER-2
REVIEW OF LITERATURE
The early analysis of Vehicle Crash data was performed to determine the effect of one or more vehicular, traffic or road features that could affect the overall crash count or accident pattern. Research done by Scott[4] reports analyses of road accident data in
Britain in which time series of monthly accident data for the period 1970-1978 have been related to a number of explanatory variables. Two-vehicle accidents were modelled by regression and because the time trends in this data appeared to be reasonably consistent, the resulting model was regarded as adequate. In the case of single-vehicle accidents, trends were not consistent over the period, and it was considered that the Box-Jenkins time series method might be more appropriate than simple regression. The tentative conclusion drawn from this comparison is that because accident series are generally very
"noisy" and autocorrelation among the residuals from standard regressions are not very strong, Box-Jenkins models are unlikely to represent the series appreciably better than regression based on the assumption of uncorrelated residuals. A major reason why this could have happened is that the data that was collected was only for 8 years and the model couldn‟t have found an appreciable trend in the data. Also, the model was built in a time period when the focus on traffic crash reduction by policy changes wasn‟t predominant in United States and so it could have been possible that the accident data for a particular year wasn‟t correlated with one from the previous year. Hence, it can be understood that data for significant year span should be considered and also the time period should range from 1970s i.e. an era without significant traffic policy changes, to present scenario with tremendous traffic policy changes.
Another research performed by Quddus[5] assessed the use of Integer–Valued
Autoregressive (INAR) Poisson model to analyze the time series count data associated with traffic crashes in Great Britain. Different types of time series count data were considered: aggregated time series data where both the spatial and temporal units of observation are relatively large (e.g., Great Britain and years) and disaggregated time series data where both the spatial and temporal units are relatively small (e.g., congestion

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M.Tech Project Thesis 2015 charging zone and months). The performance of the INAR models was compared with the class of Box and Jenkins real-valued models. The results suggest that the performance of these two classes of models was quite similar in terms of coefficient estimates and goodness of fit for the case of aggregated time series traffic accident data. This was because the mean of the counts was high in which case the normal approximations and the ARIMA model may be satisfactory. However, the performance of INAR Poisson models was found to be much better than that of the ARIMA model for the case of disaggregated time series traffic accident data where the counts were relatively low. In the analysis presented in the current research, the data is aggregated and hence, Box-Jenkins
ARIMA methodology can be used as it gives at par performance as INAR models.
Avuglah et al.[6] applied ARIMA modeling to analyze the accident trend in Ghana and performed an accident forecast using the model for the next 5 years. They used accident data from 1991 to 2011 and built an ARIMA (0,2,1) model. The analysis identified that the traffic accidents in Ghana had been continuously increasing in the past and would continue to increase for the next five years. The study showed that past years‟ accident numbers could significantly affect the same for the upcoming years but predicting these values solely on the basis of past years‟ data isn‟t logically appropriate. Hence, the current study aims to take it a step forward and include other factors affecting the total accidents to build a consolidated model for predicting total accidents.
Brijs et al.[7] analyzed the road crashes based on the age and gender group using the State
Space model. It was found that road risk was changing over the age groups according to a
U-shaped curve, and that men generally had higher risk than women. Further, the risk was decreasing over time, but not at the same rate for all age-gender groups. The highest yearly reduction in risk was found for the oldest and youngest road users. Although the results were conclusive, there was an incoherency when it came to future predictions because many other factors like the type of road user, geometry of road and other vehicular and traffic parameters weren‟t considered. Hence, there is a need to use all the relevant parameters and perform an extensive study on each of their impacts so as to make the model robust.

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A very interesting study was performed by Taylor et al.[8] where they attempted to model the variation in the traffic safety with respect to the vehicular speed. Speed is one the most important characteristic which impacts accidents and also the measurement of speed keeps varying from region to region as either average speed or 85th percentile speed etc. which makes it very complex to model. Hence, this research is one of utmost importance.
Here, statistical modeling techniques had been used to explore the relationships between these variables and to develop models in which the effect of speed on accident frequency could be quantified separately from the confounding effects of other variables like vehicle flows, pedestrian activity, road layout etc. It was found that in a given set of road and traffic conditions the frequency of accidents increased with the speed of traffic, and higher the speed the more rapidly does accident frequency rose with increase in speed.
A similar study was performed by Alijanahi et al.[9] where relationship between various measures of traffic speed, under free flow conditions (Level of Service - B), and accident rate was investigated for the Tyne and Wear County of the United Kingdom and Bahrain.
In Bahrain, researchers found that the mean speed affected the accident rate significantly whereas in Tyne and Wear, instead of the mean speed, the traffic variability affected the accident rate more strongly. Another study by Finch et al.[10], wherein after reviewing cases of imposing speed limits in different countries, it was found out that the change in the mean speed of traffic was roughly one quarter of the change in the speed limit. The above two studies provides firm evidence that speed limit highly affects the number of accidents. Hence, speed limit has been used as deterministic criteria to analyze traffic accidents in the current study.
Jovanis and Chang[11] studied the relationship of Vehicle Miles Travelled (VMT) on the
Accidents. To formulate this relationship they applied Poisson Regression model to
Indiana Toll Road data. They collected data for daily accident numbers, travel mileage and environmental factors. It was seen from the models that there was a direct relation of automobile and truck miles travelled to the automobile and truck accidents. As VMT increased for trucks, the automobile-automobile collisions reduced marginally while the automobile-truck collisions increased. They also assessed the effect of environmental factors i.e. snow and rainfall and found out that there was a strong impact of snow on all

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M.Tech Project Thesis 2015 accident types whilst rainfall had an impact only on the mean automobile accident frequency. VMT being one of the most prominent factors affecting accident numbers, the current study accounts for its effect but the seasonal parameters haven‟t been considered.
But very few researches have been done to model the trend in traffic crashes and map them with policy changes. A quantitative study to correlate the accident numbers with speed limit policies was done by Rock[12]. He examined the effect of the speed limit increase in Illinois from 55 to 65 mph in 1987, on rural interstates and limited access highways. The study applied ARIMA techniques to a monthly time series of accidents, injuries and fatalities from 5 years before the policy change to 4 years after, on highways where speed limit was increased and on those where it wasn‟t. Effect of higher limits on mean speeds, speed variance, traffic diversion etc. were considered. The study found out that the change in speed limit policy resulted in 345 more accidents, 15 more deaths and
150 more injuries monthly. The study concluded that the speed limit increase caused an increase in the mean speed as well as diversion of traffic on high speed roads. The combination of these two effects resulted in the increase of accidents.
A research by Richter et al.[13] found from statistics that the road accident related deaths dropped in UK by 33.9% while in USA it dropped by only 6.5% between 1990-99. They set out to model the reason for such a significant difference. They tracked the Crash
Fatality Rates (CFRs) in the US and the UK and performed regression analysis to analyze change in time trends of CFR. They found that the United Kingdom introduced speed cameras and an array of speed-calming measures. By contrast, in the United States, use of speed cameras was extremely rare, and speed limits increased in 32 of the 50 states, mostly in 1995 and 1996, after which CFR actually rose. The reductions in CFR, probably from small drops in speed of impact accounted for the disproportionately greater drop in death tolls in the United Kingdom compared to the United States. If the US had implemented UK-type speed control policies and not raised speed limits, there would have been an estimated 6500 to 10,000 (~16% to 25%) fewer road deaths per year during the period following speed-limit increases. It can hence be seen that policy changes immensely impact the road crashes and also that deriving ideas from the experience of other countries can be very helpful to devise an effective policy for a country.

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M.Tech Project Thesis 2015
CHAPTER-3
METHODOLOGY
Time Series Analysis is done on dataset where apart from other regressors, the regressand is dependent on the past values of regressand too. The steps followed for the time series analysis is presented in order in the flowchart shown in Figure 3.1.
Filtered Raw Dataset

Missing Value Imputation and Outlier Treatment

Autocorrelation Test
•Durbin's h test

Time Trend

Stationarity
•Augmented Dickey Fuller Test

Box-Jenkins Time Series Modeling
•Auto-correlogram
•Partial Auto-correlogram

Multicollinearity
•Variance Inflation Factor (VIF)

Time Series ARIMAX model

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M.Tech Project Thesis 2015
Figure 3.1: Flowchart indicating the process of time series modeling

3.1

Filtering of Raw Data

The data for the project has been taken from National Highway Traffic Safety
Administration (NHTSA) repository named as Fatality Analysis Reporting System
(FARS), Report of US Department of Transportation on Highway Statistics, US Census
Bureau and US Bureau of Economic Analysis, for years 1975-2012. These data contain variables ranging from vehicular parameters, driver behavior, non-motorist behavior, weather, road condition and geometry, pre and post impact scenarios, demographic parameters etc. All the variables in the dataset isn‟t of much use for the current study objectives so based on intellectual assessment, 10 explanatory variables have been chosen which will have an impact on the vehicular accident. The details on the selected Variables as well as Data Dictionary are given in Chapter 4-Data.
The data for all the variables have been converted into per capita basis. There were separate datasets for each time period with observations corresponding to all the accidents in the country. The accident count was made for each panel, based on the state indicator variable. This gave a dataset for each time period where each observation corresponded to one panel with the data for all the aforementioned variables. The data was transposed to give a time series dataset for each panel from 1975-2012. The filtered dataset was then merged together to give a consolidated data with Year and Region as the data Indicator.

3.2

Missing Value Imputation

Numerous times when data is recorded, there could be missing values in the dataset whether due to unavailability of data or due to data collection errors. These missing values might create problems during the data analysis like deteriorating the representativeness of the data or introducing a bias. Hence, they have to be replaced with a suitable value keeping in mind the reason for the occurrence of a missing value. For e.g. if the data has been left missing due to a deliberate rationale behind them, they have to be treated differently than the missing values arising due to data collection errors.

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M.Tech Project Thesis 2015
In the methodology used, the variables with at most 3% missing values are made to go through MVI. For those variables with more than 3% missing values, if the variable is making a significant engineering sense, only then it is included in the model and made to go through MVI else it is dropped because imputing so many missing values by a single value might induce bias in the model.
Missing values can be replaced with one of the following:
•

Mean

•

Median

•

Zero

•

Special Values (these involve a special character like 999 or -9999 etc. used to

signify something out of the ordinary)
Zero or Special Value is generally used for MVI when the value has been left missing due to some intentional reason behind it.
Mean or Median is used for imputation mainly when we can‟t seem to find a clear reason for that missing value and concludes that the missing value has occurred due to data collection issues. In these cases, mean or median, which is considered to be the most representative value for a sample, is used, keeping in mind that which amongst these two provides most conservatism.
After a suitable imputation value for MVI is identified for all the variables, the missing values for these variables are replaced with these values in the original dataset and a modified dataset is formed which is used for further modeling processes.

3.3

Outlier Treatment

An outlier is an observation in the dataset which significantly stands out from the rest of the data. In other words if the data set is looked wholly, an outlier will be much farther from the mean or the median of the dataset. Outliers are mainly generated due to data entry errors or due to special values being put in during data collection or Missing Value
Imputation.

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An outlier, as is clearly understandable, can skew the data significantly because it can make the mean shift from what it was actually supposed to be. Also, in a regression analysis, an outlier can make the best fit line change the most optimum course to accommodate the outlier where it could have given a much better fit with the remaining data. Hence, to treat the data for outliers before data analysis becomes very important.
Outlier treatment begins by setting a cap on how big a value got to be before it can be termed as an outlier and then treating the outlier.
For the higher percentile side, any value which is more than twice or thrice the 99th percentile value (“twice or thrice” depends on the variable, as for some variables even twice the 99th percentile value can be logically thought of very high) is an outlier unless human judgment sees logic for those values to be there and do not classify them as an outlier. The variables are then capped at twice or thrice the 99th percentile value based using the logic mentioned previously. In some special cases a special cap value can be used base on human judgment for e.g., for variable, „Percentage of vehicles traversing on a level road‟, the maximum value can‟t go beyond 100. Hence, if the 99th percentile value is 75 the variable will still be capped at 100 not 150 or 225.
For the lower percentile side if the variable is less than one-third the 1st percentile value, it is considered to be an outlier. Here also there are some special cases where human judgment is predominant. These include:
•

Human judgment does not classify the variables as outliers.

•

If the 1st percentile is very small, one-third of it is also very small. So, a value

very close to it can be termed as an outlier even though it is not.
•

If there are negative values not being treated as outliers but the variable logically

can‟t take negative values.
The variables are then floored at one-third the 1st percentile value (three times the 1st percentile if it is a negative value) or at the value which the analyst came upon by logical deduction. Page 11

M.Tech Project Thesis 2015
After the capping and flooring values have been decided for all the variables, these are applied to in the model and new dataset, which is outlier treated, is created for use in later modeling steps.

3.4

Auto-Correlation

Time series, as was stated previously deals with cases where the regressand depends on the value of regression from the previous time period. Normally, a regression equation is formulated as per the equation:
Yt = a + b1X1t + b2X2t + … + ε
Where,
a,bi = intercept, slope coefficients ε = error term
In this equation, we try to minimize the error so that the chosen regressors can explain the given variance in Yt optimally, but if even after choosing all the significant regressors, error term hasn‟t been minimized we start suspecting autocorrelation i.e. the error at time t is a combination of error at time t-1 and an stochastic error part of time t. Thus, presence of autocorrelation suggests that there is a dependency of previous time period‟s result on the result of this time period, which is when we need a time series modeling. Hence, we need to check if the data actually contains autocorrelation because if it does only then a time series modeling will be required else not.
To check for autocorrelation we use Durbin-Watson d statistic, but this generally tends to be inconclusive. This is because when we have a practical data which is judged to be dependent upon past years output, this would imply that Yt will have Yt-1 as one of its regressors, which is called an auto-regressive term, and past researches have shown that in presence of auto-regressive term Durbin-Watson d test tends to be inconclusive. Hence, we use Durbin‟s h test which is given by:

√

(

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M.Tech Project Thesis 2015
Where,
n = Number of Observations var(â) = Variance of the lagged Yt (Yt-1) ρ= ∑
∑

The computed h-statistic follows a normal distribution and if this statistic comes significant, then there is autocorrelation else there is not. If there is no autocorrelation, the model can be formed by using OLS linear regression else time series methodology has to be followed.

3.5

Time Trend

In a time series modeling, there is a strong reason to believe that the regressand has a trend i.e. it is depended upon how many years have passed since the base year. Therefore, we form a null hypothesis that there is no trend with the alternative hypothesis of the presence of trend. If null hypothesis is rejected we will have to include the trend tern in the modeling process else not. Thus, we check for the judgment upon this hypothesis using Maximum Likelihood Estimator (MLE) by assuming that there is time trend and we derive the ANOVA tables corresponding to the analysis. If the obtained t-statistic corresponding to the time trend parameter is significant, then there will be time trend in the model else not.

3.6

Stationarity

For Box-Jenkins procedure, we assume that the model is stationary i.e. it has a constant mean, constant variance and the covariance between lagged variables depends only upon the number of lags considered not on the time. Hence, we need to determine if our model is stationary before we can apply Box-Jenkins ARIMA modeling. Granger and
Newbold[9] were the first researchers to point out that if non-stationary variables are used in regression, then spurious results will occur. Consequently, a unit root test should be implemented at first, in order to avoid the problem of spurious regression. They recommend conducting the Augmented Dickey-Fuller test with and without trend to check for stationarity of variables.

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M.Tech Project Thesis 2015
Augmented Dickey-Fuller test have the null hypothesis that unit root exists in the autoregressive representation of the time series. It can be represented by:
∑

(Without trend)
∑

(With trend)

Where,
∆Yt = Yt – Yt-1 , Yt is a macroeconomic variable such as stock price at time t
= a trend variable
= White noise term m = number of lags
AIC (Akaike Information Criterion) or SBC (Schwarz Bayesian Criterion) are often used to select the optimal lag length or m .The null hypothesis H0: Unit root exists i.e. and Yt is said to have unit root if one fails to reject H0 .If null hypothesis is rejected it can be said that time series variable is stationary.
If the model is stationary we can proceed with the next step, but if it is no-stationary, we need to take the first difference of the model and check for stationarity again. If even that doesn‟t make it stationary, we need to take the second difference and keep continuing till the model is stationary.

3.7

Box-Jenkins Methodology

Box-Jenkins methodology is defined in terms of an Auto-Regressive Term, a Moving
Average Term and an Integrated i.e. differences term. Before discussing Box-Jenkins methodology, it would be wise to discuss the sub parts first.

3.7.1

Auto Regressive (AR) Process

If we model Yt as
(Yt − δ) = α1(Yt−1 − δ) + ut
Where,
δ = mean of Y ut = uncorrelated random error term with zero mean and constant variance ζ2

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M.Tech Project Thesis 2015 then we say that Yt follows a first-order autoregressive, or AR(1), stochastic process,
Here the value of Y at time t depends on its value in the previous time period and a random term; the Y values are expressed as deviations from their mean value. In other words, this model says that the forecast value of Y at time t is simply some proportion
(= α1) of its value at time (t − 1) plus a random shock or disturbance at time t;
In general, we can have
(Yt − δ) = α1(Yt−1 − δ) + α2(Yt−2 − δ) + ·· ·+αp(Yt−p − δ) + ut in which case Yt is a pth order autoregressive, or AR(p), process.

3.7.2

Moving Average (MA) Process

The AR process just discussed is not the only mechanism that may have generated
Y. Suppose we model Y as follows:
Yt = μ + β0ut + β1ut−1
Where,
μ = a constant ut = white noise stochastic error term.
Here Y at time t is equal to a constant plus a moving average of the current and past error terms. Thus, in the present case, we say that Y follows a first-order moving average, or an
MA(1), process.
More generally,
Yt = μ + β0ut + β1ut−1 + β2ut−2 + ·· ·+βqut−q is an MA(q) process.

3.7.3

ARIMA Process

Yt might be a combination of the AR, MA as well as the nth difference term that was talked about in a previous section. Hence, if it is a „p‟ order AR, „q‟ order MA and differenced „d‟ times, we call it an ARIMA(p,d,q) process.

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M.Tech Project Thesis 2015
3.7.4

Auto-Correlogram

An auto-correlogram is a graph representing the covariance of a given sample vs the lag at which we are finding the covariance. It is given by:
∑(

)(

)

Where, n = number of lags
The Auto-Correlogram gives us an estimate of the degree of moving average that is present in the model, if the Auto-Correlogram dies down after q lags then there is q degree of Moving Average.

3.7.5

Partial Auto-Correlogram

A Partial Auto-Correlogram is a graph representing the covariance of a given sample vs the lag disregarding the covariance for the intermediate lags.
Statistical Analysis Software directly gives the Auto-Correlogram and the Partial AutoCorrelogram for a given model.
The Partial Auto-Correlogram gives us an estimate of the degree of Auto Regression that is present in the model, if the Partial Auto-Correlogram becomes insignificant after p lags, there is p degree of Auto Regression.
The Box-Jenkins methodology can thus be summarized in four steps:
Step 1. Identification: That is, find out the appropriate values of p, d, and q by using the auto-correlogram and partial auto-correlogram as described above.
Step 2. Estimation: Having identified the appropriate p and q values, the next stage is to estimate the parameters of the autoregressive and moving average terms included in the model. This calculation in this study can be done by simple least squares methods.
Step 3. Diagnostic checking: Having chosen a particular ARIMA model, and having estimated its parameters, we next see whether the chosen model fits the data reasonably well, for it is possible that another ARIMA model might do the job as well. We do that by estimating few other possible models for e.g. If we are getting an ARMA(1,1) scheme, we might develop models for AR(1), AR(2) and ARMA(2,1) as well. We judge the best

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M.Tech Project Thesis 2015 model by using the AIC (Akaike Information Criterion) or SBC (Schwarz Bayesian
Criterion). If AIC of one model is lower than the other, the first model is better.
Step 4. Forecasting

3.8

Multicollinearity

Multicollinearity is the phenomena where you can explain one of the regressors as a linear combination of the others, thus making that regressor redundant. Multicollinearity has to be removed from the model because, if two or more variables are correlated that might cause reduction in the level of significance of one or more of the variables. Also, the sign of coefficient for one or more of the variables might become counter-intuitive.
For this, the Variance Inflation Factor (VIF) is checked.
VIF is a measure of the degree of multicollinearity associated with a particular independent variable i.e. what effect of a particular independent variable is explained by one or more of remaining independent variables.
VIF is computed by:

Where,
Rj2 = R-squared when a particular regressor is regressed against all the other regressors
For any variable VIF above a certain value is considered to be problematic. In the models developed during the project a cut-off value of 3 is assumed for the VIF. Now, the variable with the highest VIF is noted and using the correlation matrix the variable(s) with which it is most correlated with is/are found. Out of the highly correlated variables only those variable will be retained in the model which have the highest positive impact on the model.

3.9

ARIMAX

After building the ARIMA model i.e. determining the lag of dependent variable and the errors on which it depends, we need to improve upon the model to take other regressors at time t into account. This is done by making use of ARIMAX modeling where we simply calculate the Maximum Likelihood Estimator for a regression equation formed with the
AR terms, MA terms and the regressors at time t.

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The final model that is given after the ARIMAX step is the regression scheme which can best represent the regressand and its variation over time. The next section presents details on the data that underwent the entire modeling methodology to produce the final model to serve the stated objectives.

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M.Tech Project Thesis 2015
CHAPTER-4
DATA
The ARIMAX model has been developed for four crash parameters; Total Accidents,
Total Fatalities that took place in these accidents, Total number of Injuries and Total number of Non-Injuries observed in the accidents. The variables used as explanatory variables for the development of the said models are as follows:


Total Registered Vehicles in the given year



Total Drivers in the given region in the given year



Total Vehicle Miles Travelled (VMT)



VMT on interstate highways



VMT on arterials



Gross Domestic Product



Percentage of Male Drivers among Total Drivers



Percentage of Drivers under 25 years of age among Total Drivers



Percentage of Drivers over 65 years of age among Total Drivers



85th Percentile Speed of all vehicles travelling in the given year

The data for the crash parameters have been collected from National Highway Traffic
Safety Administration (NHTSA) repository called Fatality Analysis Reporting System
(FARS). Report of US Department of Transportation on Highway Statistics was used to obtain the data for Total Drivers, Registered Vehicles, Total Vehicle Miles Travelled
(VMT), VMT on Interstate Roads, VMT on arterials, 85th Percentile Speed, Percentage of Male Drivers and Percentage of Drivers aged less than 25 and over 65. GDP data was recorded from US Bureau of Economic Analysis and Population data from US Census
Bureau. The data for all the variables were collected, for individual years from 19752012, in either standard Ms-excel (.xlsx) format or Data File (.dat) format.
For the analysis, all the absolute variables (i.e. variables not expressed as a percentage) were modified to give data on the per capita basis by dividing the same with Total
Population of the region in consideration. The analysis was performed in Statistical
Analysis Software (SAS). All the datasets were hence converted in SAS data file

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M.Tech Project Thesis 2015
(.sas7bdat) format for its use in SAS. Since, the data was collected individually for all years; they were merged to give a consolidated dataset for all years with Year and Region as the Unique Indicator of the observations. The analysis was then run for each of the required region.
The following subsection presents the Data Dictionary corresponding to the analysis run in SAS.

4.1

Data Dictionary
Table 4.1: Data Dictionary for the data used for SAS modeling

Variable Type

Variable Code

Variable Description

Indicator

Year

Year Number

Tot_Accidents

Total recorded Accidents

Dependent

Fatalities

Total Fatalities in the recorded Accidents

Variables

Tot_Injuries

Total Injuries in the recorded Accidents

Non_Injuries

Total Non-Injuries in the recorded Accidents

Reg_Veh

Total Registered Vehicles in the given year

Tot_Drivers

Total Drivers in the given

func_total

Total Vehicle Miles Travelled (VMT)

func_intrst

VMT on interstate highways

func_arterial

VMT on arterials

GDP

Gross Domestic Product

Male_Driver_%

Percentage of Male Drivers among Total Drivers

Explanatory
Variables

Under_25

Over_65

Speed

Percentage of Drivers under 25 years of age among Total
Drivers
Percentage of Drivers over 65 years of age among Total
Drivers
85th Percentile Speed of all vehicles travelling in the given year The following Chapter presents the results for the analysis of the data discussed above following the modeling methodology given in Chapter 3.

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M.Tech Project Thesis 2015
CHAPTER-5
RESULTS
5.1 Analysis for USA data
The time trend for total accidents, total fatalities, total injuries and total non-injuries, for the consolidated data of United States, are shown in Figure 5.1 to Figure 5.4.
It is to be noted that the data used for the graphs here have been normalized with population i.e. every parameter is in its per capita value.

0.25

0.2

0.15

0.1

0.05

0
1970

1975

1980

1985

1990

1995

2000

2005

Figure 5.1: Time Trend of Total Accidents in the USA

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2010

2015

M.Tech Project Thesis 2015

0.25

0.2

0.15

0.1

0.05

0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

2010

2015

Figure 5.2: Time Trend of Total Fatalities in the USA
0.12

0.1

0.08

0.06

0.04

0.02

0
1970

1975

1980

1985

1990

1995

2000

2005

Figure 5.3: Time Trend of Total Injuries in the USA

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M.Tech Project Thesis 2015
0.45
0.4
0.35
0.3

0.25
0.2
0.15
0.1
0.05
0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.4: Time Trend of Total Non-Injuries in the USA
As can be seen from Figure 5.1 to Figure 5.4, the Total Accidents, Total Fatalities and
Total Non-Injuries follow the same trend, while the Total Injuries follow a different trend.
Thus, for the USA data two separate analyses were done; one for Total Fatalities and other for Total Injuries. It is to be noted that for the analysis of Total Fatalities, 85th percentile speed featured as a significant variable but the data for the same was available only till 1993. Hence, for Total Fatalities, further two analyses were done; one from 19751993 and other from 1975-2012. The results for the aforementioned analyses are presented in Table 5.1 to Table 5.3.
Table 5.1: ARIMAX analysis results for Total Fatalities in USA from 1975-1993
Total Fatalities (1975-1993) β-coefficient t-statistic

Significance

Constant

0.10978

1.66

0.0965

AR1

-0.4764

-1.91

0.0565

Reg_Veh

0.54116

3.89

<0.0001

VMT
Speed

0.0065097

7.16

<0.0001

0.003458

1.74

0.0818

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M.Tech Project Thesis 2015
Table 5.2: ARIMAX analysis results for Total Fatalities in USA from 1975-2012
Total Fatalities (1975-2012) β-coefficient t-statistic

Significance

Constant

0.19569

4.34

<0.0001

AR1

-0.52617

-0.2

0.0014

Over_65

-0.01516

-5.2

<0.0001

Reg_Veh

0.2639

3.92

<0.0001

VMT

0.0009032

1.96

0.0497

Table 5.3: ARIMAX analysis results for Total Injuries in USA from 1975-2012
Total Injuries β-coefficient t-statistic

Significance

Constant

0.08444

6.12

<0.0001

AR1

-0.58192

-3.77

0.0002

VMT
Func_Arterial

0.0054511

2.9

0.0037

0.01107

3.54

0.0004

Over_65

-0.000276

-1.7

0.0896

Reg_Veh

0.11772

2.52

0.0116

As can be drawn from these results, the First Order Auto-Regressive Term has a negative relationship with the dependent variables which shows that the road users as well as the policy makers learn from the past performance of the roads in terms of safety. Thus, the road users aim to maintain safe operations and the policy makers tend to improve upon the traffic policy and regulations in an attempt to improve safety in the future.
The Registered Vehicles and Vehicle Miles Travelled (VMT) have a positive effect on the dependent variables which goes in line with logical judgment as more the registered vehicles, more will be the number of vehicles on the road and more the VMT, more will be the average time for which those vehicles will be on the road. Both of the above will lead to an increase in the dependent variables.
In an accident, speed plays a major role in distinguishing any injury as a fatality or a nonfatality by affecting the severity of the impact. Hence, the 85th Percentile Speed has a significant effect on Total Fatalities and not on Total Injuries.

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Aged drivers, with years of practice behind the wheels, maintain extra caution while driving resulting in low infarctions and thus an increment in their percentage reduces the possibility of an accident, fatality or injury. This justifies a negative relationship of driver percentage over 65 years of age with the dependent variables. Thus, driver licensing laws for older drivers can be made less stringent.
Finally, arterials being high speed facilities with greater percentage of heavy vehicles, an increase in the Vehicle Miles Travelled on the arterials imply an increased possibility of injuries. Thus, it would be advisable to improve highway patrol on arterials and improve mobility on sub-arterials or collector roads so as to reduce the traffic on arterials.
After analyzing the results of the aforementioned ARIMAX analysis, it would be informative to assess the individual time trends of significant explanatory variables and correlate them with time trends of the dependent variables. The trends are given in Figure
5.5 to Figure 5.9.
0.9

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1970

1975

1980

1985

1990

1995

2000

2005

2010

Figure 5.5: Time Trend of Total Registered Vehicles in the USA

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M.Tech Project Thesis 2015
12

10

8

6

4

2

0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.6: Time Trend of Total Vehicle Miles Travelled in the USA
57.5

57

56.5

56

55.5

55

54.5
1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

Figure 5.7: Time Trend of 85th Percentile Speed of Vehicles travelling in the USA

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M.Tech Project Thesis 2015
18%

16%

14%

12%

10%

8%

6%
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.8: Time Trend of the Percentage of Drivers over the age of 65 in the USA
3.5

3

2.5

2

1.5

1

0.5

0
1970

1975

1980

1985

1990

1995

2000

2005

2010

Figure 5.9: Time Trend of Vehicle Miles Travelled on Arterials in the USA

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M.Tech Project Thesis 2015
First analysing the time trend of Total Fatalities, we have a sharp decrease in the trend in
1979, 1988 and 2006, and an increase in the trend in 1984. Following the year 1979, as can be seen from the graph of its explanatory variables, there has been a gradual increase in the Vehicle Miles Travelled and Number of Registered Vehicles but the 85th Percentile
Speed soared down bringing down the overall number of fatalities. Around the year 1983, there has been a noticeable increase in the 85th Percentile Speed, VMT and Number of
Registered Vehicles, which led to the increase in the Total fatalities in that period. In
1988, even though all of the explanatory variables have seen a gradual increase in their values, the Total Fatalities decreased. This can be attributed to the fact that in the immediate preceding year, the Number of Fatalities reached a 5 year high and the Firstorder Autoregressive Term led to the decrease in fatalities in the subsequent years.
Finally, following the year 2006, the US economy took a hit because of the economic depression and this led to a decrease in the Total Registered Vehicles and the VMT, but the Percentage of Drivers above 65 years of age started increasing at a higher rate. It is also to be noticed that the year 2006 saw a 15 year high in the Number of Fatalities leading to the First Order Auto-Regressive term affecting the fatalities in the subsequent years. The above two factors, summed together led to the decrease in the fatalities in
2006.
For the time trend of Total Injuries, we can see a sharp decrease in 1985 and 2006. In
1985, the Total Injuries saw an over 10 year high and thus the road users and the policy makers improved the highway safety practices i.e. the First-Order Auto Regressive term led to the decrease in the Total Injuries. Following the year 2006, because of the reasons mentioned previously, the Total Registered Vehicles and the VMT decreased and the
VMT on the arterials dropped heavily as the high profile travels reduced due to poor economy. This along with the fact that the Percentage of Drivers above 65 years of age started increasing at a higher rate caused the Total Injuries to drop down significantly in this year.
The aforementioned observations compels for a look into the policies and legislations that have been implemented in the United States over the years which led to the changes in the dependent variables seen before. The following paragraphs discuss the policies that

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M.Tech Project Thesis 2015 affected the dependent variables by causing the explanatory variables to change and also other policies that directly influenced the trend of the dependent variables. The policies are discussed around the years of significant change in the dependent variable as given previously i.e. years 1979, 1985-1988, 1993 and 2006
1979:


Alcohol abuse treatment program for drunk drivers



Legislation to reduce the minimum allowable Blood Alcohol Content (the limit varied from state to state)



“Implied Consent Law” stating a chemical test on subjective observation of
Driving Under Influence (DUI)



Establishment of 21 years as the minimum drinking age thus reducing DUIs



Introduction of Fatal Accident Reporting System (FARS) and National Accident
Reporting System (NARS) leading to increased assessment of the causes of accidents and improved mobility towards taking effective steps to reduce these numbers 

Data collection concerning any accident started noting the primary collision factor in fatal accidents



NHTSA required speedometers to have special emphasis on the number 55mph
(speed limit) and 85mph (maximum speed)



Reconsideration of motorcycle helmet laws by states in lieu of the centre withholding federal aid highway construction funds



Legislation mandating a prison sentence for an accident involving highway workers, thus ensuring safe driving on construction zones



Speeding tickets double or triple in construction zones, thus ensuring lower speeds on construction zones



Using cell phones on construction zones was prohibited



Texting while driving prohibited



Required emergency vehicles to have a siren which should be kept on during times of emergency (except police vehicles)

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M.Tech Project Thesis 2015


It was made an offense to put billboards which are in shape, colour or wording, similar to traffic signs



Prohibition of speed limits higher than 55 mph in some states and 50 mph in others 1985-1988:


U-turns on highways were made allowed only on openings provided in the medians 

Revision of penalty structure for DUIs, in which a minimum jail sentence was made mandatory



Heightened media and public attention to DUI problem and expanded the Crime
Victim Compensation Act to include DUI



Sobriety checks were organized at regular intervals for drivers with multiple DUIs



For driver <21 years of age, driving privileges were revoked on 2nd DUI for 3 years and on 3rd DUI for 6 years



Several social groups like RID and MADD came up against DUI and an STOPDWI legislation was launched



Speed limit raised to 65 mph on rural interstate highways in many states



Minimum speed limits were set for some highways



Seat belts became mandatory and police officers were granted power to ticket someone for not wearing seat belts



Juvenile drivers‟ license acquisition laws were made more stringent pertaining to which drivers‟ recklessness was avoided through sufficient knowledge of driving laws 

Texting was made allowable if done from a hand held device



Excessive loading of vehicles such that it starts obstructing with peripheral vision was barred



Pedestrians, animal drawn vehicles, bicycles and pushcarts on express and interstate route highways was prohibited

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M.Tech Project Thesis 2015


Drivers must stop for a school bus displaying at least 1 flashing red light while picking up or dropping children

1993:


Under the National Highway Designation Act, the states were allowed to set their own speed limits



Universal Helmet Law was introduced after a study by Kraus et al. which increased use of helmets from 50% to over 99%



Increased public education on use of safety belt and against DUI



Seat belts was made a primary law i.e. the police can charge a vehicle with violation solely for non-compliance of seat belt law without any added infarction



Law reinforcement was improved through incentives and rewards, for e.g. the drivers were informed that their licenses would be extended for 12 months for free if they maintained a clean record in the forthcoming year

2006:


It was left to the decision of the police officer to decide whether to give an option of a urine test to a person arrested for DUI



Choose Clean Cars Act was launched wherein vehicles with Clean Air Vehicle
Sticker gets free access to carpool lanes



Driverless autonomous vehicles were tested and licensed on some roads



Less driver licenses were awarded as licensure documents and proof clearance were made more stringent



Automated traffic enforcement systems were brought into practice



Child safety seat requirement for children <8 years of age



Riding an ROV with seat position altered was prohibited



Vehicles with Ignition Interlock Devices were introduced



Cell phones use while driving including a hand held device was prohibited for drivers <19 years of age



Texting while driving was made a primary offense

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M.Tech Project Thesis 2015


Driving in curfew hours (11 p.m. to 6 a.m.) was prohibited for drivers <18 years of age



Vision and road test was made mandatory while renewing license for drivers aged over 75 years



For drivers aged 21-80 years, license renewal was to be done every 4 years, for drivers aged 81-86 years, license renewal was to be done every 2 years and for drivers aged above 86, license was to be renewed annually



Time allotted for the police to report to the crash site was reduced from 1 hour to
30 minutes

The following sections give a similar accident analysis for 5 states representing various regions of the USA. The states are; California, Washington, Illinois and New York.

5.2 Analysis for California data
The time trend for total accidents, total fatalities, total injuries and total non-injuries, for the accident data of California, are shown in Figure 5.10 to Figure 5.13. Here the data have also been normalized on population.
0.00025

0.0002

0.00015

0.0001

0.00005

0
1970

1975

1980

1985

1990

1995

2000

2005

Figure 5.10: Time Trend of Total Accidents in California

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0.00025

0.0002

0.00015

0.0001

0.00005

0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

2010

2015

Figure 5.11: Time Trend of Total Fatalities in California
0.00014

0.00012

0.0001

0.00008

0.00006

0.00004

0.00002

0
1970

1975

1980

1985

1990

1995

2000

2005

Figure 5.12: Time Trend of Total Injuries in California

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0.00045
0.0004
0.00035
0.0003

0.00025
0.0002
0.00015
0.0001
0.00005
0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.13: Time Trend of Total Non-Injuries in California
Similar to the consolidated USA data, the Total Accidents, Total Fatalities and Total NonInjuries follow the same trend, while the Total Injuries graph follow a different trend.
Thus in a similar manner, two separate analyses were done; one for Total Fatalities and other for Total Injuries and further two analyses for Fatalities were done; one from 19751993 and other from 1975-2012. The results for these analyses are presented in Table 5.4 to Table 5.6.
Table 5.4: ARIMAX analysis results for Total Fatalities in California from 1975-1993
Total Fatalities (1975-1993) β-coefficient t-statistic

Significance

Constant

-0.0008596

-4.23

<0.0001

MA1

0.001082

6.27

<0.0001

AR1

-0.96155

-5.53

<0.0001

Tot_Drivers
Reg_Veh
Func_Arterial
Speed

1.34974

3.82

<0.0001

0.26638

9.96

<0.0001

-0.008676

1.52

0.1288

1.03E-07

1.92

0.0757

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Table 5.5: ARIMAX analysis results for Total Fatalities in California from 1975-2012
Total Fatalities (1975-2012) β-coefficient t-statistic

Significance

Constant

-0.001093

-5.38

0.0015

MA1

0.001727

10.01

<0.0001

AR1

-2.663824

-15.32

<0.0001

Reg_Veh

0.5360093

1.517

0.0948

Func_Arterial

0.3492894

13.06

<0.0001

Func_Intrst

0.012689

2.223

0.0384

Table 5.6: ARIMAX analysis results for Total Injuries in California from 1975-2012
Total Injuries β-coefficient t-statistic

Significance

Constant

-0.0006582

-3.091

0.0268

MA1

0.99853

17.58

0.0002

AR1

-0.67231

-25.87

<0.0001

Tot_Drivers

0.21469

2.452

0.0458

Reg_Veh

0.06168

2.074

0.0649

VMT

0.23594

19.2

<0.0001

Under_25

0.00245

21.62

<0.0001

As can be drawn from the results shown above, the First Order Auto-Regressive Term has a negative relationship with the dependent variables for the same reasons of the road users and the policy makers learning from the past performance of the roads in terms of safety and improving safety.
The Moving Average term has a positive association with the dependent variables. This shows that if model errors for any year have a high correlation with the errors for the previous year, then the model will over-predict the results for that year.
The Registered Vehicles, Total Drivers and Vehicle Miles Travelled (VMT) have a positive effect on the dependent variables for the same reasons as in the analysis for USA data i.e. the first two increases the number of vehicles on the road and VMT increases the average time for which those vehicles will be on the road.

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Drivers under 25 years of age are inexperienced and are in a rush to get the driver‟s license and take the vehicle on the road. Thus, they tend to entertain dangerous maneuvers, like driving on a high speed facility, without having acquired much driving finesse by driving on low speed facilities. Hence, an increase in their percentage tends to increase the possibility of an accidents and injuries, and in extreme cases, fatality. To encounter this, the driver licensing laws were made much stricter at various times.
Interstate being high volume, high Level of Service facilities, an increase in VMT on interstate highways leads to increasing possibility of an accident and subsequently injuries happening. But since they are relatively lower speed facilities, the accident generally results in injuries only and thus Interstate VMT is a significant determiner of Total
Injuries and not of Fatalities. Finally, arterials as discussed previously, being high speed facilities with greater percentage of heavy vehicles, an increase in their VMT would imply an increase in the possibility of injuries.
Individual time trends of the significant explanatory variables and their correlation with the time trends of the original dependent variables are given in Figure 5.14 to Figure 5.20.
0.001
0.0009
0.0008
0.0007
0.0006
0.0005
0.0004
0.0003
0.0002
0.0001
0
1970

1975

1980

1985

1990

1995

2000

2005

2010

Figure 5.14: Time Trend of Total Registered Vehicles in California

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0.00067
0.000665
0.00066
0.000655
0.00065
0.000645
0.00064
0.000635
0.00063

0.000625
0.00062
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

2010

2015

Figure 5.15: Time Trend of Total Drivers in California
0.004
0.0035
0.003
0.0025

0.002
0.0015
0.001
0.0005
0
1970

1975

1980

1985

1990

1995

2000

2005

Figure 5.16: Time Trend of Vehicle Miles Travelled on Arterials in California

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59

58.5

58

57.5

57

56.5

56
1970

1975

1980

1985

1990

1995

Figure 5.17: Time Trend of the 85th Percentile Speed in California
25

20

15

10

5

0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.18: Time Trend of the Percentage of Drivers below the age of 25 in California

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0.003

0.0025

0.002

0.0015

0.001

0.0005

0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.19: Time Trend of Vehicle Miles Travelled on Interstate Routes in California
0.01
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002

0.001
0
1970

1975

1980

1985

1990

1995

2000

2005

2010

Figure 5.20: Time Trend of Total Vehicle Miles Travelled in California

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First analyzing the time trend of Total Fatalities, we have a sharp decrease in the trend in
1979, 1988 and 2006, and a noticeable increase in the trend in 1984 and 1999. Following the year 1979, although VMT on arterials increased but the 85th percentile speed
(because of speed limit restrictions of 55 mph in the United States) and Total Drivers sharply decreased and Total Registered Vehicles slightly decreased. It can also be seen that the Total Fatality numbers having reached its peak, the Auto Regressive term also played a role in decreasing the fatalities in the successive years. Thus, the highway patrol in California was increased in the following years and other legislations as mentioned in the previous section were passed. In 1984, the speed on Interstate highways were increased which led to an increased 85th percentile speed. This increase in 85th percentile speed combined with an increase in Total Drivers and VMT on arterials, caused the fatalities to increase. 1988, the Total Fatalities saw a considerable drop. This is owing to the fact that the Total Drivers in California decreased significantly because of stringent licensing laws to minors following a sharp increase in Total Drivers in the preceding years. This fact also led to a drop in the Total Driver Percentage below 25 years of age.
In 1999, Total Drivers significantly increased along with an increase in the VMT, thus leading to increased fatalities in this year. Finally, in the year 2006, owing to the same reason of economic depression as the USA analysis, Registered Vehicles and Vehicle
Miles Travelled decreased which led to a drop in the Fatalities.
For the time trend of Total Injuries, we can see a sharp drop in 1988 and 2006 and a noticeable increase in 1984 and 1999. In 1984, the Total VMT and Total Drivers increased significantly leading to an increase in the Total Injuries. In 1988 however, Total
Injuries trend saw an over 13 year high thus the Auto-Regressive term came into play.
This combined with a drop in Total Drivers and the Percentage of Drivers under 25 years of age, led to a decrease in the Total Injuries. In 1999, similar to the case of Total
Fatalities, due to the increase in the Total Driers and VMT, Total Injuries increased. In the year 2006, because of the same reasons for the drop in Total Fatalities, Total Injuries also decreased.

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4.3 Analysis for Illinois data
The normalized time trend for total accidents, total fatalities, total injuries and total noninjuries, for the accident data of Illinois, are shown in Figure 5.21 to Figure 5.24.
0.00018
0.00016
0.00014
0.00012
0.0001
0.00008
0.00006
0.00004
0.00002
0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

2010

2015

Figure 5.21: Time Trend of Total Accidents in Illinois
0.0002
0.00018
0.00016
0.00014
0.00012
0.0001
0.00008
0.00006
0.00004
0.00002
0
1970

1975

1980

1985

1990

1995

2000

2005

Figure 5.22: Time Trend of Total Fatalities in Illinois

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0.00009
0.00008
0.00007
0.00006

0.00005
0.00004
0.00003
0.00002
0.00001
0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

2010

2015

Figure 5.23: Time Trend of Total Injuries in Illinois
0.0004
0.00035
0.0003
0.00025

0.0002
0.00015
0.0001
0.00005
0
1970

1975

1980

1985

1990

1995

2000

2005

Figure 5.24: Time Trend of Total Non-Injuries in Illinois

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Results for the analysis of Total Injuries from 1975-2012 and Total Fatalities from 19751993 (with speed) and 1975-2012 (without speed) are presented in Table 5.7 to Table 5.9.
Table 5.7: ARIMAX analysis results for Total Fatalities in Illinois from 1975-1993
Total Fatalities (1975-1993) β-coefficient t-statistic
Significance
Constant
-0.0000796
-0.6
0.5462
MA1

-0.69185

-5.26

<0.0001

AR1

-0.56748

-6.35

<0.0001

Tot_Drivers
Under_25
Reg_Veh
Func_Arterial
Speed

0.17993

2.55

<0.0001

0.00748

4.11

<0.0001

0.10941

8.97

<0.0001

0.00782

1.72

0.085

0.00665

1.83

0.0824

Table 5.8: ARIMAX analysis results for Total Fatalities in Illinois from 1975-2012
Total Fatalities (1975-2012) β-coefficient t-statistic
Significance
0.0002493
1.879
0.0785
Constant
MA1

3.5342223

26.87

<0.0001

AR1

1.9848395

22.21

<0.0001

Tot_Drivers

0.2290403

3.246

0.0238

Reg_Veh

0.0032

17.58

0.0002

Func_Arterial
Func_Intrst

0.0247972

2.033

0.0675

0.011486

2.526

0.0429

Table 5.9: ARIMAX analysis results for Total Injuries in Illinois from 1975-2012
Total Injuries β-coefficient t-statistic
Significance
Constant

0.0001142

1.69

0.0907

MA1
AR1

-0.99987

-6.78

<0.0001

-0.90881

-3.11

<0.0001

Tot_Drivers

0.09461

4.23

<0.0001

Reg_Veh

0.03329

5.05

<0.0001

Func_Intrst

0.01359

3.03

0.0025

Under_25

0.049691

6.84

<0.0001

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The First Order Auto-Regressive and First Order Moving Average terms have a negative relationship with the dependent variables as in the previous analyses.
Here an interesting observation is that VMT on arterials is affecting only the Fatalities, this may be due to the fact that the speed limits in Illinois was increased one too many times and because of which an accident on an arterial resulting in a fatality would have been more common than just an injury. Similar is the reason for the fact that interstate
VMT has become an explanatory variable for Total Fatalities in Illinois unlike any of the previous analyses. Speeds on interstate highways were also increased and because of which accidents on interstate highways which predominantly results in injuries only, started resulting in fatalities in a high number.
Drivers under 25 years of age, for reasons stated previously regarding their inexperience and tendency towards unsafe maneuvers, combined with the relatively higher speed facilities, are affecting the Total Fatalities and Total Injuries positively.
Individual time trends of the significant explanatory variables and their correlation with the time trends of the original dependent variables are given in Figure 5.25 to Figure 5.30.
0.0009

0.0008
0.0007
0.0006
0.0005
0.0004
0.0003
0.0002
0.0001
0
1970

1975

1980

1985

1990

1995

2000

2005

2010

Figure 5.25: Time Trend of Total Registered Vehicles in Illinois

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0.00066
0.00065
0.00064
0.00063
0.00062

0.00061
0.0006
0.00059
0.00058
0.00057
0.00056
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

2010

2015

Figure 5.26: Time Trend of Total Drivers in Illinois
0.0025

0.002

0.0015

0.001

0.0005

0
1970

1975

1980

1985

1990

1995

2000

2005

Figure 5.27: Time Trend of Vehicle Miles Travelled on Arterials in Illinois

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57.5

57

56.5

56

55.5

55

54.5

54
1970

1975

1980

1985

1990

1995

2000

Figure 5.28: Time Trend of the 85th Percentile Speed in Illinois
25

20

15

10

5

0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.29: Time Trend of the Percentage of Drivers below the age of 25 in Illinois

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0.003

0.0025

0.002

0.0015

0.001

0.0005

0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.30: Time Trend of Vehicle Miles Travelled on Interstate Routes in Illinois
On analysing the trend of Total Fatalities, it can be seen that there is a sharp drop in the fatalities in the years 1979, 1988 and 2006 and a rise in the same in 1985. For the trend of
Total Injuries, there is a sharp drop in the years 1979 and 1988, and a rise in the year
1985. These years are in close association with the fatality trend for the entire USA data except for the injuries in 1985, thus suggesting that Illinois is one of the states that is a close representative of the country in terms of Fatality trend and thus can be used as a promising location for future data collection attempts regarding the subject.
Coming back to the accident analysis, it can be seen that following 1979, all the explanatory variables started decreasing, except for the Total Drivers, which remained almost constant. This led to a fall in the Fatalities as well as the Total Injuries. Apart from the explanatory variables, as discussed in the USA analysis, the year 1979 saw the formulation of several new policies owing to the sharply rising Accidents and Fatalities.
Policies related to helmet laws, DUI laws, formulation of FARS led to a drop in the accident numbers and traffic accident related injuries in the subsequent years. In 1985, the increase in the dependent variables can be attributed to the sharp increase in Total Drivers and VMT on Interstate highways but an interesting observation is the increase in the

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M.Tech Project Thesis 2015 speed limit in Illinois from 55mph to 65mph leading to an increase in the 85th percentile speed. This caused the per capita fatality and injury numbers to increase by around 15%.
Following these observations, the speed limits were reverted back on many highways in
Illinois. Resulting to this revision of speed limits and addition of some other laws like compulsory seat belts and DUI penalty revision, the fatalities and injuries saw a decline in
1988. In 2006, although the Total Drivers and Registered Drivers saw a decline in the
USA, in Illinois they have increased which is a very interesting fact because even with these variables increasing, the fatalities have actually decreased. The VMT on arterials and interstates have decreased which definitely has a role to bring the Total Fatalities down but that cannot be the sole contributor considering their β-coefficients. Therefore, there must have been some other factors which haven‟t been taken into account in this research. Such factors could be speed for which data wasn‟t available beyond 1993, percentage of drunk drivers, climatic conditions and geometric parameters of the road.

4.4 Analysis for New York data
The normalized time trend for total accidents, total fatalities, total injuries and total noninjuries, for the accident data of New York, are shown in Figure 5.31 to Figure 5.34.
0.00014
0.00012
0.0001
0.00008
0.00006
0.00004
0.00002
0
1970

1975

1980

1985

1990

1995

2000

2005

Figure 5.31: Time Trend of Total Accidents in New York

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0.00016
0.00014
0.00012
0.0001
0.00008
0.00006
0.00004
0.00002
0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

2010

2015

Figure 5.32: Time Trend of Total Fatalities in New York
0.00009
0.00008

0.00007
0.00006
0.00005
0.00004
0.00003
0.00002
0.00001
0
1970

1975

1980

1985

1990

1995

2000

2005

Figure 5.33: Time Trend of Total Injuries in New York

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0.0003

0.00025

0.0002

0.00015

0.0001

0.00005

0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.34: Time Trend of Total Non-Injuries in New York
Results for the analysis of Total Injuries from 1975-2012 and Total Fatalities from 19751993 (with speed) and 1975-2012 (without speed) are given in Table 5.10 to Table 5.12.
Table 5.10: ARIMAX analysis results for Total Fatalities in New York from 1975-1993
Total Fatalities (1975-1993) β-coefficient t-statistic

Significance

Constant

-0.0004474

-3.17

0.0017

MA1

-0.99925

-6.58

<0.0001

AR1

-0.57589

-4.36

<0.0001

Male_Driver_%

0.0087

5.22

<0.0001

Reg_Veh

0.01686

4.09

<0.0001

Func_Total

0.0005504

2.636

0.0594

Speed

0.0187

2.584

0.0614

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Table 5.11: ARIMAX analysis results for Total Fatalities in New York from 1975-2012
Total Fatalities (1975-2012) β-coefficient t-statistic
Significance
-0.000388
-2.749
0.0354
Constant
-3.476114
-22.89
<0.0001
MA1
-4.883177
-36.97
<0.0001
AR1
0.001477
8.863
0.0015
Male_Driver_%
0.0098233
2.383
0.0487
Reg_Veh
0.0003468
1.661
0.0977
Func_Total
Table 5.12: ARIMAX analysis results for Total Injuries in New York from 1975-2012
Total Injuries β-coefficient t-statistic
Significance
0.0002221
3.88
0.0001
Constant
-0.99973
-6.53
<0.0001
MA1
-0.27494
-5.24
<0.0001
AR1
-0.00536
-3.93
<0.0001
Male_Driver_%
0.4061
7.56
<0.0001
Tot_Drivers
0.7007
6.88
<0.0001
Reg_Veh
0.05515
20.78
<0.0001
Func_Intrst
The First Order Auto-Regressive and First Order Moving Average terms have a negative relationship with the dependent variables as in the previous analyses.
Here Male Driver Percentage is affecting the Total Fatalities positively while Total
Injuries negatively. It is difficult to comment on this observation because for such variables, there are many factors in play because of human behavior, like tendency towards rash driving, physical potency etc. These factors vary from region to region and a thorough regional data collection and analysis have to be done separately. This is beyond the scope of the current research but can be done for micro level studies in future.
Interstate VMT is an explanatory variable for Total Injuries and is affecting it positively.
This follows same reasoning as discussed previously, that Interstate highways are low speed high Level of Service highways and hence, accidents result in more injuries without affecting fatalities. Total Drivers, Registered Vehicles and Total VMT, increase the total number of vehicles and their duration on the road respectively and thus, have a positive relationship with the dependent variables.

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Individual time trends of the significant explanatory variables and their correlation with the time trends of the original dependent variables are given in Figure 5.35 to Figure 5.40.
0.00065

0.0006

0.00055

0.0005

0.00045

0.0004
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.35: Time Trend of Total Registered Vehicles in New York
0.0006
0.00058
0.00056
0.00054
0.00052

0.0005
0.00048
0.00046
0.00044
0.00042
0.0004
1970

1975

1980

1985

1990

1995

2000

2005

Figure 5.36: Time Trend of Total Drivers in New York

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0.0075
0.007
0.0065
0.006
0.0055
0.005
0.0045
0.004
0.0035
0.003
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.37: Time Trend of Total Vehicle Miles Travelled in New York
58
57.5
57
56.5
56
55.5
55
54.5
54
1970

1975

1980

1985

1990

Figure 5.38: Time Trend of the 85th Percentile Speed in New York

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57

56

55

54

53

52

51
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

2010

2015

Figure 5.39: Time Trend of the Percentage of Male Drivers in New York
0.0015
0.0014
0.0013
0.0012
0.0011
0.001
0.0009

0.0008
0.0007
0.0006
0.0005
1970

1975

1980

1985

1990

1995

2000

2005

Figure 5.40: Time Trend of Vehicle Miles Travelled on Interstate Routes in New York

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The Total Fatalities in New York has seen a decrease in 1980 and 1988 and an increase in
1985 which is similar to the previous analyses that we have seen. But the Total Injuries unlike the previous analyses has seen a sharp increase in 1980 and a sharp decrease in
1985. In 1980, the Male Driver Percentage decreased significantly. As can be seen from the β-coefficients of Fatalities and Injuries, Male Driver Percentage affects Fatalities positively and Injuries negatively. Hence, a sharp decrease in the Male Driver Percentage heavily contributed to the increase in the Total Injuries and decrease in the Total
Fatalities. It can also be observed that the Vehicle Miles Travelled on interstate highways also increased a lot. New York being a city with immense population and that added to the drivers coming to New York from other cities will result in a lot of drivers running on the interstate highways. This would increase the Level of Service of those highways thus reducing the probability of an accident resulting in a fatality but increase one resulting in an injury. Hence, due to the combined effect of a heavy increase in Male Driver
Percentage and VMT on interstate highways and a simultaneous increase in the Total
Registered Vehicles and Total Drivers in USA, Total Injuries increased in 1980. Due to federal action on controlling speed limits, in 1980 speed limit, as was discussed in a previous section, was restricted to 55 mph but in New York the limit was further decreased to 50 mph. This caused the 85th percentile speed to decrease. This, in combination with the decrease in the Male Driver Percentage caused the Total Fatalities to decrease.
Beyond 1985, the Male Driver Percentage still kept decreasing but the 85th percentile speed increased in lieu of the increase in the speed limits. Along with this, the Total
VMT, Total Registered Vehicles and Total Drivers also increased. Thus, the Total
Fatalities increased after 1985. However, the Total injuries, despite of all its explanatory variables bringing it up, has decreased. This can be attributed to the effect of AutoRegressive and Moving Average terms because of an all time highest Total Injuries. In
1981, Mothers Against Drunk Driving (MADD) campaign and STOP-DWI legislation was launched. By 1985, these had spread far and wide. Apart from this, non-compliance to traffic laws, which was a big problem a priori, was reduced by effectively organized highway patrol in New York. These caused the Total Injuries to decrease in 1985.

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In 1988, the 85th Percentile Speed decreased following a legislation of a compulsory 15 day jail sentence for 11 mph over the speed limit which was set to 55 mph. This decrease along with a decrease in the Male Driver Percentage and Total Registered Vehicles led to a drop in the Total Fatalities in this year.

4.5 Analysis for Washington data
The normalized time trend for total accidents, total fatalities, total injuries and total noninjuries, for the accident data of Washington, are shown in Figure 5.41 to Figure 5.44.
0.00025

0.0002

0.00015

0.0001

0.00005

0
1970

1975

1980

1985

1990

1995

2000

2005

2010

Figure 5.41: Time Trend of Total Accidents in Washington

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0.0003

0.00025

0.0002

0.00015

0.0001

0.00005

0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

2010

2015

Figure 5.42: Time Trend of Total Fatalities in Washington
0.00012

0.0001

0.00008

0.00006

0.00004

0.00002

0
1970

1975

1980

1985

1990

1995

2000

2005

Figure 5.43: Time Trend of Total Injuries in Washington

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0.0005
0.00045
0.0004
0.00035
0.0003

0.00025
0.0002
0.00015
0.0001
0.00005
0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.44: Time Trend of Total Non-Injuries in Washington
Results for the analysis of Total Injuries from 1975-2012 and Total Fatalities from 19751993 (with speed) and 1975-2012 (without speed) are presented in Table 5.13 to Table
5.16.
Table 5.13: ARIMAX analysis results for Total Fatalities in Washington from 1975-1993
Total Fatalities (1975-1993) β-coefficient t-statistic

Significance

Constant

0.00002

4.09600

0.00230

MA1

-0.99997

-6.28000

<0.0001

AR1

-0.96112

-5.59000

<0.0001

Under_25
Over_65
Func_Arterial
Speed

0.00198

1.54200

0.08350

-0.00686

-4.03000

0.00250

0.00826

1.85900

0.05270

0.55241

2.93000

0.00340

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Table 5.14: ARIMAX analysis results for Total Fatalities in Washington from 1975-2012
Total Fatalities (1975-2012) β-coefficient t-statistic

Significance

Constant

0.00001

1.72200

0.06440

MA1

1.31143

-8.23600

<0.0001

AR1

1.91536

-11.14000

<0.0001

Under_25

0.00570

4.44200

0.00150

Over_65

0.00248

-1.45500

0.09450

Func_Arterial

0.00980

2.20600

0.03160

Table 5.15: ARIMAX analysis results for Total Injuries in Washington from 1975-2012
Total Injuries β-coefficient t-statistic

Significance

Constant
MA1

-0.00009

-1.71000

0.08570

-0.99971

-8.79000

<0.0001

AR1

-0.53711

-4.89000

<0.0001

Male_Driver_%

0.01438

1.65000

0.08380

Under_25

0.00748

6.38000

<0.0001

Reg_Veh

0.33844

15.16000

<0.0001

The First Order Auto-Regressive and First Order Moving Average terms have a negative relationship with the dependent variables as in the previous analyses.
Drivers under 25 years of age due to inexperience and maneuvers that lack finesse in contrast to the drivers over 65 years of age due to experience behind the wheels and safe maneuvering of the vehicle, have got a positive and negative relationship with the dependent variables respectively.
Finally, as in the previous analyses, the increase in the Registered Vehicles, VMT on
Arterials and 85th Percentile Speed positively affects the dependent variables.
An important observation is that Total Drivers, which featured in all the previous analyses hasn‟t featured here. This is due to the fact that Washington has a relatively lower population because of which the correlation between Total Registered Vehicles, VMT and Total Drivers was very high. Hence, only one of those variables would feature, in this case, the Registered Vehicles in Total Injuries, and VMT on Arterials in Total Fatalities.

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M.Tech Project Thesis 2015
Individual time trends of the significant explanatory variables and their correlation with time trends of the dependent variables are given in Figure 5.45 to Figure 5.50.
0.00095

0.0009

0.00085

0.0008

0.00075

0.0007

0.00065

0.0006
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.45: Time Trend of Total Registered Vehicles in Washington
54.5
54
53.5
53

52.5
52
51.5
51
50.5
1970

1975

1980

1985

1990

1995

2000

2005

2010

Figure 5.46: Time Trend of Percentage of Male Drivers in Washington

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M.Tech Project Thesis 2015
0.003
0.0028
0.0026
0.0024
0.0022

0.002
0.0018
0.0016
0.0014
0.0012
0.001
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.47: Time Trend of Vehicle Miles Travelled on Arterials in Washington
57.5

57

56.5

56

55.5

55

54.5
1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

Figure 5.48: Time Trend of the 85th Percentile Speed in Washington

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M.Tech Project Thesis 2015
25

20

15

10

5

0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.49: Time Trend of the Percentage of Drivers below the age of 25 in Washington
16
14
12
10

8
6
4
2
0
1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Figure 5.50: Time Trend of Percentage of Driver Over 65 year of Age in Washington

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M.Tech Project Thesis 2015
The Total Fatalities trend in Washington has seen a continuous decline over the years, but the significant drops were in years 1979, 1988 and 2006. The Total Injuries also saw a drop in these years but there was also a significant rise in the year 1984. The Percentage of Drivers under 25 years of age and the Male Driver Percentage has continuously declined over the years, while the Percentage of Drivers over 65 years of age has continuously increased. This has played a major role in the continuous drop in the Total
Fatalities and Total Injuries over the years. However for some years beyond 1984, even because of the effect of the aforementioned, there was a simultaneous increase in the
Total Registered Vehicles and Registered Vehicles having a relatively higher βcoefficient brought up the Total Injuries.
The Total Fatalities as mentioned before was brought down by the effect of Percentage of
Drivers under 25 and over 65 years of age and the Male Driver Percentage. But apart from these factors, in 1979 the Total Registered Vehicles and 85th Percentile Speed dropped with an increase in the Vehicle Miles Travelled on Arterials. Total Registered
Vehicles and 85th Percentile Speed having a higher β-coefficient than VMT, brought down the Total Fatalities. Following 1988, the Total Fatalities, the 85th Percentile Speed and the Total VMT on Arterials increased which should have brought up the Total
Fatalities because of relatively higher β-coefficients but it didn‟t. This indicates the significant effect of other variables which haven‟t been considered in this analysis and since, Washington has a relatively lower population, slight change in any of the nonconsidered variables could bring about a drastic change in the dependent variable. Finally in 2006, the Total Registered Vehicles and VMT on Arterials decreased thus dropping the
Total Fatalities.

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M.Tech Project Thesis 2015
CHAPTER-6
SUMMARY
The time trend for Total number of accidents, fatalities, injuries and non-injuries in these accidents have been analysed in this study by developing an ARIMAX model following the Box-Jenkins methodology. The models were developed for consolidated US data and data for states representative of various regions of the United States. These states include;
California, Illinois, New York and Washington. The factors significant for the trend variation have been assessed and the rationale for the same has been explained. Along with this, the road traffic policies and legislations have been mapped with significant fluctuations in the aforementioned time trends.
The analysis results indicate that Total Accidents, Total Fatalities and Total Non-Injuries follow a similar time trend while Total Injuries follow a different trend. Hence, two analyses were done; one for Total Fatalities and other for Total Injuries. In all the datasets it has been observed that for the analysis of Total Fatalities, there has been a significant drop in the number of Fatalities following the years 1979-80, 1988 and 2006 except for the analysis of New York where although the years following 2006 showed a decline but it was a gradual decline. There was a significant rise in the Total Fatalities in 1984-85 for all the datasets except Washington where the trend for Total Fatalities saw a decline throughout and California where there was a rise in 1999 also.
The analysis for Total Injuries presents a mixed behavior, even though the years experiencing significant change were same. In 1979-80, there was a drop in Accident
Injuries in Illinois and Washington but a rise in New York. In 1984-85, there was a drop in Injuries for USA and New York while a rise in all the remaining models analyzed.
There was a drop in Injuries in Illinois in 1988 and a rise in California in 1999. Finally in
2006, there was a drop in Injuries in USA, California and Washington. These observations also show that California, Illinois and New York have witnessed an almost similar trend for both Fatalities and Injuries. The rationale for this mixed behavior has also been presented in the text.

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M.Tech Project Thesis 2015
CHAPTER-7
CONCLUSION
Major findings from this study are as follows:


The First Order Auto-Regressive term is found to be significant in the analysis of all the models developed in this study. Thus, previous year‟s accident numbers/fatalities/injuries/non-injuries affects the same for the current year. This indicates that road users and policy makers learn from their past mistakes, so generally a year with very high accident numbers/fatalities/injuries/non-injuries is followed by a year with their lower values.



The First Order Moving Average Term has also been seen as significant for state level analysis resulting in the inference that the error in the model results for last year affects the dependent variable value for the current year at state level.



Among the other variables 85th percentile speed, VMT, Total Drivers and Total
Registered Vehicles have significant effect on for almost all the analysis and hence are seen as the most important variables to be considered for the data collection for similar studies in future.



The effect of Total Drivers, 85th Percentile Speed and Total Registered Vehicles has always been positive on the dependent variable i.e. if more is the Total Drivers in a particular region more will be the accidents/fatalities/injuries/non-injuries.
The VMT however, being split into Total VMT, VMT on Arterials and VMT on
Interstate Highways, sees a varying relationship with the dependent variables from state to state.



Based on the findings it can also be concluded that The most dominating effect on the dependent variables are laid on by Total Drivers and Vehicle Miles Travelled and the least dominating, by Male Driver Percentage and Percentage of Driver under 25 years of age and over 65 years of age. Regulation of these significantly affecting parameters should be kept in check by efficient policy formulation. For an instance, Total Drivers can be regulated by making the licensing policies more stringent such that either less drivers come on the road or good drivers come on the road or both; VMT on the highway category having a positive relationship

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M.Tech Project Thesis 2015 with the dependent variables can be reduced by redirecting the traffic on other alternative routes.


Finally, it has been seen that the years seeing significant change in the trend of
Total Fatalities and Total Injuries have also witnessed significant change in other extraneous policies. These policies in combination with the analysis results give way for the proper understanding of the aforementioned time trends. Few policies have improved the safety on the road while few have reduced the same. But after taking guidance from past decisions, improvements were made to get the traffic legislations which give an optimum mix between safety and efficiency. In the
Indian scenario many of these policies are absent hence, performing a similar study for India would give the macro level changes that should be made in the traffic operations while at the same time steps should be taken to formulate policies for the aforementioned extraneous variables like seat belt laws, licensing laws, DUI laws, speeding laws, law enforcement etc.

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