📝 Original Info
- Title: Markov switching models: an application to roadway safety
- ArXiv ID: 0808.1448
- Date: 2008-12-09
- Authors: Researchers from original ArXiv paper
📝 Abstract
In this research, two-state Markov switching models are proposed to study accident frequencies and severities. These models assume that there are two unobserved states of roadway safety, and that roadway entities (e.g., roadway segments) can switch between these states over time. The states are distinct, in the sense that in the different states accident frequencies or severities are generated by separate processes (e.g., Poisson, negative binomial, multinomial logit). Bayesian inference methods and Markov Chain Monte Carlo (MCMC) simulations are used for estimation of Markov switching models. To demonstrate the applicability of the approach, we conduct the following three studies. In the first study, two-state Markov switching count data models are considered as an alternative to zero-inflated models for annual accident frequencies, in order to account for preponderance of zeros typically observed in accident frequency data. In the second study, two-state Markov switching Poisson model and two-state Markov switching negative binomial model are estimated using weekly accident frequencies on selected Indiana interstate highway segments over a five-year time period. In the third study, two-state Markov switching multinomial logit models are estimated for severity outcomes of accidents occurring on Indiana roads over a four-year time period. One of the most important results found in each of the three studies, is that in each case the estimated Markov switching models are strongly favored by roadway safety data and result in a superior statistical fit, as compared to the corresponding standard (non-switching) models.
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Deep Dive into Markov switching models: an application to roadway safety.
In this research, two-state Markov switching models are proposed to study accident frequencies and severities. These models assume that there are two unobserved states of roadway safety, and that roadway entities (e.g., roadway segments) can switch between these states over time. The states are distinct, in the sense that in the different states accident frequencies or severities are generated by separate processes (e.g., Poisson, negative binomial, multinomial logit). Bayesian inference methods and Markov Chain Monte Carlo (MCMC) simulations are used for estimation of Markov switching models. To demonstrate the applicability of the approach, we conduct the following three studies. In the first study, two-state Markov switching count data models are considered as an alternative to zero-inflated models for annual accident frequencies, in order to account for preponderance of zeros typically observed in accident frequency data. In the second study, two-state Markov switching Poisson mode
📄 Full Content
arXiv:0808.1448v2 [stat.AP] 8 Dec 2008
MARKOV SWITCHING MODELS:
AN APPLICATION TO ROADWAY SAFETY
A Dissertation
Submitted to the Faculty
of
Purdue University
by
Nataliya V. Malyshkina
In Partial Fulfillment of the
Requirements for the Degree
of
Doctor of Philosophy
December 2008
Purdue University
West Lafayette, Indiana
ii
To my husband Leonid and my parents Nadezhda and Vladimir
iii
ACKNOWLEDGMENTS
First of all, I would like to thank my advisor, Professor Fred Mannering. Without
his interest, encouragement and financial assistance none of this research would be
possible. He supported me during all my three and a half years at Purdue. He also
gave me a lot of freedom in research. I feel very lucky to be his student.
I would like to thank Professor Andrew Tarko, my co-advisor, for his very help-
ful comments and encouragement. I am especially grateful to him for the accident
frequency data that he provided for the study reported in this dissertation.
In addition, I would like to thank Jose Thomaz for preparing the accident severity
data that was used in this study.
I would like to thank Professor Kristofer Jennings and Professor Jon Fricker for
their helpful comments and for carefully reading this dissertation. I also would like to
thank my colleagues and friends for their help and support during my stay on Purdue
campus.
Finally, I feel infinite love and gratitude to my wonderful family – my husband
Leonid, my mother Nadezhda and my father Vladimir. I owe everything I have to
them and to their love and support.
iv
TABLE OF CONTENTS
Page
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vi
LIST OF FIGURES
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
viii
LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
ABSTRACT
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
CHAPTER 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1
Motivation and research objectives
. . . . . . . . . . . . . . . . . .
1
1.2
Organization
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
CHAPTER 2. LITERATURE REVIEW . . . . . . . . . . . . . . . . . . . .
4
2.1
Accident frequency studies . . . . . . . . . . . . . . . . . . . . . . .
4
2.2
Accident severity studies . . . . . . . . . . . . . . . . . . . . . . . .
8
2.3
Mixed studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
CHAPTER 3. MODEL SPECIFICATION . . . . . . . . . . . . . . . . . . .
15
3.1
Standard count data models of accident frequencies . . . . . . . . .
16
3.2
Standard multinomial logit model of accident severities . . . . . . .
19
3.3
Markov switching process
. . . . . . . . . . . . . . . . . . . . . . .
20
3.4
Markov switching count data models of annual accident
frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
3.5
Markov switching count data models of weekly accident
frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
3.6
Markov switching multinomial logit models of accident
severities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
CHAPTER 4. MODEL ESTIMATION AND COMPARISON . . . . . . . .
29
4.1
Bayesian inference and Bayes formula . . . . . . . . . . . . . . . . .
29
4.2
Comparison of statistical models . . . . . . . . . . . . . . . . . . . .
31
4.3
Model performance evaluation . . . . . . . . . . . . . . . . . . . . .
32
CHAPTER 5. MARKOV CHAIN MONTE CARLO SIMULATION
METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
5.1
Hybrid Gibbs sampler and Metropolis-Hasting algorithm . . . . . .
34
5.2
A general representation of Markov switching models . . . . . . . .
37
v
Page
5.3
Choice of the prior probability distribution . . . . . . . . . . . . . .
43
5.4
MCMC simulations: step-by-step algorithm
. . . . . . . . . . . . .
47
5.5
Computational issues and optimization . . . . . . . . . . . . . . . .
53
CHAPTER 6. FREQUENCY MODEL ESTIMATION RESULTS . . . . . .
59
6.1
Model estimation results for annual frequency data
. . . . . . . . .
59
6.2
Model estimation results for weekly frequency data
. . . . . . . . .
74
CHAPTER 7. SEVERITY MODEL ESTIMATION RESULTS
. . . . . . .
89
CHAPTER 8. SUMMARY AND CONCLUSIONS
. . . . . . . . . . . . . .
109
LIST OF REFERENCES
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
114
APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
118
VITA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
122
vi
LIST OF TABLES
Table
Page
6.1
Estimation results for standard Poisson and negative binomial models of
annual accident frequencies
. . . . . . . . . . . . . . . . . . . . . . . .
63
6.2
Estimation results for zero-inflated and Markov switching Poisson models
of annual accident frequencies . . . . . . . . . . . . . . . . . . . . . . .
65
6.3
Estimation results for zero-inflated and Markov switching negative bino-
mial models of annual accident frequ
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