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Paper-Based Dissertation

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Sajjad Mohammadi

on 29 July 2014

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Transcript of Paper-Based Dissertation

Why safety in transportation is important?

5,505,000 traffic crashes
33,808 people killed
2,217,000 people injured.
Ranked 9th in 1990 >> 3rd in 2020
- for global burden of disease and injury
Traditional crash frequency models:
Poisson regression models,
Negative binomial (NB), and
Their generalized forms

Assumption of independent observations
Underestimated variance, inefficient model estimates
Overestimated significance crash-related factors
Paper I.
Safety effect of Missouri’s strategic highway safety plan - Missouri’s blueprint for safer roadways
Paper II
Crash frequency modeling using negative binomial models: an application of generalized estimating equation to longitudinal data
Paper III
Seasonal effects of crash contributing factors on highway safety

PHD Defense
Mojtaba Ale Mohammadi
PhD Candidate
Civil, Architectural, and Environmental Engineering
Missouri University of Science and Technology

Advisor: Dr. Samaranayake
Co-Advisor: Dr. Ghulam Bham

Main explanatory variables
Area Type (Urban - Rural)
Number of lanes (1 - 7 lanes)
Lane width (min 10 ft - max of 18 ft)
Shoulder width (min 3 ft - max 12 ft)
AADT (1865 min - 115901 max)
Speed limit (55, 60, 65, 70 mph)
Congestion index
Pavement serviceability rate (PSR), and
Truck percentage
Seasonal dummy variables


MODOT portal of safety investigation
Data Integration, Clean up, Aggregation
Identify missing, unusual, or extreme data values
Aggregation of crash frequency for segments

All severity types of motor-vehicle crashes
17 interstate highways
Over the years 2002-2011
Overall length 1200 mi, 65% rural, 35% urban
6000+ segments with, average length 2.2 miles
Total 167783 crashes, 37% rural, 63% urban

Sample Size
Combinatory Dummy Variables


Interaction Terms:
Area type with main variables
Area type with seasonal dummies
Seasonal dummies with main variables
Seasonal dummies with combinatory variables
Durbin-Watson test of positive correlation

Limitations in Literature
Regression to the mean in before/after analysis
Misleading countermeasure
EB is complex and requires training
Data requirements for EB can be extensive

Five years of data used (2002-2007)
NB models for before-through-change conditions for
1- All crash types,
2- Head-on,
3- Rear-end,
4- Sideswipe-same direction,
5- Sideswipe-opposite direction,
6- Angle crash frequency
1- Only fatal
2- Only non-fatal
Continuous variable: “transition”, in NB model
Zero for pre-implementation years (before 2005)
Gradual increase over the implementation years
(2005 through 2007) >> .25, .5, .75
One for 2008
Transition is significant: correlation between the drop in the crashes and the completion level of safety plan

Safety Evaluation: Parameter Estimates and Standard Errors for the NB Models
Predicted Crash Frequency Properties for 2008
Percent Reduction in the Expected Number of Crashes Predicted in 2008

Effects of temporal correlation
Developing traditional NB (using MLE technique)
Developing longitudinal NB (using the GEE technique)
Assessing the efficiency of parameter estimates
Comparisons of

NB Model Estimates With/Without Temporal Correlation Structure
Effect of number of lanes within each class of speed limit
Effect of speed limit within each class of number of lanes
> Standard Errors
> Chi-square Values
> Cumulative Residual Plots
Statistical significance of the effect of change in the number of lanes and speed limit
Generalized Estimating Equation method Maximum Likelihood Estimation method
Comparison of the Models’ Chi-sqare Values
Cumulative residuals plot for LnAADT
GEE (top) and MLE (bottom)
Crash causing factors and countermeasures
Costs should have justification
Few studies addressing seasonal effects
Improving safety policies accordingly

GEE technique
Ten years of data 2002-2011
Seasonal variables and interactions added
Model estimates
Effect of number of lanes within each class of speed limit
Effect of speed limit within each class of number of lanes
Statistical significance of the effect of change in the number of lanes and speed limit
Same analysis for the significant interactions of combinatory variables and winter


> A simple new approach for the evaluation of MSHSP implementation
> Traditional NB models developed using MLE method
> First phase of the MSHSP over the years 2005-2007:
> MSHSP was effective treatment for highway crash fatalities
30% reduction in fatal crashes
10% reduction in all crashes
18-37% reduction in the number of different collision types
> Larger effect in summer and smaller effect in winter, compared to fall

> Longitudinal and traditional NB models developed using GEE and MLE methods
> GEE model allowing for temporal correlations proved to be a superior
Lower standard error values for MLE model
Higher X2 values for MLE model
More accurate and less biased model estimates using GEE method
Autoregressive correlation structure was found an appropriate structure

> Higher traffic volume results in higher crash frequency
Larger effect in spring and smaller in winter, compared to the fall
Smaller effect in urban than rural areas
> Crash reducing effect of PSR was highest for spring and lowest for winter
> Congestion has a smaller effect in urban areas compared to rural

> Higher percentage of heavy vehicles showed to reduce the crash frequency
Larger effect in urban than rural areas
Larger effect in summer
> An increase in speed limit found to be associated with fewer crashes
> No consistent trend was found in the effect of number of lanes
> All seasons showed increasing effect on crash frequency compared to fall
Winter season had the highest effect followed by summer and spring

Ale Mohammadi, M., V. A. Samaranayake, and G. H. Bham. The Effect of Incorporating Temporal Correlations into Negative Binomial Count Data Models. In Proceedings of the 4th International Conference on Road Safety and Simulation, 2013, Rome, Italy.

Ale Mohammadi M., V. A. Samaranayake, and G. H. Bham. Safety Effect of Missouri’s Strategic Highway Safety Plan - Missouri’s Blueprint for Safer Roadways. Transportation Research Records, journal of the Transportation Research Board, National Research Council, Washington, D.C. 2014.

Ale Mohammadi, M., V. A. Samaranayake, and G. H. Bham. Longitudinal Negative Binomial Crash Frequency model on Missouri Interstate Highways: An Application of GEE. Analytic Methods in Accident Research. 2014. (In Press)

Submitted for Publication
Ale Mohammadi, M., V. A. Samaranayake, and G. H. Bham. An Analysis of the Effect of Seasonal patterns on the Efficiency of Crash Frequency Models. Transportation Research Records, journal of the Transportation Research Board, National Research Council, Washington, D.C.

Area Type, Number of Lanes, and Speed Limit
It was found that there is significant correlation
NHTSA, 2009
July 29, 2014
Model of crash frequency observations

Roadway segment i = 1, 2, ..., N
k by 1 vector of parameters
t by k matrix of covariates
During time t = 1, 2, ..., T

Quasi-likelihood estimate of is then the solution
to a set of k “quasi-score” differential equations


The main theme of this study is to overcome these limitations
Accounting for the temporal correlation
Using Generalized Estimating Equation method
When a variable is nearly a linear combination of other variables
1. Pavement Serviceability Rate
2. Pavement Condition Index
3. Congestion Index Rate
(Shankar et al., 1995b; Poch and Mannering, 1996; Abdel-Aty and Radwan, 2000; Savolainen and Tarko, 2005; Mohammadi et al., 2014a)
Verifying that there are no unobserved heterogeneity effects on the model covariates
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