LOGO
An Examination of the Endogeneity of Speed Limits and Accident Counts in Crash Models
ITE Presentation June 27, 2012
Presenter:Jung-Han Wang
Contents
1. Introduction1. Introduction
2. Literature Review2. Literature Review
4. Data Description4. Data Description
3. Methodology3. Methodology
5. Result5. Result
7. Q&A7. Q&A
6. Conclusion6. Conclusion
Speed limit should be set realistically for the majority of drivers on the road
Previous researches have treated the predictor variable for a certain speed limit as exogenous
Single equation modeling techniques used by previous researches have resulted in widely variable data
Research was delivered by running single equation models individually involving crash counts, speed limits and then comparing them with a simultaneous equation model (SEM)
1.Introduction2.Literature
Review3. Methodology 4. Data
Description5. Results 6. Conclusions 7. Q & A
Single equation modeling techniques used by previous researches have resulted in widely variable data
W/O Endogeneity With Endogeneity
Single equation modeling techniques will result in widelyVariable data
It is anticipated to obtain less biased estimators by using simultaneous equation models.
1.Introduction2.Literature
Review3. Methodology 4. Data
Description5. Results 6. Conclusions 7. Q & A
19731. NMSL speed limit is 55 mph, but actual speed limit
varied from state to state.
1987
1995
National Maximum Speed Law
2. Congress permitted states to raise speed limits to 65 mph (105 km/h) on rural Interstate highways
3. Repeal of federal limits. Federal returns all speed limit determination authority to the states.
1.Introduction2.Literature
Review3. Methodology 4. Data
Description5. Results 6. Conclusions 7. Q & A
Speed Limit Increment and Accidents
California
55–65 mph increase in collision
65-70 mphnot significantly change
55-65 mphnot significantly change
65-70not significantlychange
North Carolina
urban interstate highway increase in acc counts
Rural interstate highway not significantly change
Utah
1.Introduction2.Literature
Review3. Methodology 4. Data
Description7. Q & A5. Results 6. Conclusions
1.Introduction2.Literature
Review3. Methodology 4. Data
Description5. Results 6. Conclusions 7. Q & A
AZ Department of Transportation
i. Speed zoning in Arizona is basedon 85 percentile of the drivers are traveling.
ii. This speed is subject to downward revision based upon such factors as: accident experience, roadway geometrics, and adjacent development
1.Introduction2.Literature
Review3. Methodology 4. Data
Description7. Q & A5. Results 6. Conclusions
Model Selection
Poisson distribution restricts the mean and the variance to be equal:
(E[yi] = VAR[yi]). When this equality does not hold, the data are said to be under dispersed (E[yi] > VAR[yi]) or over dispersed (E[yi] < VAR[yi]).
So Negative Binomial Model was chosen
Traditional Model for Crash Counts
Negative Binomial Model
λi = EXP (βxi +εi = EXP (βxi) * EXP (εi)
whereλi = Accident Countsxi = Speed Limitεi = Error Termβ = coefficient of xi
1.Introduction2.Literature
Review3. Methodology 4. Data
Description7. Q & A5. Results 6. Conclusions
Simultaneous Equation Model
Negative Binomial Model
λi = EXP (β1xi +ε1i = EXP (β1xi) * EXP (ε1i)
Multiple Linear Regression Model
xi= β2λi+ε2i
whereλi = Accident Countsxi = Speed Limitε1i, ε2i = Error Term
1.Introduction2.Literature
Review3. Methodology 4. Data
Description7. Q & A5. Results 6. Conclusions
Collect Data
Set up ModelIn R
Single Equation Model (NB)
Simultaneous Equation Model
(NB+MLR)
Compare Results
Summary
Research Procedure
Model forMinor Road
Model for Major Road
Simultaneous Equation Model
(NB+MLR)
Single Equation Model (NB)
Compare Results
1.Introduction2.Literature
Review3. Methodology 4. Data
Description7. Q & A5. Results 6. Conclusions
Data Retrieved City of Corona
Locations: 298 intersections
Duration: 2000 to 2009
Crash types: Rear end, head on, side swipe, broad side, hit object, over turn, vehicle vs. pedestrian, etc. 10 different types total.
Crash severities: fatal, severe injury, other visible injury, complaint of pain, and non-injury
Crash Type
Severity
1.Introduction2.Literature
Review3. Methodology 4. Data
Description7. Q & A5. Results 6. Conclusions
Comparison Coefficient for Major Road Approach
Single Equation Model for Crashes Estimated Coefficient t-statistic p-value
Constant -3.5021 -3.01 0Log of AADT on Major Road 0.4215 3.57 0Log of AADT on Minor Road 0.2615 3.21 0SPDLIMAJ 0.3543 1.85 0.03SPDLIMIN 0.2112 1.78 0.35PEDMAJ 0.4518 4.21 0.04α (dispersion parameter) 0.4387 4.53 0
1.Introduction2.Literature
Review3. Methodology 4. Data
Description7. Q & A5. Results 6. Conclusions
Simultaneous Equation Models on Major Road Estimated Coefficient
t-statistic p-value
Equation1: Crashes (dependent variable)Constant -2.6035 -5.43 0.000Log of AADT on Major Road 0.5692 6.91 0.000Log of AADT on Minor Road 0.1128 2.45 0.000SPDLIMAJ 0.4676 2.33 0.012PEDMAJ 0.5560 7.42 0.020α (dispersion parameter) 0.4387 4.53 0.000Equation2: Speed Limit on Major Road (dependent variable)Constant -2.7863 -3.63 0.001Log of AADT on Major Road -0.4216 -2.34 0.001Number of crashes 2.0320 4.67 0.045Number of lanes on major road 0.0235 1.98 0.065Number of driveways on the major road within 250 ft of the intersection center
-0.1158 -1.56 0.076
Comparison Coefficient for Minor Road Approach
Single Equation Model for Crashes Estimated Coefficient t-statistic p-value
Constant -3.5021 -3.01 0Log of AADT on Major Road 0.4215 3.57 0Log of AADT on Minor Road 0.2615 3.21 0SPDLIMAJ 0.3543 1.85 0.03SPDLIMIN 0.2112 1.78 0.35PEDMAJ 0.4518 4.21 0.04α (dispersion parameter) 0.4387 4.53 0
1.Introduction2.Literature
Review3. Methodology 4. Data
Description7. Q & A6. Conclusions
Simultaneous Equation Models on Minor Road
Estimated Coefficient
t-statistic p-value
Equation1: Crashes (dependent variable)Constant -2.8033 -4.67 0.000Log of AADT on Major Road 0.4895 5.64 0.001Log of AADT on Minor Road 0.1988 2.43 0.001SPDLIMAJ 0.2876 1.12 0.026SPDLIMIN 0.1887 1.23 0.282PEDMAJ 0.5641 7.53 0.035α (dispersion parameter) 0.2266 2.67 0.001Equation2: Speed Limit on Major Road (dependent variable)Constant 4.2268 8.25 0.000Log of AADT on Major Road -0.0231 -0.93 0.006Number of crashes 1.4526 3.54 0.280Number of lanes on major road 0.1761 2.18 0.007
Number of driveways on the major road within 250 ft of the intersection center
-3.6887 -6.82 0.084
5. Results
Comparison Coefficient for Major Road Approach
1.Introduction2.Literature
Review3. Methodology 4. Data
Description7. Q & A6. Conclusions5. Results
Simultaneous Equation Models on Major Road Estimated Coefficient
t-statistic p-value
Equation1: Crashes (dependent variable)
Constant -2.6035 -5.43 0.000
Log of AADT on Major Road 0.5692 6.91 0.000
Log of AADT on Minor Road 0.1128 2.45 0.000
SPDLIMAJ 0.4676 2.33 0.012
PEDMAJ 0.5560 7.42 0.020
α (dispersion parameter) 0.4387 4.53 0.000
Equation2: Speed Limit on Major Road (dependent variable)
Constant -2.7863 -3.63 0.001
Log of AADT on Major Road -0.4216 -2.34 0.001
Number of crashes 2.0320 4.67 0.045
Number of lanes on major road 0.0235 1.98 0.065
Number of driveways on the major road within 250 ft of the intersection center
-0.1158 -1.56 0.076
1. From all the 298 intersections that were analyzed, there was no significant difference in the results accounting
and not accounting for endogeneity since all the signs associated with different coefficients remain the same.
2.The differences illustrated in the magnitude of the coefficients also suggest one might make erroneous judgment if the endogeneity between speed limit and accidents are totally ignored.
3.The study indicates crashes are endogenously related with a speed limit on major approach
4.Re-estimate the predictor variables by running the models with only the most significant variables
1.Introduction2.Literature
Review3. Methodology 4. Data
Description7. Q & A5. Results 6. Conclusions
LOGOQ & A
1.Introduction2.Literature
Review3. Methodology 4. Data
Description5. Conclusion
6. Recommen-dation
7. Q & A
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