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