1. Incorporating Temporal Effect into Crash Safety Performance Functions Wen Cheng, Ph.D., P.E., PTOE Civil Engineering Department Cal Poly Pomona

2. Presentation Outline General safety background Description of the research method and crash data Illustration of the results Discussion and Conclusions

3. General Safety Background

4. Crashes in Real Life: Huge Burden

5. Crashes in the U.S. 42,116 fatalities (i.e., 115 persons killed/day) 1.51 fatalities/100M VMT 14.79 fatalities/100K Population 231 Billion Economic Cost 41% alcohol-related fatalities 29.7% Speed-related fatal crashes Source: 2005 NHTSA

6. Crashes in California Source: 2005 CA Statistical Abstract

7. Powerful Tool: SPF Definition: Based on AASHTO HSM, SPFs are equations that estimate expected average crash frequency as a function of traffic volume and/or roadway characteristics. It is a powerful tool to determine the influential factors of crashes. Popular Modeling Technique: The basic negative binomial regression which can account for the over- dispersion of crash data. – Main Drawback: the temporal effect associated with cross section and time series data is deficiently considered.

8. Hence, the main research objective Conduct Generalized Estimating Equations (GEEs) which can provide an extension of generalized linear models to the analysis of longitudinal data and account for the correlation in the repeated observations for a given intersection.

9. Research Method and Data Descption

10. Normal Linear Regression Requires Three strong assumptions Normally distributed errors (i.e., residues) Constant variance of errors No relationships among the independent variables (i.e., regressor variables, or predictors)

11. In This Study The independent variable y (accident number) is nonnegative count data, which is not normally distributed Therefore, the Normal Linear Regression is not appropriate herein. Instead, we can use a Count Data Regression Model.

12. The Typical Negative Binomial Model has advantage over Poisson Model in accounting for the over-dispersion of crash data. However, the temporal effect of the crash data over the time period is not considered

13. Two GEE Models in this study The GEE model with autoregressive correlation It weighs the correlation between two observations by their separate gap (order of measure). As the distance increases the correlation decreases. The GEE model with unstructured correlation structure It assumes different correlations between any two observations taken at the same time. Both Models sufficiently consider the temporal effect associated with cross section and time series data!

14. Crash Data Used Obtained through Crossroads Collision Database 298 intersections from the City of Corona, CA – 141 signalized – 157 unsignalized Total crashes: 7594 Crash period: 10 years (2000~ 2009)

15. Data Used in the Study Major road speed limit Minor road speed limit Major road ADT Major road ADT year Minor road ADT Minor road ADT year Signalized intersection (Yes or No) Total number of through lanes Presence of at least one exclusive right turn lane on major road (Yes or No) Presence of at least one exclusive left turn lane on major road (Yes or No) Presence of at least one exclusive right turn lane on minor road (Yes or No) Presence of at least one exclusive left turn lane on minor road (Yes or No)

16. Research Results

17. Modeling Results of the Three Models

18. Discussion of Results GEE models have slightly higher estimated standard errors than do traditional negative Binomial models – reason: accounting for the temporal correlation will inflate the standard errors. The three models produce unequal coefficients, which means considering temporal effect of crash data could result in different modeling estimations.

19. Discussion (Cont’d) The crash data from other states or places might yield different results. The impact of the modeling estimation difference (due to the temporal effect) on other safety applications (e.g. hot spot identification) needs to be further evaluated.

20. THANK YOU!