1 Validation and Implication of Segmentation on Empirical Bayes for Highway Safety Studies Reginald R. Souleyrette, Robert P. Haas and T. H. Maze Iowa State University, SAIC and Iowa State University ENVIRONMENTAL HEALTH RISK 2007 Fourth International Conference on The Impact of Environmental Factors on Health MALTA; June, 2007

2 The highway safety problem Source: World Health Organization

3 Mitigation approaches – 4Es Education Enforcement Emergency Response Engineering

4 Engineering studies Limited resources Highest benefit desired High Crash Locations Before and After Studies Small sample size  high variance Selection bias  regression to the mean (RTM)

5 Objectives Validate the state of the art statistical approach, known as empirical Bayesian Demonstrate tradeoffs between model quality and data quantity Investigate effect of data aggregation … to improve identification and therefore mitigation of high crash locations

6

7

8 Statistical approaches we could take… Use long periods Use large number of locations Use Empirical Bayes (EB) –Substitutes “similar” locations for longer observation time –“Weights” site and similar-site data

9 Mr. Smith Mr. Smith had no crashes last year The average of similar drivers is 0.8 crashes per year What do we expect is the number of crashes Mr. Smith will have next year … 0?, 0.8? … Answer … use both pieces of information and weight the expectation Hauer, E., D.W. Harwood, F.M. Council, M.S. Griffith, “The Empirical Bayes method for estimating safety: A tutorial.” Transportation Research Record 1784, pp National Academies Press, Washington, D.C

10 Empirical Bayes (EB) We have two types of information We compute an estimate which is an average of both How much to weight the two depends on… –Quantity –Quality Accepted practice… small scale What should the weight be???

11 ________ 1+(μ∙Y)/φ 1 w = mean # crashes/year from model number of years overdispersion factor weight applied to model estimate EB estimate = w∙(model estimate) + (1-w)∙(site average) Need: site data Need: - model for similar sites (neg. binomial)

12 Objective #1 Test effectiveness of EB by comparing: 1.a single year of data from many locations, with different models and the Empirical Bayes formula, vs. 2.several years of crash data at specific locations

13 Objective #2 explore the relationship between segmentation and accuracy of estimates

14 Description of Data Roads (Iowa) –All (19,400km) –Freeways (1400km) –Multilane (8000km) –2-lane (10,000km) Low ADT (1200 VPD) Med ADT (2400 VPD) High ADT (4400 VPD) –Segments 400m (short) 4km (med) 6.8km (long)

15 Description of Data Intersections (California) –Multiphase (873) –Single Phase (374) –Thru-stop (3047) 5 years of data large-scale validation

16 Analysis – Intersections Three model forms: a)Crashes = α(mainline traffic) β, b)Crashes = α(mainline traffic) β (cross street traffic) γ c)Crashes = α (mainline traffic) β (cross street lanes) δ Three types of intersections –multiphase signals –Single phase signals –Stop sign control Intersection model parameters and descriptive statistics

17 Example intersection crash models (only 2 dimensions shown)

18 Intersection Results Top 10 high crash locations in 2003* * California HSIS Multiphase 4 leg Not intuitive Highest in 2003 Trying to predict this EB model “a” lowest error 4 year average “better” slightly more often than EB

19 Using 4 years of data + EB Now, EB better more often Now, model “d” never best estimate, but still best model four times?

20 Intersection Results Effect on Ranking EB does slightly better than 4 year average, or 2003 alone all models “comparable”

21 Analysis – Roads crashes=α(length)(ADT) β 3 types of roads –Freeway –Multilane divided –2-lane 3 segmentations –0.4, 3.8, and 11.6 km, on average 3 traffic ranges (L,M,H) 15 models Road segment model parameters and descriptive statistics

22 Effect of Segmentation on Correction Freeway-type segments Longest segments Average length 11.6 km Medium segments Average length 3.8 km Shortest segments Average length 0.4 km Note higher EB correction for short segments

23 Conclusions EB+1yr ≈ 4yrs of data Better model did not necessarily improve prediction (at least for the 10 intersections selected) Longer segment models are more accurate Intersection 4-year averages and models are relatively poor predictors –But when combined using EB, better

24 Thank you