ce 552 week 9 crash statistical approaches identification of problem areas - high crash locations
TRANSCRIPT
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CE 552 Week 9
Crash statistical approachesIdentification of problem areas - High
crash locations
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NCHRP 295
• purpose of its synthesis was to summarize the current practice and research on statistical methods in highway safety analysis, useful for:– establishing relationships between crashes and
associated factors – identifying locations for treatment– evaluating the safety effect of engineering
improvements
– Also useful for driver and vehicle safety analyses
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The Empirical Bayes Method for Before and
After Analysis
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Key Reference
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. 126-131. National Academies Press, Washington, D.C.. 2002
http://www.ctre.iastate.edu/educweb/CE552/docs/Bayes_tutor_hauer.pdf
Open This Document and read through as you go along on PPT
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Safety
Definition: expected number of crashes, by type and severity
What is expected cannot be knownMust be estimatedPrecision of estimates measured in standard deviation
Need a high frequency at a site to have a precise estimate
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The “imprecision” problem …
Assume 100 crashes per year, and 3 years of data, we can reliably estimate the number of crashes per year with (Poisson) standard deviation of about…
However, if there are relatively few crashes per time period (say, 1 crash per 10 years) the estimate varies greatly …
or 5.7% of the mean
or 180% of the mean!
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Regression to the mean problem …
High crash locations are chosen for one reason (high number of crashes!)
Even with no treatment, we would expect, on average, for this high crash rate to decrease
This needs to be accounted for, but is often not, e.g., reporting crash rate reductions after treatment by comparing before and after rates over short periods
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The Empirical Bayes Approach
Empirical Bayes: an approach to before and after crash studies that attempts to estimate more accurately the real impact of high crash location countermeasuresSimply comparing what occurred before with what happened after is naïve and potentially very inaccurate
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The Empirical Bayes Approach
Simple definition:Compares what safety was versus what safety would have been with no change.
Uses that comparison as the basis for making an estimate of the real impact of a change.
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Empirical Bayes
Increases precisionReduced RTM biasUses information form the site, plus …Information from other, similar sites
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Concept
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? … neither! (pretend you would like to insure Mr. Smith)
Answer … use both pieces of information and weight the expectation
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EB applications
IHSDMCHSIM (now Safety Analyst)
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EB Procedures
AbridgedLast 2-3 years dataTraffic volume
FullCan use more data Includes other factors
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Empirical Bayes Procedure
Actual change or improvement in safety=B-A
Where:B is the estimate of the expected number of crashes that would have occurred in a location in the before time period without a change or safety project
A is the actual number of crashes reported in the after period
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Empirical Bayes
Weight should be based on sound logic and real data
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Maryland Modern Roundabout Conversion Data (Five Locations 1994)
Empirical Bayes Estimate Of Expected Crashes Without Improvement (B)
Actual After Period Crash Count (A) with treatment
Crash Reduction Estimate
36.71 14 22.71 (62%)
24.63 14 10.63 (43%)
14.38 2 12.38 (86%)
14.33 10 4.33 (30%)
15.16 4 11.16 (74%)
Treatment effects often vary considerably!
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The SPF – Safety Performance Function
An example SPF:
So, if ADT = 4000
So what is the expected number of crashes for facilities of this type? Develop a (negative binomial) regression model to fit all the data – must have data to do this!
Note: this SPF depends only on ADT … it needn’t
μ=average crashes/km-yr (or /yr for intersections)
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The overdispersion parameter
The negative binomial is a generalized Poisson where the variance is larger than the mean (overdispersed)
The “standard deviation-type” parameter of the negative binomial is the overdispersion parameter φ
variance = η[1+η/(φL)] Where …
μ=average crashes/km-yr (or /yr for intersections) η=μYL (or μY for intersections) = number of crashes/time φ=estimated by the regression (units must be complementary with L, for intersections, L is taken as one)
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Example 1:
How many crashes should we have expected last year???
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Example 1: road segment, 1 yr. of data
Is this distribution “over” dispersed???
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Example 1: computing the weight
What happens when Y is large (compared to μ/φ)? When μ is small compared to φ?
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Example 1 (cont):
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Example 2:
3 years of data: 12, 7, 8 4000 vpd Step 1: Step 2: Step 3:
Note effect of more data
As before
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Example 3: AMFs
1.2 meter shoulders (instead of 1.5) AMF = 1.04 (4% increase in crashes) Step 1: Step 2: Step 3:
Why is weight lower?
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Example 4: subsections
Total length = 1.5km, 11 crashes in 2 years
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Example 5: Severity
2.41 x 0.019 = 0.046 … 1.8 x 3 x 0.046 = 0.247
Note: φ stays same (mult dist. by constant);
Large for fatals (helps you not to “chase” them
Note: 20.357 ≠ 23.9 (from prob 2) … why? What is an ad hoc solution?
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Example 6: intersection
ADT=230
ADT=4520
AMF = 1.277 crashes in 3 years
Step 1:
Step 2:Step 3:
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Example 7: group of intersections
11 crashes in 3 years
Step 1: Step 2: (simplistic)
However, not clear what to use
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Example 7: (cont)
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Example 7: (cont)
Step 3: using w=0.088,
Why so much confidence in the actual number?Is it because we have 3 yrs of data?Is it because 11 is smaller than 20.7?What would happen if 11 had been, say, 32?
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The full procedure
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Example 8
1.8 km, 9 yrs. Unchanged road ADT varies, AMF = 0.95, 74 total crashes
μ =
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Example 8, cont.
(If all μ are equal)
Why so small???
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Example 9: Secular Trends
Yearly multipliers can be used like AMFs to account for weather, technology changes (must be able to get them)
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Example 10: Projections
Projections can be made by using a simple ratio of ADTs (raised to the appropriate power) multiplied by the corresponding ratio of AMFs or yearly multipliers
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Some thought questions
Does EB eliminate RTM as stated? What happened if the SPF is not appropriate for your
site What does appropriate mean?
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Software for Homework
You will need some software to develop the NB regression model for your SPF – that is the “R project” program. Investigate that now (see HW).
http://www.r-project.org/ (info on “R”) http://cran.mtu.edu/bin/windows/base/R-2.8.1-
win32.exe (download “R”) R for Windows FAQ
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Dr. Souleyrette, May I be excused? My brain is full.
Gary Larson, The Far Side, ©1986