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### Weighted Adjustment for EB Method

Posted: Mon May 06, 2013 1:44 pm
I was reading through a paper titled: "Estimating Safety by the Empircal Bayes Method: A Tutorial" found online at: http://www.oocities.org/hauer@rogers.co ... Bpaper.pdf. The equation for calculating the weighted adjustment is different than that given in the HSM Appendix A for Part C (Equation A-5, Page A-19, Volume 2). In the paper, the calculation for the weighting factor (equation 2 on page 5 of the paper) includes a term that divides the predicted crash frequency by the overdispersion parameter whereas in the HSM equation the same term multiplies the predicted crash frequency by the overdispersion parameter. Can anyone shed some light on why there is a difference between the two equations? Is one right and the other wrong? Do they simply represent two different weighting methodologies? Or am I just completely confused as to what is going on?

### Re: Weighted Adjustment for EB Method

Posted: Wed May 08, 2013 8:44 am
From what I understand the two equations are the same except that the overdispersion factors that are used are actually inverse of each other.

### Re: Weighted Adjustment for EB Method

Posted: Fri Dec 13, 2013 9:43 am

I'm sorry I never responded to you on this issue. I checked back into the forum today and thought I'd follow up with you.

I agree that the overdispersion parameters used in the paper compared to the HSM are the inverse of each other. That was the basis of my question. I haven't had a statistics class in a very long time but it seems like there would be a specific definition of the "overdispersion factor" and that if one does the math and calculates such a factor it would meet that definition. Assuming that is true using the inverse of that value would give a different (wrong?) result.

So the question is why is the overdispersion factor defined differently in the HSM versus the tutorial paper I referenced? How is an end user supposed to know if the reported overdispersion factor should be used or if the inverse should be used? Presumably one should use the reported values in the reported equations if using the HSM SPFs. But what if someone decides to use an SPF from another source?

That's actually the reason for my question. I'm using SPFs developed by my State DOT. I applied their reported overdispersion parameter as per the HSM equation but subsequently saw the tutorial paper that says to use the inverse. Hence my confusion.

### Re: Weighted Adjustment for EB Method

Posted: Fri Dec 13, 2013 12:01 pm
"overdispersion" parameter discussed in the paper defined as overdispersion per unit length (mi). "overdispersion" parameter in HSM is determined as a function of segment length. They are not inversely proportional.
HSM chapters 18,19 adress this confusion in terms. There are 2 definitions now: "Inverse Dispersion Parameter K" per-unit-length and "Overdispersion Parameter, k" which is 1/K*L