Empirical Bayes method in the study of traffic safety via heterogeneous negative multinomial model
Shin, Kangwon & Washington, Simon (2010) Empirical Bayes method in the study of traffic safety via heterogeneous negative multinomial model. Transportmetrica.
In the study of traffic safety, expected crash frequencies across sites are generally estimated via the negative binomial model, assuming time invariant safety. Since the time invariant safety assumption may be invalid, Hauer (1997) proposed a modified empirical Bayes (EB) method. Despite the modification, no attempts have been made to examine the generalisable form of the marginal distribution resulting from the modified EB framework. Because the hyper-parameters needed to apply the modified EB method are not readily available, an assessment is lacking on how accurately the modified EB method estimates safety in the presence of the time variant safety and regression-to-the-mean (RTM) effects. This study derives the closed form marginal distribution, and reveals that the marginal distribution in the modified EB method is equivalent to the negative multinomial (NM) distribution, which is essentially the same as the likelihood function used in the random effects Poisson model. As a result, this study shows that the gamma posterior distribution from the multivariate Poisson-gamma mixture can be estimated using the NM model or the random effects Poisson model. This study also shows that the estimation errors from the modified EB method are systematically smaller than those from the comparison group method by simultaneously accounting for the RTM and time variant safety effects. Hence, the modified EB method via the NM model is a generalisable method for estimating safety in the presence of the time variant safety and the RTM effects.
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|Item Type:||Journal Article|
|Keywords:||empirical Bayes, highway safety, negative multinomial mode, before-and-after study, random effects model|
|Subjects:||Australian and New Zealand Standard Research Classification > MEDICAL AND HEALTH SCIENCES (110000) > PUBLIC HEALTH AND HEALTH SERVICES (111700)|
|Divisions:||Current > Research Centres > Centre for Accident Research & Road Safety - Qld (CARRS-Q)|
Past > QUT Faculties & Divisions > Faculty of Built Environment and Engineering
Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Psychology & Counselling
|Copyright Owner:||Copyright 2010 Taylor & Francis|
|Copyright Statement:||This is an electronic version of an article published in [Transportmetrica]. [Transportmetrica] is available online at informaworldTM|
|Deposited On:||08 Mar 2011 10:46|
|Last Modified:||01 Mar 2012 00:31|
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