Empirical Bayes method in the study of traffic safety via heterogeneous negative multinomial model

摘要: In the study of traffic safety, expected crash frequencies across sites are generally estimated via negative binomial model, assuming time invariant safety. Since safety assumption may be invalid, Hauer (1997) proposed a modified empirical Bayes (EB) method. Despite modification, no attempts have been made to examine generalisable form marginal distribution resulting from EB framework. Because hyper-parameters needed apply method not readily available, an assessment is lacking on how accurately estimates in presence variant and regression-to-the-mean (RTM) effects. This derives closed distribution, reveals that equivalent multinomial (NM) which essentially same as likelihood function used random effects Poisson model. As result, this shows gamma posterior multivariate Poisson-gamma mixture can using NM model or also estimation errors systematically smaller than those comparison group by simultaneously accounting for RTM Hence, estimating