Effects of informative priors on spatial transferability of safety performance functions

The impact of crash contributing factors estimated by Safety Performance Functions (SPFs) is not consistent over the world due to spatial and geographic reasons. Thus, a SPF estimated in one region may not be suitable elsewhere. One possible channel to provide this spatial transferability is to develop SPFs in Bayesian Inference where local data is combined with any prior information (“informative prior”) obtained from other parts of the world. However, non-informative priors have routinely been used because incorporating prior information in SPFs is not straightforward. As a result the effects of informative priors are by and large unexplored, yet can play a vital role in parameter estimates and reflect spatial transferability of SPFs. This study aims to illuminate this spatial transferability by incorporating informative priors into SPFs. To formulate and develop priors, the means and variances of parameter estimates from previous studies were critically reviewed. Informative priors were generated using three methods: 1) distribution fitting, 2) endogenous specification of the dispersion parameter, and 3) hypothetically increasing the strength of priors obtained from distribution fitting. A total of 24 Bayesian Negative Binomial models were estimated for different types of informative priors across four different sample sizes. The means and standard errors of regression parameters are then compared. It is found that SPFs are transferable in general, but if the sample size is small, appropriate informative priors are needed. In small sample size, the conventional use of Normal distribution for regression parameters and Gamma distribution for dispersion parameter may not yield accurate estimates. Proper distribution types derived to develop priors for each parameter are found to perform more accurately in SPFs