Effects of globally obtained informative priors on bayesian safety performance functions developed for Australian crash data

Abstract

The precision and bias of Safety Performance Functions (SPFs) heavily rely on the data upon which they are estimated. When local (spatially and temporally representative) data are not sufficiently available, the estimated parameters in SPFs are likely to be biased and inefficient. Estimating SPFs using Bayesian inference may moderate the effects of local data insufficiency in that local data can be combined with prior information obtained from other parts of the world to incorporate additional evidence into the SPFs. In past applications of Bayesian models, non-informative priors have routinely been used because incorporating prior information in SPFs is not straightforward. The previous few attempts to employ informative priors in estimating SPFs are mostly based on local prior knowledge and assuming normally distributed priors. Moreover, the unobserved heterogeneity in local data has not been taken into account. As such, the effects of globally derived informative priors on the precision and bias of locally developed SPFs are essentially unknown. This study aims to examine the effects of globally informative priors and their distribution types on the precision and bias of SPFs developed for Australian crash data. To formulate and develop global informative priors, the means and variances of parameter estimates from previous research were critically reviewed. Informative priors were generated using three methods: 1) distribution fitting, 2) endogenous specification of dispersion parameters, and 3) hypothetically increasing the strength of priors obtained from distribution fitting. In so doing, the mean effects of crash contributing factors across the world are significantly different than those same effects in Australia. A total of 25 Bayesian Random Parameters Negative Binomial SPFs were estimated for different types of informative priors across five sample sizes. The means and standard deviations of posterior parameter estimates as well as SPFs goodness of fit were compared between the models across different sample sizes. Globally informative prior for the dispersion parameter substantially increases the precision of a local estimate, even when the variance of local data likelihood is small. In comparison with the conventional use of Normal distribution, Logistic, Weibull and Lognormal distributions yield more accurate parameter estimates for average annual daily traffic, segment length and number of lanes, particularly when sample size is relatively small.

Keywords: Bayesian inference; Crash prediction model; Distribution fitting; Informative prior; Random parameters model; Safety performance function.