Improving reliability of road safety estimates based on high correlated accident counts

Calibrating a safety performance function (SPF) with many years of accident data creates a temporal correlation that traditional model calibration procedures cannot deal with. It is well known that generalized estimating equations (GEE) models are able to incorporate trends into accident data and thus overcome difficulties in accounting for correlation; the usual application of GEEs to safety analysis uses robust (or sandwich) estimates of regression coefficients under the independence hypothesis for the working correlation matrix. This practice is justified by the robustness of the GEE procedure against misspecification of the response correlation structure. Nevertheless, with this method, one has to renounce the entirety of the advantages of GEE estimates, and—especially when correlation within the subject is high—significant losses in efficiency and misleading conclusions in model interpretation can occur. In such a case, losses in efficiency of the estimates will be transferred to the reliability of the final safety estimation, for example, by the empirical Bayes method. On the basis of these considerations, the main idea of this study is that, in safety modeling, additional effort to obtain the true data correlation structure will result in better precision in the estimation of SPF parameters. An example to illustrate the methodological aspects of the proposed approach is included.