Accounting for dispersion and correlation in estimating Safety Performance Functions. An overview starting from a case study

In statistical analysis of crash count data, as well as in estimating Safety Performance Functions (SPFs), the failure of Poisson equidispersion hypothesis and the temporal correlation in annual crash counts must be considered to improve the reliability of estimation of the parameters. After a short discussion on the statistical tools accounting for dispersion and correlation, the paper presents the methodological path followed in estimating a SPF for urban four-leg, signalized intersections. Since the case study exhibited signs of underdispersion, a Conway-Maxwell-Poisson Generalized Linear Model (GLM) was fitted to the data; then a quasi-Poisson model in the framework of Generalized Estimating Equations (GEEs) was performed in order to account for correlation. Results confirm that dispersion and correlation are phenomena that cannot be eluded in the estimation of SPFs under penalty of loss of efficiency in estimating model parameters. Generalized Estimating Equations overcome this problem allowing to incorporate together dispersion and temporal correlation when a quasi-Poisson distribution is used for modeling crash data. Moreover, whereas GEE regression is handy (many statistical software packages have already implemented GEE functions), the interest of COM-Poisson regression, because of difficulties in interpreting the model parameters and in arranging COM-Poisson codes, is still limited to the research field.