Crash frequency modeling using negative binomial models: An application of generalized estimating equation to longitudinal data

• We present a longitudinal NB model for 10 years crash count of Missouri interstates.
• Temporal correlation in crash data is incorporated in the model using GEE procedure.
• Autoregressive correlation structure was found appropriate for longitudinal data.
• GEE procedure did not underestimate the variance of the model estimated coefficients.
• χ2 values and cumulative residual method showed that GEE estimates are more efficient.

The prediction of crash frequency models can be improved when several years of crash data are utilized, instead of three to five years of data most commonly used in research. Crash data, however, generates multiple observations over the years that can be correlated. This temporal correlation affects the estimated coefficients and their variances in commonly used crash frequency models (such as negative binomial (NB), Poisson models, and their generalized forms). Despite the obvious temporal correlation of crashes, research analyses of such correlation have been limited and the consequences of this omission are not completely known. The objective of this study is to explore the effects of temporal correlation in crash frequency models at the highway segment level.In this paper, a negative binomial model has been developed using a generalized estimating equation (GEE) procedure that incorporates the temporal correlations amongst yearly crash counts. The longitudinal model employs an autoregressive correlation structure to compare to the more traditional NB model, which uses a Maximum Likelihood Estimation (MLE) method that cannot accommodate temporal correlations. The GEE model with temporal correlation was found to be superior compared to the MLE model, as it does not underestimate the variance in the coefficient estimates, and it provides more accurate and less biased estimates. Furthermore, an autoregressive correlation structure was found to be an appropriate structure for longitudinal type of data used in this study. Ten years (2002–2011) of Missouri Interstate highway crash data have been utilized in this paper. The crash data comprises of traffic characteristics and geometric properties of highway segments.