The statistical properties of four regression models - two conventional linear regression models and two Poisson regression models - are investigated in terms of their ability to model vehicle accidents and highway geometric design relationships. Potential limitations of these models pertaining to their underlying distributional assumptions, estimation procedures, functional form of accident rate, and sensitivity to short road sections, are identified. Important issues, such as the treatment of vehicle exposure and traffic conditions, and data uncertainties due to sampling and nonsampling errors, are also discussed. Roadway and truck accident data from the Highway Safety Information System (HSIS), a highway safety data base administered by the Federal Highway Administration (FHWA), have been employed to illustrate the use and the limitations of these models. It is demonstrated that the conventional linear regression models lack the distributional property to describe adequately random, discrete, nonnegative, and typically sporadic vehicle accident events on the road.
As a result, these models are not appropriate to make probabilistic statements about vehicle accidents, and the test statistics derived from these models are questionable. The Poisson regression models, on the other hand, possess most of the desirable statistical properties in developing these relationships. However, if the vehicle accident data are found to be significantly overdispersed relative to its mean, then using the Poisson regression models may overstate or understate the likelihood of vehicle accidents on the road. More general probability distributions may have to be considered.
Shaw-Pin Miaou and Harry Lum. Modeling Vehicle Accidents and Highway Geometric Design Relationships. Accident Analysis and Prevention, Vol. 25, No. 6, pp. 689-709, 1993.