Choice of Functional Form for Independent Variables in Accident Prediction Models

Abstract

The development of multivariate statistical models to identify factors that explain systematic variation in accident counts has been an active field of research in the past 20 years. During this period many different models and functional forms have been applied. This study, based on data for national roads in Norway, tests alternative functional forms of the relationship between independent variables and the number of injury accidents. The paper compares six different functional forms (sets of independent variables and specifications of the form of their relationship to accident occurrence) by means of Poisson-lognormal regression. The best model was identified in terms of five goodness of fit measures and a graphical method – the CURE plot (CURE = cumulative residuals). The coefficients estimated for the independent variables were found to vary according to functional form. It is therefore important to compare different functional forms as part of an exploratory analysis when developing accident prediction models.