The effect of data transformation on the severe event prediction in road traffic using extreme value theory

Extreme Value Theory (EVT) is the state-of-the-art method for proactive prediction of accident frequency from traffic interactions on a microscopic scale. The main advantage of using EVT is to predict unobserved critical events based on one or more Surrogate Measures of Safety (SMoS) (single- or multivariate EVT) through a mathematical extrapolation of extreme interactions. Such interactions are quantitatively described by SMoS, which commonly measure the proximity of two road users, increasing the probability of a collision as the proximity decreases. Those events with a higher likelihood of turning into an accident are defined as severe interactions, and they are considered extremes and are used in the EVT model. Since EVT analysis focuses on the upper tail of the distribution, decreasing transformations are a prerequisite, without which it is impossible to model the extremes. However, prediction results depend on the shape of the indicators' distributions. Some studies use simple transformations, such as negation, while others employ nonlinear methods that adjust the relationship between proximity and severity. In the present study, the theory of tail analysis has been used to rigorously formulate the effect of a set of conventional linear and nonlinear transformations of SMoS. The approach was tested on a Swedish dataset, and the effects of the transformations on the prediction of extreme events were evaluated based on an accident model built on local data and Empirical Byes correction. The novelty of this study is that one of the most fundamental concepts in traffic conflict theory, such as conflict-crash relationships, has been examined with mathematical interpretation. The results of this study can be further extended to become a standard procedure in modelling traffic conflicts using EVT.