**1. Introduction**

The level crossing (LX) is railway property upon which road users are given permission to cross [1]. Accidents at LXs give rise to serious material and human damage, and the majority of accidents are caused by vehicle driver violations. As demonstrated by accident statistics, LX safety is one of the most critical issues that railway stakeholders need to deal with [2, 3]. In 2012, there were more than 118,000 LXs in the 28 countries of the European Union (E.U.) [4]. In some E.U. countries, LX accidents account for up to 50% of railway accidents [5]. In the UK, LXs account for 11.8 fatalities and weighted injuries on average per year, comprising 8.4% of the total system risk for the railway network [6]. There were 49 collisions between road vehicles and trains at LXs in Australia in 2011 [7]. In France, the railway network incorporates more than 18,000 LXs for 30,000 km of railway lines and around 13,000 LXs show heavy road and railway traffic [8]. In 2016, 111 trainvehicle collisions at French LXs led to 31 deaths [9]. This number was half the total number of collisions per year at LXs a decade ago, but still too large [10]. Due to nondeterministic causes, complex operation background, and the lack of thorough

statistical analysis based on detailed accident/incident data, the risk assessment of LXs remains a challenging task. Therefore, there is a pressing need for a series of thorough analyses to understand the potential reasons for these accidents and to identify practical countermeasures to prevent accidents at LXs, thus significantly reducing the LX accidents.

In recent years, the Poisson regression model, negative binomial (NB) regression model, and other variants of the Poisson regression model [11, 12] have gained popularity to deal with risk/accident statistics. Ref. [13] adopted the expressions of the estimated expectation value ^*λ* as shown in Eq. (1) corresponding to the Poisson regression and NB regression models, respectively. Ref. [14] employed the variants of Poisson regression model, namely, the zero-inflated Poisson (ZIP) model and the hurdle Poisson model, to deal with LX accident prediction involving the data in North Dakota. Ref. [15] compared the zero-inflated negative binomial (ZINB) model with the USDOT model [16] by using the LX accident data from Illinois, in terms of accident prediction accuracy. The results of this study show that the ZINB model has higher accuracy of prediction. It is worth noticing that the expressions of estimated ^*λ* as shown in Eq. (1) are not appropriate in our current study, since they are limited to handling zero observations and some impacting variables should not be in the exponential form. Ref. [17] developed another model of ^*λ* as shown in Eq. (2). In this model, the product of the average daily road traffic *V* and the average daily railway traffic *T* (known as the conventional traffic moment) is adopted. However, using the conventional traffic moment hinders improving the accuracy of the prediction model:

$$\begin{aligned} \hat{\lambda}\_{\text{Poi}} &= \exp\left(\sum\_{j=1}^{m} \beta\_0 + \beta\_j \mathbf{x}\_j\right), \\\\ \hat{\lambda}\_{\text{NB}} &= \exp\left(\sum\_{j=1}^{m} \beta\_0 + \beta\_j \mathbf{x}\_j + \varepsilon\right), \end{aligned} \tag{1}$$

where *β* is the estimated regression coefficient, *x* is the impacting variable, and *ε* is the gamma-distributed error in NB regression model:

$$\hat{\lambda} = (V \times T)^{\beta\_1} \exp\left(\sum\_{j=1}^m \beta\_j \mathbf{x}\_j + \sigma\right),\tag{2}$$

where *σ* ¼ *β*<sup>0</sup> in Poisson regression model or *σ* ¼ *β*<sup>0</sup> þ *ε* in NB regression model.

Based on these investigations, it is clear that there is a pressing need for an appropriate accident prediction model that should comprehensively consider contributing factors toward LX safety. Moreover, such a model should have high predictive accuracy. Therefore, in the present study, a new accident prediction model is developed to predict the accident frequency at LXs. Specifically, we focus on the SAL2 type of LX (i.e., an automated LX system with two half barriers and flashing lights), which is the most widely used type of LX in France and contributed most to the total number of accidents at French LXs from 1974 to 2014.

*Accident Prediction Modeling Approaches for European Railway Level Crossing Safety DOI: http://dx.doi.org/10.5772/intechopen.109865*
