**3.2 A comparison between** *λ***10***<sup>Y</sup>* **and two existing reference models**

In this section, we compare the present model *λ*10*<sup>Y</sup>* with other two models which are widely used in existing related works. As mentioned in Section 1, the first widely used model is given in Eq. (1) [13, 14, 18]. In our study, this model can be specified as follows:

$$\lambda\_{TV} = \begin{pmatrix} \exp\left(K\_2 + \mathcal{C}\_V \times V + \mathcal{C}\_T \times T + \mathcal{C}\_F \times F\_{\text{RAcc}} + \mathcal{C}\_{\text{Projfile}} \times I\_{\text{Projfile}} + \mathcal{C}\_{\text{Align}}\\ \times I\_{\text{Align}} + \mathcal{C}\_{\text{Wid}} \times \text{Wid} + \mathcal{C}\_{\text{Leng}} \times \text{Leng} + \mathcal{C}\_{\text{RSL}} \times \text{RSL} + \mathcal{C}\_{\text{Reg}} \times F\_{\text{Rg}} \end{pmatrix},\tag{27}$$

where the average daily road traffic *V* and the average daily railway traffic *T* are applied separately in exponential form.

The second model as shown in Eq. (2) (e.g., [17, 32]) is specified as Eq. (28) in our study:

$$\lambda\_{\text{Mon}} = \begin{array}{c} \exp\left(K\_3 + \mathcal{C}\_{\text{M}} \times \ln\left(V \times T\right) + \mathcal{C}\_{\text{F}} \times F\_{\text{RAcc}} + \mathcal{C}\_{\text{Projfile}} \times I\_{\text{Projfile}} + \mathcal{C}\_{\text{Align}}\\\\ \times I\_{\text{Align}} + \mathcal{C}\_{\text{Wid}} \times \text{Wid} + \mathcal{C}\_{\text{Long}} \times \text{Length} + \mathcal{C}\_{\text{RSL}} \times \text{RSL} + \mathcal{C}\_{\text{Rag}} \times F\_{\text{Rag}}\right), \end{array} \tag{28}$$

where the conventional traffic moment *V* � *T* is applied.

It should be noted that the ZIP and ZINB models were also investigated for *λTV* and *λMon* but resulted in no higher goodness-of-fit values and a quite small number of significant parameters compared with the Poisson and NB models and, hence, were not reported in this section. The Poisson and NB regression results of the *λTV* and *λMon* are shown in **Tables 11**–**14**, respectively. One can notice that the impacts of road profile and road accident are still not significant in the *λTV* and *λMon*. The AIC, BIC, PCS, and LL tests and observed/estimated accident frequency comparison are given in **Table 15**. According to the quality test results discussed in Section 3.1, the *λ*10*<sup>Y</sup>* combined with the NB distribution (NB-*λ*10*<sup>Y</sup>*) shows the best prediction performance among the four investigated combinations. Therefore, we will only compare the NB-


#### **Table 11.** *Poisson regression results of λTV*.

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


#### **Table 12.**

*NB regression results of λTV*.


#### **Table 13.**

*Poisson regression results of λMon.*


## **Table 14.**

*NB regression results of λMon*.


#### **Table 15.**

*Model GOF comparison among λ*10*<sup>Y</sup>* , *λTV,* and *λMon*.

*λ*10*<sup>Y</sup>* with the *λTV* and *λMon* combined with the Poisson and NB distributions, respectively, in the following content.

As shown in **Table 15**, the AIC, BIC, and PCS results related to the *λ*10*<sup>Y</sup>* model are better than those for the *λTV* and *λMon* models. Moreover, in terms of the LL test, the NB-*λ*10*<sup>Y</sup>* is still the most preferred one.
