## 2 Literature Review  
Crash modeling and prediction are critical for establishing systems for evaluating and managing traffic safety [2; 3; 4; 5; 6]. Policymakers and traffic engineers often use these models to analyze the performance of safety interventions and assess the safe functioning of the transportation system. For highway intersections or segments, as well as HRGCs, the links between vehicle crashes and geometric design, traffic characteristics, and engineering factors have been well researched using statistical models. Train-vehicle crash injury and mortality rates are greater than other forms of traffic crashes, mostly due to the significant mass difference between trains and motor vehicles, making HRGCs just as significant as highway intersections for crash modeling and prediction [2; 6]. The Poisson regression model, including its variants, have served as examination tools for vehicular crash frequency [7], as well as drivers' unsafe maneuvers at HRGCs in the presence of trains [8]. Negative Binomial (NB) and Zero-inflated Poisson (ZIP) are two widely used Poisson model variations [9]. These models cope with issues like data over-dispersion (when the sample variance is greater than the sample mean) and prevalence of zeros in crash data. On occasion, crash data may be under-dispersed, i.e., sample variance is less than sample mean. Standard distributions such as Poisson and Negative Binomial do not handle this well [10; 11], but a family of Generalized Poisson (GP) regression models are suitable in such situations [12]. To elucidate further, the published literature provides several studies focused on crash modeling for HRGCs [13; 14; 15; 16; 17; 18]. Table 1 presents an overview of the studies on HRGCs crash prediction models, including the methodology used, data resources utilized, and explanatory variables considered in the predictive modeling process. Figure 1: Research framework for crash prediction analysis [2]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Year** & **Authors** & **No of Observations** & **Data Type** & **Location** & **Context** & **Method Used** & \begin{tabular}{c} **Types of** \\ **Explanatory** \\ **Variables** \\ \end{tabular}  \\ \hline
2003 &
\begin{tabular}{c} [PERSON] \\ et al. [15] \\  
With the availability of machine learning methods, new strategies for modeling crash predictions at HRGCs have emerged that overcome the limitations of Generalized Linear Modeling (GLM) [13; 14]. The Generalized Linear Modeling methods use a mathematical formula to represent the relationship between dependent and independent variables. In this regard, [PERSON] et al. [13] in a recent study used a Neural Network (NN) system to assess train-vehicle crash risk at HRGCs to receive meaningful rankings of crash-contributory-variable significance based on different criteria, as well as to produce dependent nonlinear contributor-crash curves with all other contributors considered for a specific contributor variable. Likewise, [PERSON] et al. [14] used Deep Neural Network (DNN) models to model crash frequency and examined predictions and model interpretability in comparison to Generalized Linear Models. In the past, various transportation agencies have utilized the US Department of Transportation's Accident Prediction (AP) model, which was developed in 1986 (henceforth referred to as the 1986 AP model), to assess the probability of accidents at HRGCs [3]. While this model did include a severity prediction component, the primary focus of this research was on predicting crash frequency. In 2020, the Federal Railroad Administration (FRA) updated this model for several reasons, including low variance in the 1986 AP model's generated crossing ratings, the utilization of three distinct models for crash prediction  
\begin{table} \begin{tabular}{c} \end{tabular}  \\  & & & & & & & \\  & &  
based on the type of crossing, and the absence of a statistical evaluation of crash risk at HRGCs [3].