# Road Crash Analysis and Modeling: A Systematic Review of Methods, Data, and Emerging Technologies
## 4 Methodological Approaches in Crash Research
### Traditional Statistical Foundations  
The evolution of crash analysis methodologies began with fundamental statistical approaches that established the empirical foundation for road safety research. [PERSON] and [PERSON] [12] provide context for the evolution of statistical methods in highway-accident research, highlighting persistent challenges like unobserved heterogeneity and endogeneity. [PERSON] and [PERSON] [53] further elaborate on these methodological challenges, particularly in crash-frequency analysis, addressing issues such as data overdispersion, underreporting, and omitted-variable bias. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Methodological Approach** & **Key Characteristics** & **References** \\ \hline \multirow{6}{*}{Multinomial Generalized Poisson (MGP)} & MGP model with error components showed superior fit in analyzing crash frequency and severity together. Spatial exogenous-EMGP model best captures spatial dependencies in crash data. Complexity in interpreting factors contributing to both frequency and severity. Model complexity increases with alternative spatial structures. & [38; 39] \\ \cline{1-1}  & Curve radius AMFs derived for Texas showed higher crash risks on curves. Variability in intersection data may impact AMF accuracy. & [40] \\ \hline \multirow{6}{*}{Statistical and machine learning methods} & Nearest-Neighbor Classification (NNC) had the best predictive performance; K-means clustering improved model performance; latent class clustering lowered NNC performance. Results may vary by method. & [41] \\ \cline{1-1}  & Random-parameter negative-binomial (RPNB) and S-GWPR models. S-GWPR model better captures spatial heterogeneity and crash data correlation, improving regional crash modeling; requires high spatial granularity data; and may not apply to broader regions. & [42] \\ \hline \multirow{6}{*}{Statistical modeling models} & Bivariate negative-binomial spatial models; multilevel models; Full Bayes models; logistic regression; multivariate tobit models; comparative analysis with Generalized Linear Models. & [34; 43; 44] \\ \cline{1-1}  & Account for heterogeneity; handle unobserved elements; incorporate correlated parameters; use instrumental variables. & [31; 45] \\ \cline{1-1}  & Surrogate safety measures & Traffic conflict techniques; in-vehicle data analysis; kinetic parameters for risk assessment & [46; 47] \\ \cline{1-1}  & Ordered probit models; neural networks; analysis & \\ \cline{1-1}  & Ordered probit models; neural networks; multivariate probit models; flexible econometric structures. & [48; 49] \\ \cline{1-1}  & Real-time risk prediction & Bayesian hierarchical models; temporal–spatial dependencies; weather and geometry factors. & [50; 51] \\ \cline{1-1}  & Connected/autonomous vehicles & HMM prediction methods; time-varying risk maps; real-time assessment. & [52] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cont. The foundation of crash analysis often begins with basic statistical approaches. [PERSON] [54] demonstrates the application of logistic regression methodology in analyzing accident severity, identifying location and cause as significant variables. Building on these fundamentals, [PERSON] and [PERSON] [44] show how multilevel modeling frameworks can better account for residual variation across accidents and geographical locations, revealing significant intra-unit correlation in accident outcomes. [PERSON] et al. [34] calibrated comprehensive accident models using extensive road characteristics data, demonstrating the application of Generalized Linear Modeling approaches with variables such as exposure, AADT, driveway density, curvature ratio, and roadside hazard rating. A significant advancement came with the development of random-parameter models to address unobserved heterogeneity. [PERSON] and [PERSON] [45] explored random-parameter count models for analyzing vehicle accident frequencies, demonstrating methodological approaches for accounting for heterogeneity across various factors. [PERSON] et al.