Lucas Reymond

This work analyzes and models the frequency of accidents, breakdowns, and fires in motorway tunnels using Generalized Linear Models. The dataset used includes tunnel-specific covariates such as traffic volume, heavy goods vehicle proportion, slope, tunnel length, speed limit, and structural characteristics.

Given that the response variables represent count data, the initial approach utilized Poisson regression models. However, exploratory analysis revealed overdispersion, as evidenced by dispersion parameters significantly greater than 1. To address this, I transitioned to Negative Binomial regression models, which provided a better fit by incorporating an additional dispersion parameter.

To optimize variable selection and reduce multicollinearity, I applied:

• Stepwise selection based on Bayesian Information Criterion (BIC)
• Least Absolute Shrinkage and Selection Operator (LASSO) regression for feature selection
• Log-transformation of key covariates to align with theoretical expectations of multiplicative relationships

To assess model performance, a Cook’s Distance vs. Leverage Analysis was conducted, revealing outliers and influential points. As a result, two extreme tunnel observations were excluded to improve model reliability. Cross-validation error and BIC criteria were used to compare different model performances, ultimately favoring the Negative Binomial model over Quasi-Poisson for both accidents and breakdowns. Furthermore, residual analysis confirmed that applying log transformations improved linearity, ensuring better adherence to theoretical Poisson assumptions.

The analysis revealed that tunnel length and traffic volume are the most significant predictors across all incident types. Additionally, tunnels featuring continuous or roof slope designs exhibited lower accident and breakdown rates, suggesting that specific structural features could enhance safety. Also, unidirectional tunnels showed an unexpectedly high accident rate, challenging conventional safety assumptions. Finally, certain tunnel construction companies were associated with higher-than-expected accident frequencies. This study highlights the effectiveness of regression-based risk assessment in tunnel infrastructure, demonstrating how tunnel design, slope, and traffic patterns influence incident occurrences.