Applying a Correlated Random Parameters Negative Binomial Lindley Model to Examine Crash Frequency Along Highway Tunnels in China

Highway tunnels have a higher risk of crashing than open roads, which require a systematic approach to tunnel safety. However, previous research had the following problems: 1) Studies have largely focused on open roads, with very little research on tunnels. 2) The collected crash contributing factors involve narrow ranges, with very little tunnel crash data including both tunnel design features, traffic conditions and pavement conditions. 3) None of the studies considered both excess zero observations and unobserved heterogeneity with its interactions. To address these issues, this paper first established an appropriate tunnel dataset containing 3 to 5 years of crash data from several highways in China and the influence factors of tunnel design features, traffic conditions and pavement conditions. A correlated random parameters negative binomial Lindley (CRPNB-L) model that considers both excess zero observations and unobserved heterogeneity with its interaction effects was then proposed. Compared to the uncorrelated random parameters negative binomial Lindley (URPNB-L) model, fixed parameters negative binomial Lindley (FPNB-L) model and fixed parameters negative binomial (FPNB) model, the CRPNB-L model solves the deviation that arises from excess zero observations by introducing the Lindley distribution and considers the unobserved heterogeneity with its interactions by introducing correlated random parameters. In the comparisons, the CRPNB-L model achieves the best effects in the goodness-of-fit. Furthermore, the estimated results of the CRPNB-L model showed that segment length, traffic volume, proportion of class 5 vehicle (heavy trucks and trailers), tunnel entrance and exit segments, and steep uphill and downhill segments were associated with higher crash frequency, while curvature, tunnel length, pavement damage condition index (PCI) and skid resistance index (SRI) were associated with lower crash frequency. In addition, the random variables of the curvature, the steep downgrade indicator, the proportion of class 5 vehicle and SRI were identified and their intercorrelations were analyzed.