A copula-based poisson-mixed multinomial logit model for joint analysis of vessel incident types and fatality counts: Evidence of tail dependence from commercial fishing data

Commercial fishing remains one of the most hazardous occupations worldwide, with high fatality rates and complex incident dynamics, making the joint understanding of incident type and fatality frequency critically important. This study addresses the limitation of conventional approaches that model these outcomes independently by proposing a copula-based joint modeling framework. Specifically, a Copula-Based Poisson-Mixed Multinomial Logit Model is developed to simultaneously analyze five categories of vessel incidents and associated fatality counts using vessel-level data derived from the Commercial Fishing Incident Database. The approach integrates a multinomial logit model for incident type with a negative binomial model for fatality frequency, linked through alternative copula structures to capture unobserved dependence. Empirical results indicate that the negative binomial specification provides the best fit for fatality counts, while the Student-t copula outperforms Gaussian and FGM alternatives, achieving the highest AIC and BIC values and revealing strong dependence between outcomes. Key determinants include vessel characteristics, human factors, and operational conditions, with drowning and crew exposure emerging as dominant contributors to fatalities. The findings demonstrate that accounting for dependence significantly improves model performance and yields more reliable inference, offering valuable insights for safety management and policy interventions in commercial fishing operations.