Modeling shark bycatch: The zero-inflated negative binomial regression model with smoothing

The zero-inflated negative binomial (ZINB) regression model with smoothing is introduced for modeling count data with many zero-valued observations, and its use is illustrated with shark bycatch data from the eastern Pacific Ocean tuna purse-seine fishery for 1994-2004. Based on the generalized information criterion, the ZINB regression model provided a better fit to the data than either Poisson, negative binomial or zero-inflated Poisson regression models. To demonstrate the utility of the ZINB regression model for the standardization of catch data, standardized temporal trends in bycatch rates estimated with the ZINB regression model are computed and compared to those obtained from fits of the other three types of models to the same data. With the exception of the negative binomial, estimated temporal trends were more similar among models than would have been inferred from an analysis of model fit. Comparison of trends among models suggests that the negative binomial regression model may overestimate model coefficients when fitted to data with many zero-valued observations.