No. 978

Title:

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

Author(s):

Minami, Mihoko (The Institute of Statistical Mathematics and the Graduate University for Advanced Studies);
Lennert-Cody, Cleridy E. (Inter-American Tropical Tuna Commission);
Gao, Wei (Northeast Normal University of China);
Roman-Verdesoto, Marlon H. (Inter-American Tropical Tuna Commission)

Key words:

GIC; penalized likelihood; thin plate regression splines; UBRE

Abstract:

    The zero-inflated negative binomial (ZINB) regression model with smoothing is introduced for modeling count data. Methods for estimation of confidence interval bands for model coefficients, and guidance on model selection and on estimation of the negative binomial scale parameter are also presented. Use of the ZINB regression model is illustrated with shark bycatch data from the eastern Pacific Ocean tuna purse-seine fishery for 1994-2004. These data are characterized by a large percentage of zero-valued observations and also large non-zero counts. 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 compared to those obtained from fitting Poisson, negative binomial and zero-inflated Poisson regression models to the same data. Comparison of trends among models suggests that the negative binomial model may be more likely to overestimate model coefficients for some types of highly skewed catch and bycatch data.