| In fisheries, catch counts consist of non-negative values, usually with excess zeros and a heavy right tail. Several generalized linear models can be used in the analysis of such data since these methods do not rely on the assumption of normality. In our study, the question of interest is to determine the effect of vent sizes in fishing pots on the count of legal and sublegal black sea bass, after removing important effects such as vessel, string within vessel, soaking time, and fishing pot position. In the experiments, four pots were investigated with various circular escape vent sizes (2.38", 2.75", 3.10", and 3.40" as the diameter). Our main interest is to find out the ideal vent size which gives the best legal size black sea bass catch count and minimizes the sublegal size catch count.;The Poisson regression model is the most widely used methodology to analyze count data. Different Poisson models are used in the analysis of the black sea bass catch count. We start with the standard Poisson model, and continue with the regression for Poisson rates. In order to account for over-dispersion, a Poisson model with scaled deviance as well as a negative binomial regression model are discussed. Since the count data contain excess zero counts, a Zero Inflated Poisson (ZIP) model is used. From the results of the last analysis, we can conclude that over-dispersion is not only induced by excess zero counts in the data, but also contributed by the right tail.;Because of the hierarchical structure in parts of the data, random components are introduced in the above mentioned models by assuming random intercepts. The mixed effect models are fitted to the black sea bass catch count data using Poisson, negative binomial, ZIP and Zero Inflated Negative Binomial (ZINB) models. All mixed effect models are fitted using both parametric and Bayesian approaches to analysis. After comparison of the performance of all models, the ZINB model is recognized as the best fitting model as indicated by smallest Deviance Information Criterion (DIC) and Negative Cross-validatory Log-likelihood (NLL) values when using a Bayesian approach.;Ninety-five percent credible intervals are computed for both legal and sublegal size black sea bass, and we conclude that vent sizes of 2.38" and 2.75" have larger average counts of legal size black sea bass than pots with vent sizes of 3.10" or 3.40", after adjusting for important covariates; vent sizes of 2.75" have significantly less sublegal catch counts than vent sizes of 2.38" and 3.10", as well as having a tendency to hold less sublegal catch than 3.40". Therefore, we can conclude that a vent size of 2.75" is the ideal choice, since it maximizes the retention of legal size black sea bass and at the same time minimizes the retention of sublegal size black sea bass in the fishing pots. |
