VGLMs and VGAMs: An overview for applications in fisheries research

The vector generalized linear and additive model (VGLM/VGAM) classes of statistical regression models implement general maximum likelihood estimation and smoothing. The VGLM/VGAM framework is very general and is shown to include many popular fisheries regression models such as GLMs and GAMs, the negative binomial (NB), the zero-inflated Poisson (ZIP) and ZINB, the zero-altered Poisson (ZAP) and ZANB as special cases. The primary purpose of this article is to introduce the VGLM/VGAM methodology into fisheries science. To this end, data from the 2008 FIPS-MOUCHE World Fly Fishing Championships is used to illustrate the chief advantages of the framework, viz. its large size and its ability to fit each model in a very flexible manner. Having a large framework leads to greater efficiencies in the practical modelling of data. The specific questions examined fall under two categories: (i) what distribution do the fish lengths have in each of the sectors? (ii) can fish catch reduction be detected and if so, how can the effects be ameliorated? As well as the above models, the utility of several other seemingly disparate regression models to fisheries research are presented, such as the bivariate odds-ratio model, the generalized extreme value distribution, and several quantile regression techniques.