MODELLING CATCH AND EFFORT DATA USING GENERALISED LINEAR MODELS, THE TWEEDIE DISTRIBUTION, RANDOM VESSEL EFFECTS AND RANDOM STRATUM-BY-YEAR EFFECTS

Abstract

The current standard method for modelling catch and effort data for Patagonian toothfi sh (Dissostichus eleginoides) for CCAMLR areas is to model the haul-by-haul ratios of catch to effort as the response variable in a generalised linear model (GLM) with a square-root link function and a unit variance function. A time series of standardised CPUE estimates and their precision can be obtained from the ‘fi shing year ’ parameter estimates together with ‘baseline ’ parameter estimates, their variance–covariance matrix, and the inverse-link function. An alternative GLM with a more rigorous theoretical basis is introduced here. Catch is modelled as the response variable using a GLM with a power variance function, with the power parameter (λ) estimated using a profi le extended quasi-likelihood, and a log link function with log of effort as an offset. For 1 < λ < 2 this model is equivalent to assuming a compound Poisson-gamma distribution (i.e. Tweedie distribution) for catch that, unlike lognormal or gamma distributions, admits zero values. In addition, random vessel effects are introduced into the GLM, as specifi ed by a generalised linear mixed model (GLMM), in order to provide more effi cient estimates of