Article,
Modelling catch and effort data using generalised linear models, the Tweedie distribution, random vessel effects and random stratum-by-year effects
Ccamlr Science, (2004)
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 \textless λ \textless 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
the standardised CPUE time series and more realistic estimates of their precision. Extra
effi ciency is gained by recovery of inter-vessel information as a result of the imbalance in
the number of hauls in the year-by-vessel cross-classifi cation. Further, the inclusion of an
area stratum by fi shing year interaction as an additional random effect in the GLMM is
investigated. Fitting the stratum-by-year interaction as a fi xed effect is problematic since
it requires weighting of the individual stratum estimates by the areal extent of the stratum
in order to obtain overall yearly standardised catch-per-unit-effort (CPUE) estimates.
Without stratifi ed random sampling, the determination of stratum areas that will give
unbiased standardised CPUE estimates may be diffi cult. Fitting the stratum-by-year
interaction as a random effect avoids this diffi culty, and diagnostic methods to evaluate
the validity of considering this interaction as random are described.
