Modelling catch and effort data using generalised linear models with random cruise and stratum-by-year effects: trawl fishery for Dissostichus eleginoides in CAMLR Area 58.5.2

A set of procedures for modelling catch and effort data using generalized linear mixed models (GLMMs) including data analytic methods for examining the appropriateness of model structure and parameter values was presented in WG-FSA-SAM 03-12 using Dissostichus eleginoides in Subarea 48.3 of the CAMLR area as an example dataset. Further development of these procedures is presented in this report using trawl catches for Dissostichus eleginoides in Subarea 58.5.2. The extension described here deals with calculating an overall standardised CPUE series when the Subarea has been divided into sampling strata by incorporating ‘Stratum’ as a fixed effect term and the Stratum-by-Year interaction (S x Y) as a random effect term in the GLMM.
Statistical methods are presented for examining the validity of considering the S x Y term as random. A random S x Y term avoids the difficulty in calculating an overall standardised time series of CPUE estimates of weighting by the areal extent of each stratum which is necessary when the S x Y term is included in the GLMM as a fixed effect. Defining an areal extent of each stratum that is valid for use in calculating a weighted mean over all strata using the formula based on stratified random sampling is problematic given that hauls are not a spatially random sample within each stratum. Including the stratum term as fixed simply results in uniform scaling of the CPUE series as is the case with other additive fixed terms in the GLMM.
It was concluded that there was an increase in CPUE in the second year of the fishery with a sharp decline in the following year followed by a relatively stable series of CPUEs. It was also shown that the influence on the series of the random effects estimates for Stratum-by-Year is small.
For the trawl catch and effort data it was found that considering the S x Y term as random was valid. The precision of the standardised CPUE estimates was considerably poorer than that of the longline data for Subarea 48.3. A weak trend of decreasing CPUE values with entry into the winter months was detected using a cubic smoothing spline.