Standardizing compositional data for stock assessment

Stock assessment models frequently integrate abundance index and compositional (e.g. age, length, sex) data. Abundance indices are generally estimated using index standardizationmodels, which provide estimates of index standard errors while accounting for: (i) differences in sampling intensity spatiallyorover time; (ii) non-independence of availabledata; and (iii) the effect of covariates.However, compositional data are not generally processed using a standardizationmodel, so effective sample size is not routinely estimated and these three issues are unresolved. I therefore propose a computationally simple “normal approximation” method for standardizing compositional data and compare this with design-based and Dirichlet-multinomial (D-M) methods for analysing compositional data. Using simulated data from a populationwithmultiple spatial strata, heterogeneity within strata, differences in sampling intensity, and additional overdispersion, I show that the normal-approximation method provided unbiased estimates of abundance-at-age and estimates of effective sample size that are consistentwith the imprecisionof these estimates. A conventional design-basedmethodalso producedunbiasedage compositions estimates but no estimate of effective sample size. TheD-M failed to account for knowndifferences in sampling intensity (the proportion of catch for each fishing trip that is sampled for age) and hence provides biased estimates when sampling intensity is correlatedwith variation in abundance-at-age data. I end by discussing uses for “composition-standardization models” and propose that future research develop methods to impute compositional data in strata with missing data.

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