Standardizing compositional data for stock assessment

Abstract

Stock assessment models frequently integrate abundance index and compositional (e.g. age, length, sex) data. Abundance indices are generally estimated using index standardization models, which provide estimates of index standard errors while accounting for: (i) differences in sampling intensity spatially or over time; (ii) non-independence of available data; and (iii) the effect of covariates. However, compositional data are not generally processed using a standardization model, 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 population with multiple 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 consistent with the imprecision of these estimates. A conventional design-based method also produced unbiased age compositions estimates but no estimate of effective sample size. The D-M failed to account for known differences 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 correlated with 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. © 2014 International Council for the Exploration of the Sea. All rights reserved.