The multivariate-Tweedie: a self-weighting likelihood for age and length composition data arising from hierarchical sampling designs

Weighting data appropriately in stock assessment models is necessary to diagnose model mis-specification, estimate uncertainty, and when combining data sets. Age- and length-composition data are often fitted using a multinomial distribution and then reweighted iteratively, and the Dirichlet-multinomial ("DM") likelihood provides a model-based alternative that estimates an additional parameter and thereby "self-weights" data. However, the DM likelihood requires specifying an input sample size (n(input)), which is often unavailable and results are sensitive to n(input). We therefore introduce the multivariate-Tweedie (MVTW) as alternative with three benefits: (1) it can identify both overdispersion (downweighting) or underdispersion (upweighting) relative to the n(input); (2) proportional changes in n(input) are exactly offset by parameters; and (3) it arises naturally when expanding data arising from a hierarchical sampling design. We use an age-structured simulation to show that the MVTW (1) can be more precise than the DM in estimating data weights, and (2) can appropriately upweight data when needed. We then use a real-world state-space assessment to show that the MVTW can easily be adapted to other software. We recommend that stock assessments explore the sensitivity to specifying DM, MVTW, and logistic-normal likelihoods, particularly when the DM estimates an effective sample size approaching n(input).