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

Abstract 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...

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Veröffentlicht in:ICES journal of marine science 2023-12, Vol.80 (10), p.2630-2641
Hauptverfasser: Thorson, James T, Miller, Timothy J, Stock, Brian C
Format: Artikel
Sprache:eng
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Zusammenfassung:Abstract 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 (ninput), which is often unavailable and results are sensitive to ninput. 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 ninput; (2) proportional changes in ninput 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 ninput.
ISSN:1054-3139
1095-9289
DOI:10.1093/icesjms/fsac159