The surprising sensitivity of index scale to delta-model assumptions: Recommendations for model-based index standardization
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The surprising sensitivity of index scale to delta-model assumptions: Recommendations for model-based index standardization

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  • Alternative Title:
    Delta-models (a.k.a. hurdle models) are widely used to fit biomass samples that include zeros and a skewed response for positive catches, and spatio-temporal extensions of these models are increasingly used to quantify trends in abundance (i.e., estimate abundance indices). Previous research has shown estimated indices are proportional to changes in abundance. However, little research has tested the performance of delta-models for estimating “scale”; that is, whether abundance indices are not just proportional to population changes but also have the correct absolute value. We use data for twenty species in the eastern Bering Sea and Gulf of Alaska as well as a factorial experiment conditioned on data for Gulf of Alaska Pacific cod to support five conclusions related to scale in spatio-temporal delta-models. First, we show that conventional (nonspatial) delta-models are surprisingly sensitive to the a priori choice of probability distribution for positive catches, where gamma and Tweedie models give similar scale estimates but other distributions generally differ. Second, these same distributions also estimate widely different scales when using spatio-temporal delta-models, and the delta-gamma and Tweedie models provide similar scale to design-based indices. Third, model selection using marginal AIC often identifies the lognormal distribution as most parsimonious, despite it resulting in systematically higher abundance than design-based indices for many species. Fourth, scale is sensitive to the spatial resolution (i.e., number of knots) used in fitting the spatio-temporal model when using a naïve “empirical Bayes” estimator, but less sensitive when applying an epsilon bias-correction estimator. Fifth, the factorial simulation experiment suggests that the Tweedie and delta-gamma distributions perform well even when applied to data simulated from an inverse-Gaussian or lognormal distribution, whereas the opposite is not true. We conclude that index scale is sensitive to delta-model specification, and we make five recommendations when using spatio-temporal delta-models for index standardization: (1) apply the epsilon or other bias-correction methods to reduce sensitivity of index scale on spatio-temporal model resolution; either (2) compare the scale of delta-model indices with that of design-based indices when design-based indices are available or (3) use the delta-gamma or Tweedie distribution by default when design-based indices are not available; (4) do not assume that AIC will identify the model specification that results in the most appropriate scale; and (5) consider apparent mismatches in index scale depending upon whether an assessment model specifies or estimates the associated catchability coefficient and whether the design-based index is believed to measure total abundance for a fully-selected age or length-class.
  • Journal Title:
    Fisheries Research
  • Description:
    Delta-models (a.k.a. hurdle models) are widely used to fit biomass samples that include zeros and a skewed response for positive catches, and spatio-temporal extensions of these models are increasingly used to quantify trends in abundance (i.e., estimate abundance indices). Previous research has shown estimated indices are proportional to changes in abundance. However, little research has tested the performance of delta-models for estimating “scale”; that is, whether abundance indices are not just proportional to population changes but also have the correct absolute value. We use data for twenty species in the eastern Bering Sea and Gulf of Alaska as well as a factorial experiment conditioned on data for Gulf of Alaska Pacific cod to support five conclusions related to scale in spatio-temporal delta-models. First, we show that conventional (nonspatial) delta-models are surprisingly sensitive to the a priori choice of probability distribution for positive catches, where gamma and Tweedie models give similar scale estimates but other distributions generally differ. Second, these same distributions also estimate widely different scales when using spatio-temporal delta-models, and the delta-gamma and Tweedie models provide similar scale to design-based indices. Third, model selection using marginal AIC often identifies the lognormal distribution as most parsimonious, despite it resulting in systematically higher abundance than design-based indices for many species. Fourth, scale is sensitive to the spatial resolution (i.e., number of knots) used in fitting the spatio-temporal model when using a naïve “empirical Bayes” estimator, but less sensitive when applying an epsilon bias-correction estimator. Fifth, the factorial simulation experiment suggests that the Tweedie and delta-gamma distributions perform well even when applied to data simulated from an inverse-Gaussian or lognormal distribution, whereas the opposite is not true. We conclude that index scale is sensitive to delta-model specification, and we make five recommendations when using spatio-temporal delta-models for index standardization: (1) apply the epsilon or other bias-correction methods to reduce sensitivity of index scale on spatio-temporal model resolution; either (2) compare the scale of delta-model indices with that of design-based indices when design-based indices are available or (3) use the delta-gamma or Tweedie distribution by default when design-based indices are not available; (4) do not assume that AIC will identify the model specification that results in the most appropriate scale; and (5) consider apparent mismatches in index scale depending upon whether an assessment model specifies or estimates the associated catchability coefficient and whether the design-based index is believed to measure total abundance for a fully-selected age or length-class.
  • Source:
    Fisheries Research, 233
  • Document Type:
  • Rights Information:
    Accepted Manuscript
  • Compliance:
    Submitted
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