Northwest Fisheries Science Center

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Document Type: Journal Article
Center: NWFSC
Document ID: 4631
Title: A comparison of parametric, semi-parametric, and non-parametric approaches to selectivity in age-structured assessment models
Author: James T. Thorson, Ian G. Taylor
Publication Year: 2014
Journal: Fisheries Research
Volume: 158
Pages: 7483
DOI: 10.1016/j.fishres.2013.10.002
Keywords: selectivity at age,semi-parametric,non-parametric,spline,penalized likelihood,Gaussian process

 Integrated assessment models frequently track population abundance at age, and hence account for fishery removals using a function representing fishery selectivity at age.  However, the aggregate effect of contact selectivity, fish availability, and spatial differences in fishing intensity may cause fishery selectivity at age to have an unusual shape that does not match any parametric selectivity function.  For this reason, previous research has developed flexible ‘non-parametric’ models for selectivity at age that specify a penalty on changes in selectivity as a function of age.  In this study, we describe an alternative ‘semi-parametric’ approach to selectivity at age, which specifies a penalty on differences between estimated selectivity at age and a pre-specified parametric model whose parameters are freely estimated, while also using a novel cross-validation approach to select the magnitude of penalty in both semi- and non-parametric models.  We then compare parametric, semi-parametric, and non-parametric models using simulated data and evaluate the bias and precision of estimated depletion and fishing intensity given different sample sizes for compositional data and difference forms for ‘true’ fishery selectivity at age.  Results show that semi- and non-parametric models result in little decrease in precision relative to the parametric model when the parametric model matches the true data-generating process, but that the semi- and non-parametric models have less bias and greater precision when the parametric function is mis-specified.  As expected, the semi-parametric model reverts to its pre-specified parametric form when sample sizes are low but performs similarly to the non-parametric model when sample sizes are high, thus resulting in biased estimates of depletion and fishing intensity given a mis-specified parametric model and low sample sizes.  Overall, results indicate few disadvantages to using the non-parametric model given the range of simulation scenarios explored here, and that the semi-parametric model provides a selectivity specification that is intermediate between parametric and non-parametric forms.  We conclude by recommending future research regarding semi- and non-parametric selectivity models, in particular regarding variat

Theme: Recovery, Rebuilding and Sustainability of Marine and Anadromous Species
Foci: Develop methods to use physiological and biological information to predict population-level processes.
Investigate ecological and socio-economic effects of alternative management strategies or governance structures.