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Hui-Hua Lee, Mark Maunder, Alexandre Aires-da-Silva Kevin Piner, and...

Evaluation of a practical method to estimate the variance parameter of random effects for time varying selectivity . Hui-Hua Lee, Mark Maunder, Alexandre Aires-da-Silva Kevin Piner, and... . Purposes.

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Hui-Hua Lee, Mark Maunder, Alexandre Aires-da-Silva Kevin Piner, and...

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  1. Evaluation of a practical method to estimate the variance parameter of random effects for time varying selectivity Hui-Hua Lee, Mark Maunder, Alexandre Aires-da-Silva Kevin Piner, and...

  2. Purposes • A practical method to estimate the variance parameter of random effects for time varying selectivity • Evaluation the time-varying selectivity using simulation approach

  3. Time varying selectivity using functional forms with time varying parameters implemented using random effects or is the base parameter is the value of offsets in time t

  4. Options in SS blocks, trends, environmental linkage, and annual devs SS Control: Random deviance ) penalized by the dev_std.dev () dev_std.dev is fixed at some level (not a true random effect).

  5. Issues • True likelihoods require integrating across the random effects (devy) • Integration is computationally intensive • Integration is not available in Stock Synthesis unless Bayesian MCMC is used • The standard deviation needs to be estimated • The MLE of the standard deviation estimated using penalized likelihood is not statistically consistent and is degenerative towards zero

  6. Grant Thompson’s method using penalized likelihood • Estimate the parameter deviates with as little penalty as possible: σ1. • Set the standard deviation of the distributional penalty to a large number and estimate deviates • Remove outliers • Estimate the standard deviation of the deviates. • Iteratively estimate the standard deviation σ2 • Set the standard deviation at a reasonable value • Estimate the deviates • Estimate the standard deviation of the deviates • Repeat b and c by using the new standard deviation from c until the standard deviation converges • Calculate the standard deviation as

  7. BET application • Stock Synthesis • Simplified version of the stock assessment model • Two fisheries • Longline • Purse Seine • Starts in 1975 (modeled as seasonal time step) • Data • CPUE for longline fishery • Length composition for both fisheries • Age-at-length for purse seine fisheries • Fixed growth, natural mortality, and steepness of the stock-recruitment relationship (h = 1) • Fishing mortality by fishery and year as parameters (avoids population crash issues when using random recruitment in simulator)

  8. Simplified BET : Selectivity P2 estimated • Purse seine • Double normal length based • Estimate • Peak • Ascending width • Descending width • Fixed • Smallest length = 0 • Largest length = 0 • Plateau size small • Longline • Logistic P2 fixed

  9. Simplified BET : Time varying • Purse seine • Peak: multiplicative normal sd = ? • Ascending width: additive lognormal sd = ? • Descending width : additive lognormal sd = ? • Parameters that were transformed were used additive deviations and parameter that was not transformed was used multiplicative deviations. • Grant Thompson’s method to estimate actual σ

  10. Grant Thompson’s method:Iteratively estimate the standard deviation σ2 How little penalty is for σ1 ? Depend on parameter

  11. Grant Thompson’s method:Calculate the standard deviation σ

  12. Constant Time varying

  13. Simulation approach • Fit model with time varying selectivity or constant selectivity to original data • Use estimated parameters and random recruitment deviates to randomly simulate data with same characteristics as original data • Fit the model to the simulated data with time varying selectivity , constant selectivity, • Repeat 2-3 many times

  14. Simulation approach SimulatorS1: operating model with constant selectivity SimulatorS2: operating model with time varying selectivity EstimatorE1: estimate models with constant selectivity EstimatorE2: estimate models with time varying selectivity EstimatorF1: estimate models with original weighting on effective sample size for pure seine fleets EstimatorF2: estimate models with down weighting on effective sample size for pure seine fleets

  15. Simulation approach

  16. Effect of time varying selectivity • Misspecify selectivity as time-varying when selectivity is constant in true model may not be too bad. • It is not the case for misspecifying selectivity as constant when selectivity is time-varying in true model. In particular, B0, B2012, B2012/B0, C2012_F1, terminal recruitments.

  17. Effect of down weighting on effective sample size • Misspecify lower effect on effective sample size may not be too bad except for 1. C2012_F1, SSB0, SSBMSYwhen selectivity is constant in true model. 2. MSY, SSBMSY when selectivity is time-varying in true model.

  18. Comments, thoughts, criticism? • Get rid of the age-at-length data • Add random selectivity deviations in the simulation process • other?

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