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. PurposesPurposes  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

4. Options in SS LOHIINITPR_typePRIORSDPHASEenv- var use_ dev dev_ minyr dev_ maxyr dev_ stddev BlockBlock_ Fxn 2519946.2200201761480.1400 -1515400302761480.9200

5. IssuesIssues True likelihoods require integrating across the random effects (dev y ) 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 1.Estimate the parameter deviates with as little penalty as possible: σ 1. 1.Set the standard deviation of the distributional penalty to a large number and estimate deviates 2.Remove outliers 3.Estimate the standard deviation of the deviates. 2.Iteratively estimate the standard deviation σ 2 a.Set the standard deviation at a reasonable value b.Estimate the deviates c.Estimate the standard deviation of the deviates d.Repeat b and c by using the new standard deviation from c until the standard deviation converges 3.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 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 P2 estimated

9. 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 Simplified BET : Time varying

10. Grant Thompson’s method: Iteratively estimate the standard deviation σ2 How little penalty is for σ 1 ? Depend on parameter

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

12. Time varying Constant

13. Simulation approach 1.Fit model with time varying selectivity or constant selectivity to original data 2.Use estimated parameters and random recruitment deviates to randomly simulate data with same characteristics as original data 3.Fit the model to the simulated data with time varying selectivity, constant selectivity, 4.Repeat 2-3 many times

14. Simulator S1: operating model with constant selectivity Simulator S2: operating model with time varying selectivity Estimator E1: estimate models with constant selectivity Estimator E2: estimate models with time varying selectivity Estimator F1: estimate models with original weighting on effective sample size for pure seine fleets Estimator F2: estimate models with down weighting on effective sample size for pure seine fleets Simulation approach

15. S1: constant selectivity S2: time varying selectivity Corrected specified models S1E1F1S2E2F1 Effect of time varying selectivity S1E2F1S2E1F1 Effect of down weighting on effective sample size S1E1F2S2E2F2

18. 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, B 0, B 2012, B 2012 /B 0, C 2012_F1, terminal recruitments. Effect of time varying selectivity

19. Misspecify lower effect on effective sample size may not be too bad except for 1. C 2012_F1, SSB 0, SSB MSY when selectivity is constant in true model. 2. MSY, SSB MSY when selectivity is time-varying in true model. Effect of down weighting on effective sample size

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