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-SilvaKevin Piner, and...

Purposes

A practical method to estimate the variance parameter of random effects for time varying selectivity

Evaluation the time-varying selectivity using simulation approach

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

Options in SS

blocks, trends, environmental linkage, and annual devsSS Control:

Random deviance ) penalized by the dev_std.dev ()

dev_std.dev is fixed at some level (not a true random effect).

LO HI INIT PR_type PRIOR SD PHASE env-var

use_dev

dev_minyr

dev_maxyr

dev_ stddev

Block Block_Fxn

25 199 46.22 0 -1 0 2 0 1 76 148 0.14 0 0

-15 15 4 0 -1 0 3 0 2 76 148 0.92 0 0

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

Grant Thompson’s method using penalized likelihood

1. Estimate the parameter deviates with as little penalty as possible: σ1.

1. Set the standard deviation of the distributional penalty to a large number and estimate deviates

2. Remove outliers3. Estimate the standard deviation of the deviates.

2. Iteratively estimate the standard deviation σ2 a. Set the standard deviation at a reasonable valueb. Estimate the deviatesc. Estimate the standard deviation of the deviatesd. Repeat b and c by using the new standard deviation from c until the

standard deviation converges

3. Calculate the standard deviation as𝜎=√𝜎12−𝜎 2 (𝜎1−𝜎 2 )

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)

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

• 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

Grant Thompson’s method:Iteratively estimate the standard deviation σ2

tune 1 tune 2 tune 3 tune 4 tune 50.08

0.1

0.12

0.14

0.16

0.18Peak

initial=0.1 initial=0.5 initial=1 initial=2initial=10

tune 1 tune 2 tune 3 tune 4 tune 50.5

0.6

0.7

0.8

0.9

1

1.1Ascending width

initial=1 initial=5 initial=10 initial=20initial=100

tune 1 tune 2 tune 3 tune 4 tune 50.7

0.8

0.9

1

1.1Descending width

initial=1 initial=5 initial=10 initial=20initial=100

How little penalty is for σ1 ?Depend on parameter

Grant Thompson’s method:Calculate the standard deviation σ

tune 1 tune 2 tune 3 tune 4 tune 50.08

0.1

0.12

0.14

0.16

0.18Peak

initial=0.1 initial=0.5 initial=1 initial=2initial=10

tune 1 tune 2 tune 3 tune 4 tune 50.5

0.6

0.7

0.8

0.9

1

1.1Ascending width

initial=1 initial=5 initial=10 initial=20initial=100

tune 1 tune 2 tune 3 tune 4 tune 50.7

0.8

0.9

1

1.1Descending width

initial=1 initial=5 initial=10 initial=20initial=100

Time varyingConstant

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

Simulator S1: operating model with constant selectivity Simulator S2: operating model with time varying selectivity

Estimator E1: estimate models with constant selectivityEstimator E2: estimate models with time varying selectivityEstimator 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

Simulation approach

S1: constant selectivity

S2: time varying selectivity

Corrected specified models

S1E1F1 S2E2F1

Effect of time varying selectivity

S1E2F1 S2E1F1

Effect of down weighting on effective sample size

S1E1F2 S2E2F2

• 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.

Effect of time varying selectivity

• Misspecify lower effect on effective sample size may not be too bad except for

1. C2012_F1, SSB0, SSBMSY when selectivity is constant in true model. 2. MSY, SSBMSY when selectivity is time-varying in true model.

Effect of down weighting on effective sample size

Comments, thoughts, criticism?

• Get rid of the age-at-length data • Add random selectivity deviations in the

simulation process • other?