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Comparison with the ADMB model

Source: vignettes/sbt_vs_admb.qmd

Introduction

This vignette compares outputs from the ADMB model to the RTMB model within the sbt package. This is done using a fixed parameter run and then by optimising. In the fixed parameter run the parameter values from a single cell of the ADMB model are used as fixed value inputs to sbt and outputs from sbt are generated then compared to the ADMB outputs.

Fixed parameter run

Comparison table

Table 1 includes transformed parameters (i.e., in natural space), derived quantities, priors, penalties, likelihoods, and objective function values for the ADMB model, the RTMB model, and the difference and percent difference between the two models:

Table 1: Comparison of ADMB and RTMB model outputs including transformed parameters, derived quantities, priors, penalties, likelihoods, and objective function values.
ADMB RTMB Difference Percent difference
Parameters
B0 1.08358e+07 1.083578e+07 18.0862526 0.0002
psi 1.50000e+00 1.500000e+00 0.0000000 0.0000
sigmaR 6.00000e-01 6.000000e-01 0.0000000 0.0000
h 5.50000e-01 5.500000e-01 0.0000000 0.0000
q HSP 1.00000e+00 1.000000e+00 0.0000000 0.0000
m0 4.00000e-01 4.000000e-01 0.0000000 0.0000
m4 1.67050e-01 1.670507e-01 -0.0000007 0.0004
m10 6.50000e-02 6.500000e-02 0.0000000 0.0000
m30 4.57410e-01 4.574100e-01 0.0000000 0.0000
Derived quantities
R0 8.74439e+06 8.744386e+06 3.9612256 0.0000
alpha 1.09929e+07 1.099294e+07 -42.4487450 0.0004
beta 2.78634e+06 2.786344e+06 -3.9206779 0.0001
tau_ac2 6.44716e-01 6.447156e-01 0.0000004 0.0001
Priors & penalties
kludge 0.00000e+00 0.000000e+00 0.0000000 0.0000
sel.change 7.06247e+01 7.062467e+01 0.0000305 0.0000
sel.smooth 3.42249e+01 3.422494e+01 -0.0000408 0.0001
rec -3.03390e+01 -3.033900e+01 0.0000045 0.0000
m0 0.00000e+00 0.000000e+00 0.0000000 0.0000
m10 0.00000e+00 0.000000e+00 0.0000000 0.0000
steep 0.00000e+00 0.000000e+00 0.0000000 0.0000
omega 0.00000e+00 0.000000e+00 0.0000000 0.0000
expl 0.00000e+00 0.000000e+00 0.0000000 0.0000
sel.init 2.00000e-07 2.000000e-07 0.0000000 0.0002
hstar 7.63360e+00 7.633597e+00 0.0000030 0.0000
Likelihoods & objective function
LL1 1.94607e+02 1.946072e+02 -0.0002198 0.0001
LL2 3.09202e+01 3.092031e+01 -0.0001054 0.0003
LL3 3.48981e+01 3.489813e+01 -0.0000286 0.0001
LL4 3.82627e+01 3.826276e+01 -0.0000591 0.0002
Indo 9.30514e+01 9.305138e+01 0.0000202 0.0000
Aus 4.54265e+01 4.542650e+01 -0.0000019 0.0000
CPUE -6.46131e+01 -6.461295e+01 -0.0001494 0.0002
Tags 1.76553e+02 1.765530e+02 0.0000081 0.0000
Aerial 3.98139e+00 3.981441e+00 -0.0000505 0.0013
Troll -1.20015e+01 -1.200157e+01 0.0000656 0.0005
POP 1.75465e+03 1.754654e+03 -0.0037102 0.0002
HSP 2.19884e+03 2.199118e+03 -0.2776306 0.0126
GT 1.45904e+03 1.459035e+03 0.0046028 0.0003
ObjF 6.03576e+03 6.036037e+03 -0.2771518 0.0046

Comparison figures

The following figures compare outputs from the ADMB and RTMB models: average weight at age (Figure 1), natural mortality at age (Figure 2), initial numbers at age (Figure 3), recruitment deviates (Figure 4), recruitment (Figure 5), total numbers (Figure 6), spawning biomass (Figure 7), CPUE (Figure 8), phi at age (Figure 9), selectivity at age (Figure 10), and age-frequency observations and predictions (Figure 12, Figure 13).

Figure 1: Average weight (kg) at age.
Figure 2: Natural mortality (M) at age.
Figure 3: Initial numbers at age in the population.
Figure 4: Recruitment deviates each year.
Figure 5: Recruitment each year.
Figure 6: Total number of inidividuals each year.
Figure 7: Spawning biomass (tonnes).
Figure 8: Catch per unit effort (CPUE).
Figure 9: Phi at age for a subset of years.
Figure 10: Selectivity at age for a subset of years.

There was a reason why the LF observations are different (Figure 11) but I cannot remember why. Must be something to do with post processing in the code as the likelihoods are the same.

Figure 11: LF observations for a subset of years. 
#> [1] NA
Figure 12: AF observations for a subset of years. 
#> [1] NA NA
Figure 13: AF predictions for a subset of years.

Optimising

Now the model is optimised using nlminb to see if RTMB produces the same result. The nlminb function finds the same optimum as ADMB (Figure 14):

Figure 14: Spawning biomass (tonnes).