===== Model estimating only 3 year olds and older =====

In this section we test a model which does not use data for 0-2 year olds, and does not estimate these age groups. It is equivalent to the [[admb_real:admb_real#simple_model|simple model]], with the catch and survey data shifted.

We perform the same experiment as for [[admb_real:admb_real#model_with_two_separate_catchabilities|the model with two catchabilities]], namely [[admb_real:two_qs_cohorts_per_run|trying out different numbers of cohorts]] which are to be estimated at the same time.

=== Summary ===

:!: :!: Unlike for [[admb_real:two_qs_cohorts_per_run|the experiments]] with [[admb_real:admb_real#model_with_two_separate_catchabilities|the model with two catchabilities]], the parameter estimates are in general inside their bounds. This means that the computed standard deviations are meaningful.

:!: The estimates are sometimes smaller than the corresponding VPA estimates, and sometimes larger, unlike for the model with two catchabilities, where they were always larger.

:!: There are some issues with stability, especially regarding the number of years we follow a cohort. Although not plotted below, for the experiment with a single cohort born in 1994, it makes a huge difference whether we follow it for 6 or 7 years.

:!: As more cohorts are added the population sizes at age 3 become more stable, but not always at the levels estimated when only following a single cohort. This can be seen in the following table:

^ N3<sub>birthyear</sub> ^ N3<sub>1994</sub> ^ N3<sub>1995</sub> ^ N3<sub>1996</sub> ^ N3<sub>1997</sub>  ^ N3<sub>1998</sub> ^ N3<sub>1999</sub> ^ N3<sub>2000</sub>  ^
^ Single estimate | 0.516109  | 0.364052 |0.343280 |0.893856 | | | |
^ Multiple estimates | 0.803846 | 0.413922 | | | | | |
| |0.628584 | 0.362537 | 0.300540  | | | | |
| | 0.622791| 0.359443 |0.298084| 0.589102| | | |
| | |  0.369516 | 0.306418 | |  | |  | 
| | |  0.381369 | 0.316046 | 0.631374 | | |  | 
| | | 0.437240 | 0.361336 | 0.727927 | 0.930341 | | | 
| | | |  0.405056 | 0.840858 | |  |  |
| | | |   0.503421| 1.07145 | 1.43532 | | | 
| | | | 0.297859 | 0.590654 | 0.738234 | 0.622872 | | 
| | | | | 0.900099 | 1.17791 | | |
| | | | | 0.389587 | 0.467355 | 0.360528 | |
| | | | | 0.395227 | 0.474633 | 0.367218 | 0.426952 |

==== First cohort born 1994 ====
:!: **NOTE** Although the population variables are called N0, they represent the population level at **age 3**.

:!: The run with two cohorts did not converge when the maximum age was set to 10, so is set to 9.
^ Num. cohorts ^ Trajectories ^ Estimates ^
|1 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_94_94.png?180|}} |<file txt cod.par># Number of parameters = 4  Objective function value = -3.37978  Maximum gradient component = 1.95145e-06
# N0:
 0.516109
# q:
 0.475306
# logs:
-0.922473038606
# M:
0.229629359685
 </file>|
|2 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_94_95.png?180|}} |<file txt cod.par># Number of parameters = 5  Objective function value = -9.55295  Maximum gradient component = 2.32779e-05
# N0:
 0.803846 0.413922
# q:
 0.327094
# logs:
-1.18235361737
# M:
0.336813802520
 </file>|
|3 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_94_96.png?180|}} |<file txt cod.par># Number of parameters = 6  Objective function value = -12.5230  Maximum gradient component = 7.21299e-05
# N0:
 0.628584 0.362537 0.300540
# q:
 0.350674
# logs:
-1.02179235777
# M:
0.289443475648
 </file>|
|4 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_94_97.png?180|}} |<file txt cod.par># Number of parameters = 7  Objective function value = -18.7801  Maximum gradient component = 0.000328611
# N0:
 0.622791 0.359443 0.298084 0.589102
# q:
 0.344332
# logs:
-1.08687795940
# M:
0.286208904677
 </file>|

==== First cohort born 1995 ====
:!: **NOTE** Although the population variables are called N0, they represent the population level at **age 3**.
^ Num. cohorts ^ Trajectories ^ Estimates ^
|1 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_95_95.png?180|}} |<file txt cod.par># Number of parameters = 4  Objective function value = -5.59638  Maximum gradient component = 7.74232e-05
# N0:
 0.364052
# q:
 0.360699
# logs:
-1.19954713216
# M:
0.291272410377
 </file>|
|2 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_95_96.png?180|}} |<file txt cod.par># Number of parameters = 5  Objective function value = -10.9818  Maximum gradient component = 6.07228e-05
# N0:
 0.369516 0.306418
# q:
 0.313287
# logs:
-1.18636245551
# M:
0.294287629410
 </file>|
|3 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_95_97.png?180|}} |<file txt cod.par># Number of parameters = 6  Objective function value = -17.9526  Maximum gradient component = 4.47329e-05
# N0:
 0.381369 0.316046 0.631374
# q:
 0.305620
# logs:
-1.24802508061
# M:
0.304658857253
 </file>|
|4 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_95_98.png?180|}} |<file txt cod.par># Number of parameters = 7  Objective function value = -19.9411  Maximum gradient component = 3.61072e-05
# N0:
 0.437240 0.361336 0.727927 0.930341
# q:
 0.290922
# logs:
-1.12315927867
# M:
0.349501204632
 </file>|

==== First cohort born 1996 ====
:!: **NOTE** Although the population variables are called N0, they represent the population level at **age 3**.
^ Num. cohorts ^ Trajectories ^ Estimates ^
|1 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_96_96.png?180|}} |<file txt cod.par># Number of parameters = 4  Objective function value = -6.57862  Maximum gradient component = 3.41763e-05
# N0:
 0.343280
# q:
 0.253697
# logs:
-1.32232734466
# M:
0.328278664602
 </file>|
|2 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_96_97.png?180|}} |<file txt cod.par># Number of parameters = 5  Objective function value = -13.7544  Maximum gradient component = 3.38158e-06
# N0:
 0.405056 0.840858
# q:
 0.233947
# logs:
-1.35965206122
# M:
0.380156075941
 </file>|
|3 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_96_98.png?180|}} |<file txt cod.par># Number of parameters = 6  Objective function value = -15.2285  Maximum gradient component = 5.62207e-05
# N0:
 0.503421 1.07145 1.43532
# q:
 0.208151
# logs:
-1.13451875040
# M:
0.443069717196
 </file>|
|4 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_96_99.png?180|}} |<file txt cod.par># Number of parameters = 7  Objective function value = -18.8363  Maximum gradient component = 8.67845e-05
# N0:
 0.297859 0.590654 0.738234 0.622872
# q:
 0.328860
# logs:
-1.08863375308
# M:
0.285142576059
 </file>|

==== First cohort born 1997 ====
:!: **NOTE** Although the population variables are called N0, they represent the population level at **age 3**.
^ Num. cohorts ^ Trajectories ^ Estimates ^
|1 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_97_97.png?180|}} |<file txt cod.par># Number of parameters = 4  Objective function value = -7.30997  Maximum gradient component = 5.91774e-06
# N0:
 0.893856
# q:
 0.230683
# logs:
-1.41374631937
# M:
0.397902182138
 </file>|
|2 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_97_98.png?180|}} |<file txt cod.par># Number of parameters = 5  Objective function value = -9.22716  Maximum gradient component = 2.99965e-06
# N0:
 0.900099 1.17791
# q:
 0.252102
# logs:
-1.07669731352
# M:
0.407261698083
 </file>|
|3 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_97_99.png?180|}} |<file txt cod.par># Number of parameters = 6  Objective function value = -14.2602  Maximum gradient component = 0.000175596
# N0:
 0.389587 0.467355 0.360528
# q:
 0.483771
# logs:
-1.09417574178
# M:
0.138538549318
 </file>|
|4 |{{:admb_real:cod_simple_re_catch_n3_vs_vpa_97_00.png?180|}} |<file txt cod.par># Number of parameters = 7  Objective function value = -21.4434  Maximum gradient component = 0.000408809
# N0:
 0.395227 0.474633 0.367218 0.426952
# q:
 0.488868
# logs:
-1.17010474477
# M:
0.144620261549
 </file>|