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===== Preliminary experiments =====

We test the [[admb_real:all_cohorts:model_description|model following all cohorts]] on a simple data set, and compare with the ICES VPA estimates.

We follow all cohorts aged 3 to 12 in the period 1994 to 2001. This gives the following .dat file:

<file txt cod.dat>
# Auto-generated datfile

# Startyear
1994

# Endyear
2001

# Min age
3

# Max age
12

# Catch
6531.000000 59444.000000 102548.000000 59766.000000 32504.000000 10019.000000 6163.000000 3671.000000 7528.000000 995.000000 
4879.000000 42587.000000 115329.000000 98485.000000 32036.000000 7334.000000 3014.000000 1725.000000 1174.000000 1920.000000 
7655.000000 28782.000000 80711.000000 100509.000000 54590.000000 10545.000000 2023.000000 930.000000 462.000000 230.000000 
12827.000000 36491.000000 69633.000000 83017.000000 65768.000000 28392.000000 4651.000000 1151.000000 373.000000 213.000000 
31887.000000 88874.000000 48972.000000 40493.000000 34513.000000 26354.000000 6583.000000 965.000000 197.000000  69.000000 
7501.000000 77714.000000 92816.000000 31139.000000 15778.000000 15851.000000 8828.000000 1837.000000 195.000000  40.000000 
4701.000000 33094.000000 93044.000000 47210.000000 12671.000000 6677.000000 4787.000000 1647.000000 321.000000  71.000000 
5044.000000 35019.000000 62139.000000 62456.000000 22794.000000 5266.000000 1773.000000 1163.000000 343.000000  84.000000 
# Survey data
349.800000 404.500000 217.500000  89.500000  22.500000  11.900000   9.400000   3.900000  18.000000   2.700000 
166.200000 159.800000 216.600000 104.000000  29.000000   4.400000   4.300000   3.000000   2.600000   8.100000 
 92.900000  70.500000  87.200000  89.100000  44.600000   6.500000   1.100000   0.400000   0.900000   1.400000 
188.300000  51.700000  49.700000  42.200000  49.900000  20.500000   2.200000   0.500000   0.000000   0.800000 
427.700000 182.600000  42.400000  33.800000  34.000000  24.700000   4.900000   0.700000   0.200000   0.100000 
150.000000  96.400000  45.400000  12.200000  11.200000  18.700000   9.200000   1.000000   0.200000   0.200000 
245.200000 158.900000 145.700000  49.300000  12.900000   6.900000   5.200000   1.200000   0.600000   0.200000 
138.200000 171.600000  81.600000  57.300000  19.800000   2.400000   0.800000   0.600000   0.300000   0.100000 
</file>

We then run the model and plot the results for two classes, namely 4-6 year olds:

|{{:admb_real:all_cohorts:n46_vs_vpa_1994_2001.png?180|}} |

...and 7+ year olds:

|{{:admb_real:all_cohorts:n7plus_vs_vpa_1994_2001.png?180|}} |

As one can see, the curves follow the VPA estimates relatively closely, with the added bonus of 95% confidence intervals.

Additional output files:

<file txt cod.std>
 index   name        value      std dev   
     1   N_firstcol  5.7680e-01 1.2847e-01
     2   N_firstcol  3.3147e-01 6.5800e-02
     3   N_firstcol  2.6470e-01 4.9345e-02
     4   N_firstcol  5.0882e-01 9.7472e-02
     5   N_firstcol  6.0897e-01 1.3346e-01
     6   N_firstcol  4.0682e-01 9.9672e-02
     7   N_firstcol  5.6034e-01 1.5143e-01
     8   N_firstcol  3.2939e-01 1.1510e-01
     9   N_firstrow  6.4811e-01 1.0516e-01
    10   N_firstrow  4.1597e-01 4.5215e-02
    11   N_firstrow  1.3496e-01 9.5606e-03
    12   N_firstrow  4.9804e-02 2.3641e-03
    13   N_firstrow  1.7001e-02 9.4253e-04
    14   N_firstrow  1.3497e-02 1.7978e-03
    15   N_firstrow  1.0894e-02 1.8848e-03
    16   N_firstrow  3.6266e-02 8.7802e-03
    17   N_firstrow  1.0000e-02 1.2991e-07
    18   q           4.1956e-01 4.2876e-02
    19   logs       -1.0961e+00 7.9556e-02
    20   M           2.6468e-01 7.0564e-02
    21   N           5.7680e+02 1.2847e+02
    22   N           6.4811e+02 1.0516e+02
    23   N           4.1597e+02 4.5215e+01
    24   N           1.3496e+02 9.5606e+00
    25   N           4.9804e+01 2.3641e+00
    26   N           1.7001e+01 9.4253e-01
    27   N           1.3497e+01 1.7978e+00
    28   N           1.0894e+01 1.8848e+00
    29   N           3.6266e+01 8.7802e+00
    30   N           1.0000e+01 1.0607e-04
    31   N           3.3147e+02 6.5800e+01
    32   N           4.3766e+02 6.7737e+01
    33   N           4.5178e+02 4.8836e+01
    34   N           2.4053e+02 1.7731e+01
    35   N           5.7707e+01 3.2758e+00
    36   N           1.3277e+01 8.9379e-01
    37   N           5.3581e+00 3.6515e-01
    38   N           5.6282e+00 1.0838e+00
    39   N           5.5434e+00 1.2267e+00
    40   N           2.2055e+01 6.1780e+00
    41   N           2.6470e+02 4.9345e+01
    42   N           2.5064e+02 3.2854e+01
    43   N           3.0320e+02 3.0630e+01
    44   N           2.5821e+02 1.9271e+01
    45   N           1.0902e+02 5.9225e+00
    46   N           1.9701e+01 1.1417e+00
    47   N           4.5608e+00 3.8507e-01
    48   N           1.7990e+00 1.7612e-01
    49   N           2.9955e+00 7.0934e-01
    50   N           3.3533e+00 8.6059e-01
    51   N           5.0882e+02 9.7472e+01
    52   N           1.9727e+02 2.4140e+01
    53   N           1.7027e+02 1.3283e+01
    54   N           1.7075e+02 1.1536e+01
    55   N           1.2103e+02 6.2763e+00
    56   N           4.1769e+01 1.6163e+00
    57   N           7.0268e+00 4.1142e-01
    58   N           1.9476e+00 1.8589e-01
    59   N           6.6689e-01 1.0747e-01
    60   N           1.9443e+00 4.9340e-01
    61   N           6.0897e+02 1.3346e+02
    62   N           3.8065e+02 5.0292e+01
    63   N           1.2339e+02 1.0167e+01
    64   N           7.7231e+01 4.8966e+00
    65   N           6.7328e+01 4.2341e+00
    66   N           4.2407e+01 1.8814e+00
    67   N           1.0266e+01 5.4591e-01
    68   N           1.8233e+00 2.1457e-01
    69   N           6.1138e-01 1.1853e-01
    70   N           2.2555e-01 7.6723e-02
    71   N           4.0682e+02 9.9672e+01
    72   N           4.4288e+02 7.9336e+01
    73   N           2.2392e+02 2.6089e+01
    74   N           5.7110e+01 4.3414e+00
    75   N           2.8195e+01 2.0010e+00
    76   N           2.5184e+01 1.6863e+00
    77   N           1.2320e+01 6.7331e-01
    78   N           2.8266e+00 2.5306e-01
    79   N           6.5870e-01 1.3781e-01
    80   N           3.1802e-01 8.3697e-02
    81   N           5.6034e+02 1.5143e+02
    82   N           3.0646e+02 6.5070e+01
    83   N           2.8025e+02 5.0347e+01
    84   N           1.0062e+02 1.6075e+01
    85   N           1.9931e+01 2.4839e+00
    86   N           9.5291e+00 1.1012e+00
    87   N           7.1627e+00 9.6720e-01
    88   N           2.6801e+00 3.9571e-01
    89   N           7.5949e-01 1.6064e-01
    90   N           3.5587e-01 9.6655e-02
    91   N           3.2939e+02 1.1510e+02
    92   N           4.2643e+02 1.0619e+02
    93   N           2.0979e+02 4.5924e+01
    94   N           1.4367e+02 3.5894e+01
    95   N           4.0989e+01 1.1479e+01
    96   N           5.5719e+00 1.7762e+00
    97   N           2.1888e+00 7.8471e-01
    98   N           1.8233e+00 6.8775e-01
    99   N           7.9283e-01 2.8001e-01
   100   N           3.3652e-01 1.1264e-01
   101   N46         1.1990e+03 1.5992e+02
   102   N46         1.1300e+03 1.3425e+02
   103   N46         8.1204e+02 8.2613e+01
   104   N46         5.3828e+02 4.8486e+01
   105   N46         5.8127e+02 6.3160e+01
   106   N46         7.2392e+02 9.7449e+01
   107   N46         6.8733e+02 9.6888e+01
   108   N46         7.7989e+02 1.2866e+02
   109   N7plus      1.3746e+02 1.2931e+01
   110   N7plus      1.0957e+02 9.6420e+00
   111   N7plus      1.4143e+02 8.1178e+00
   112   N7plus      1.7438e+02 8.5379e+00
   113   N7plus      1.2266e+02 6.6942e+00
   114   N7plus      6.9502e+01 4.0555e+00
   115   N7plus      4.0419e+01 3.6522e+00
   116   N7plus      5.1703e+01 1.2142e+01

</file> 

<file txt cod.rep>
576.804 648.115 415.967 134.959 49.8038 17.0007 13.4966 10.8941 36.2665 10
 331.468 437.656 451.776 240.534 57.7067 13.2768 5.35808 5.62816 5.54335 22.0554
 264.695 250.641 303.196 258.207 109.015 19.701 4.5608 1.79897 2.99548 3.35326
 508.821 197.266 170.266 170.747 121.025 41.7689 7.02678 1.94763 0.66689 1.94432
 608.97 380.651 123.387 77.2309 67.3283 42.4074 10.2661 1.8233 0.611378 0.225546
 406.822 442.883 223.925 57.1097 28.1946 25.1842 12.3202 2.82662 0.6587 0.318015
 560.339 306.459 280.249 100.62 19.9312 9.5291 7.16274 2.68007 0.759487 0.355867
 329.392 426.425 209.794 143.671 40.9893 5.57188 2.18885 1.82327 0.792831 0.336517
</file>


==== Spawning stock biomass ====

Using these estimates, along with weight and maturity proportion data from ICES reports, we can make similar curves for the spawning stock biomass:

{{:admb_real:all_cohorts:ssb_vs_vpa_1994_2001.png?180|}}

Here the spawning stock biomass is a weghted sum including age groups 3-12 (13 for the VPA estimate), where the weights are the weight at age, and proportion maturity at age.