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--- admb_real:admb_real [2010/05/05 08:30] – lennartfr
+++ admb_real:admb_real [2010/09/09 08:39] (current) – lennartfr
@@ Line 444: / Line 444: @@
  </file>|
-For 2, 4, and 5 cohorts, the trajectories don not change much, and are consistent with the case of three cohorts.
+For 2, 4, and 5 cohorts, the trajectories do not change much, and are consistent with the case of three cohorts.
 cohorts: ({{:admb_real:cod_1985_2cohorts_dat.txt|.dat-file}})
@@ Line 494: / Line 494: @@
 ^ Catchability ^ = ^ q0 exp(a x + b)/(1+exp(a x + b)) ^
 where the x represents the age of the cohort.
+:!: **NOTE** this means that instead of one q per survey, there are now three parameters, q, a, and b (called q0, q_alpha and q_beta in the code), //regardless of the number of surveys//.
+The model is implemented in {{:admb_real:sigmoid_model_rename_to_cod_tpl.txt|this .tpl file}}. Note that the parameter structure is now different, so a .pin file for three cohorts should look like:
+<file txt cod.pin>
+# N0
+.000000  1.000000  1.000000
+# q  alpha beta
+.60 1 1
+# log(s)
+.1
+# M
+.2
+</file>
+We run the model on the same dataset as before, and get:
+| {{:admb_real:sigmoid_model85_87.png?200|}} | <file txt cod.cor> The logarithm of the determinant of the hessian = 25.2341
+ index   name      value      std dev       1       2       3       4       5       6       7       8
+   N0       3.0186e+01 1.1253e+01   1.0000
+   N0       1.1064e+01 3.9272e+00   0.5094  1.0000
+   N0       9.4634e+00 3.7190e+00   0.5202  0.5138  1.0000
+   q0       5.0006e-02 5.8935e-03  -0.2905 -0.2920 -0.2677  1.0000
+   q_alpha  9.3271e-01 2.0696e-01  -0.3959 -0.3923 -0.4035 -0.0115  1.0000
+   q_beta  -4.5843e+00 5.2739e-01  -0.1483 -0.1427 -0.1564 -0.0168 -0.6298  1.0000
+   logs    -2.3144e-01 1.3868e-01  -0.0001 -0.0001 -0.0001  0.0003 -0.0000 -0.0000  1.0000
+   M        5.0000e-01 8.6228e-04   0.0185  0.0192  0.0171 -0.0000  0.0012 -0.0115 -0.0004  1.0000
+</file> |
+| {{:admb_real:sigmoid_q85_87.png?200|}}| ::: |
+As one can see, the effective catchability is very low, due to the fact that q0 is at its lower bound of 0.05. Therefore we set the lower bound to be 0.5, (which requires editing of the .tpl file and recompilation), and then get:
+|{{:admb_real:sigmoid_model_q05_85_87.png?200|}} |<file txt cod.cor> The logarithm of the determinant of the hessian = 39.2739
+ index   name      value      std dev       1       2       3       4       5       6       7       8
+   N0       5.4677e+00 1.6838e+00   1.0000
+   N0       2.5934e+00 4.7455e-01   0.3641  1.0000
+   N0       2.0265e+00 5.4008e-01   0.4213  0.3511  1.0000
+   q0       5.0000e-01 2.0633e-03  -0.0064 -0.0065 -0.0054  1.0000
+   q_alpha  8.1589e-01 1.4679e-01  -0.4167 -0.3754 -0.4119 -0.0023  1.0000
+   q_beta  -5.1365e+00 4.4860e-01  -0.0600 -0.0124 -0.0439 -0.0045 -0.7160  1.0000
+   logs    -2.2158e-01 1.3868e-01  -0.0000 -0.0000 -0.0000  0.0004 -0.0000  0.0000  1.0000
+   M        5.0000e-01 1.0834e-03   0.0268  0.0424  0.0288 -0.0000  0.0050 -0.0165 -0.0004  1.0000
+</file> |
+|{{:admb_real:sigmoid_q_q05_85_87.png?200|}} | ::: |
+As one can see, q is still at its lower bound, which seems to be the most important parameter for this model on this dataset.
+===== Model with two separate catchabilities =====
+This model has two q variables for each survey, one which is applied to age groups 0-2, and one which is applied to age group 3 and up. It is implemented in {{:admb_real:cod_two_q_rename_to_cod_tpl.txt|this .tpl file.}} A .pin file for three cohorts may read:
+<file txt cod.pin>
+# N0
+.07 2.95 2.9
+# q02
+.20
+# q3plus
+.2
+# log(s)
+.1
+# M
+.1
+</file>
+We run it on the usual data set, and get:
+|{{:admb_real:two_q_model_85_87.png?200|}}| <file txt cod.cor> The logarithm of the determinant of the hessian = 50.7902
+ index   name     value      std dev       1       2       3       4       5       6       7
+   N0      2.0581e-01 8.4094e-02   1.0000
+   N0      1.1073e-01 2.3668e-02   0.7116  1.0000
+   N0      9.2034e-02 2.6383e-02   0.7050  0.6679  1.0000
+   q02     1.1075e-01 4.9119e-02  -0.5731 -0.5228 -0.5390  1.0000
+   q3plus  2.5265e-01 1.3221e-01  -0.8607 -0.8178 -0.8072  0.5695  1.0000
+   logs   -1.5297e-01 1.3868e-01   0.0000  0.0000  0.0000 -0.0000 -0.0000  1.0000
+   M       2.0589e-06 1.4559e-03   0.0336  0.0514  0.0403 -0.0223 -0.0140  0.0004  1.0000
+</file> |
+As one can see the catchability for the classes age 3 and up is larger than for 0-2 year olds, which is consistent with our expectations.
+===== Model with two separate catchabilities and two mortalities =====
+This model is a combination of the models with two Ms and two qs. The .tpl file can be found {{:admb_real:cod_two_q_two_m_rename_to_cod_tpl.txt|here.}} A .pin file should look like
+<file txt cod.pin>
+# N0
+.07 2.95 2.9
+# q02
+.20
+# q3plus
+.2
+# log(s)
+.1
+# M
+.1
+# Mvec
+
+</file>
+We run it on the standard dataset and get:
+| {{:admb_real:two_q_two_m_model_85_87.png?200|}} | <file txt cod.cor> The logarithm of the determinant of the hessian = 82.4993
+ index   name     value      std dev       1       2       3       4       5       6       7
+   N0      5.9029e-01 2.4390e-01   1.0000
+   N0      2.4613e-01 8.6909e-02   0.6200  1.0000
+   N0      2.0132e-01 7.4850e-02   0.5779  0.5697  1.0000
+   q02     5.0000e-02 7.1973e-09  -0.0000 -0.0000 -0.0000  1.0000
+   q3plus  9.9498e-02 4.1441e-02  -0.7242 -0.6946 -0.7115  0.0000  1.0000
+   logs   -1.7842e-01 1.4154e-01   0.0122  0.0161  0.0102  0.0000 -0.0092  1.0000
+   M       1.2339e-08 5.4534e-05   0.0000  0.0000  0.0000 -0.0000  0.0000  0.0000  1.0000
+   Mvec    3.7216e-01 1.7757e-01  -0.2653 -0.3269 -0.1560  0.0000 -0.0631 -0.0195  0.0000  1.0000
+</file>|
+Note that the catchability for 0-2 year olds, q02, is at its lower bound of 0.05, whereas the catchability q3plus is not.