[Feature]: create comprehensive approach for survey Q and parm dev link functions

[k-doering-NOAA]

Imported from redmine, Issue #12352
Opened by @RickMethot on 2015-10-08
Status when imported: Under Review

Have already changed specification of special selectivities (e.g. len selex=30 to 37) from the len selex input section to the survey units section of the data file.

Next need to modify the Q_power option to be a entry point for entering a variety of link functions

Need to decide whether to require 3 parameters (intercept, slope, power) for all link functions, or to make the N parameters specific to the requested function.

proposed set of links is:
Code Function
1 Y=qX
2 Y=a+qX
3 Y=a+q*(X^(1+c))
4 ln(Y)=ln(q)+ln(X)
5 ln(Y)=ln(q)+(1+c)ln(X)
6 Y=q(X-Xbar)
7 Y=a+q*(X/Xbar)^(1+c)
8 Y=qX/(a+X)
9 Y=a/(1+exp(-q(X-Xbar))
10 Y=a+b*ln(X)

[k-doering-NOAA]

comment from @RickMethot on 2016-04-20:
From Rick:

matrix Q_setup(1,Nfleet,1,5)
1 do power,
2 env-var,
3 extra sd,
4 devtype(<0=mirror, 0=float_nobiasadj 1=float_biasadj, 2=parm_nobiasadj, 3=rand, 4=randwalk, 5=set parameter equal to the scaling coefficient so can then have a prior)
5 Q offset
fundamentally, do power and devtype could be replaced by a link designator;
and the Q offset need not be mandatory; instead it is just one possible added parameter depending on the link function that is chosen

Proposaed New Q_setup
1: fleet index number - by specifying this we do not need input for all fleets, only those that have survey data
2: link type
3: 0/1 to select extra sd parameter
4: 0/1 for biasadj or not
5: 0/1/2 to float q: where 0 means not float (old option 2), 1 means float in phase 1 only, 2 means float continuously (old option 5)

So, the q parameter will always show up in the list of parameters as long parameter lines
As a long parameter, it can invoke additional parameters to implement: block/trend, env linkage, and mean-reverting random walk (invokes 2 parameters for the stddev of q and rho for autocorrelation)

The family of possible link functions needs flexibility because the survey obs could be a time series of an environmental index, which could have + and - values
and not be linear in relation to the model factor which could be abundance, dev vector, or a derived process parameter
Link types, where "x" is a model quantity as selected by Svy_units:
<=-1: mirror
1: proportional - y=qx
2: proportional with offset - y=q(x-a)
3: proportional with offset and power: y=q*(x-a)^c
4: logistic

QUESTIONS:

1. can q use any of the time-varying options and also float? I think it can if the time-varying component of q is separated from the component that can float or have a prior.
   e.g. y = q1q2x
   where q1 can float or have a prior
   and q2 starts with a value of 1.0 in the first year and can be time-varying after that

2. Is it feasible to allow the non-q parameters, e.g. a and c in list above or the env link parameter, to be time-varyin

[k-doering-NOAA]

comment from @RickMethot on 2016-04-22:
progress on conversion of Q parms

1. test with Q as parm, Qlink as power fxn, and float Q
2. still need to test with env effect on Q, and to test mirror
3. random devs approach currently is disabled
4. still need to update ss_write.tpl to output the new format
5. the new approach will create a q for any fleet with survey obs, even with the float option
6. still need to revise ss_readctl_330 to be able to read the new format
7. then need to create block/trend approach and dev approach like that for mgparm and selparm

New format is:
//Q_setup for 3.30
// 1: link type
// 2: extra input for link, i.e. mirror fleet
// 3: 0/1 to select extra sd parameter
// 4: 0/1 for biasadj or not
// 5: 0/1 to float

but need to add another field with fleet id so that not all fleets will need to be read

the above info populates a fleet x 5 matrix with parameter index for each type of parameter needed
Q_setup_parms(1,Nfleet,1,5) // index of first parameter for: 1=base q; 2=env; 3=block/trend; 4=dev; 5=extrastd;

current link functions are:
// Link types
// 1 simple q, 1 parm
// 2 mirror simple q, 1 mirrored parameter
// 3 q and power, 2 parm

[k-doering-NOAA]

comment from @RickMethot on 2020-08-25:
consolidate and rename this issue