[Refactor]: Align logL approach across lencomp, agecomp, gen_sizecomp

[Rick-Methot-NOAA]

Refactor request

The approach to calculating logL is inconsistent across lencomp, agecomp, and gen_sizecomp. gen_size calculates logL across females and males at same time and includes ALL bins, even those in tails. It does not include a tail compression feature. So, it is dependent on the small added constant to allow logL calculation for bins with no fish. This difference is a major impediment to merging the logL calcs across the three comp methods.
Inconsistencies include:
a. whether or not a very tiny constant is added to expected values even when the user has not specified using an added constant
b. whether or not tail compression is used

Expected behavior

Potential solution:
if there are zeroes in the comp data, then adding a small constant is needed, but only because of the ln() term in:
SzFreq_like(SzFreq_LikeComponent(f, k)) -= SzFreq_sampleN(iobs) * SzFreq_obs(iobs)(z1, z2) * log(SzFreq_exp(iobs)(z1, z2));

but if a very tiny constant is added only to that term, the nan is avoided.
SzFreq_like(SzFreq_LikeComponent(f, k)) -= SzFreq_sampleN(iobs) * SzFreq_obs(iobs)(z1, z2) * log(SzFreq_exp(iobs)(z1, z2) + 1.0e-15);

This approach is already used in agecomp logL by this line:
exp_a(f, i) /= (1.0e-15 + sum(exp_a(f, i)));
Note that this adjustment is in addition to the user-specified constant added to both the obs and expected.
The agecomp approach is a bit more accurate as it is scaling to 1.0 after adding the tiny constant, whereas the proposed gen_size approach adds it at the final logL calculation so is off by a miniscule amount in terms of summing to 1.0, but avoids another divide computation.

Also note that the this approach is not used for length comp observations. They rely on the user specified constant.

comments please: @kellijohnson-NOAA @iantaylor-NOAA @chantelwetzel-noaa @puntae

[iantaylor-NOAA]

This seems reasonable to me.
We will want to take the time to look at comparisons of the impact of these changes across a range of models. That is, even if our automated tests don't find changes above our chosen thresholds, we should probably look at the differences to make sure we don't see anything unusual.

[k-doering-NOAA]

Good point @iantaylor-NOAA . One of the .csv files saved as an artifact shows all model changes, which you could look at even if the gha doesn't flag the run as failing.

[Rick-Methot-NOAA]

A composition vector has the females in the first half of the vector and the males in the second half. Combined sex obs occupy only the first half.

Lencomp and agecomp approach addresses these two halves of the vector separately with code like
obs_l(f, i)(tails_l(f, i, 1), tails_l(f, i, 2)) to address the first half of the vector
obs_l(f, i)(tails_l(f, i, 3), tails_l(f, i, 4)) to address male half
gen_size approach processes the whole vector in one operation, effectively uses just tails_l(f, i, 1) and tails_l(f, i, 4). This works because the added constant prevents log(0.0) from happening for any bins with no expected fish.

[iantaylor-NOAA]

Does this mean that the generalized size-comp likelihood would be a tiny bit different for a 1-sex model (where the male half of the vector doesn't exist) vs a 2-sex model with only combined-sex samples (where the male half is all zeros)? That's wouldn't be ideal, I think, but I suppose the difference would be pretty tiny anyway.

[Rick-Methot-NOAA]

With use of 1.0e-12, the difference would not be noticeable.

Also, I now realize that the efficient way to do this is to make the adjustment when calculating the tails, which happens just once in readdata. A combined sex obs in a 2-sex model would have the upper tail set to upper end of the first half of the vector so the male bins are not included, which is what happens in the gen_size approach now.

[kellijohnson-NOAA]

Isn't some tail compression possible with the use of a negative bin in the generalized size comps? Second question, in theory would it be possible to move all length composition information to the generalized size composition section of the dat file (with some massaging of course) and not enter length compositions? Just things I am trying to think through while reading this thread.

[Rick-Methot-NOAA]

gen_size can replicate lencomp approach. Kathryn recently did such a test.
gen_size cannot do tail compression at all.
a negative value in a gen_size bin would create an error.
lencomp and agecomp have some bells&whistles beyond tail compression that are not available in gen_size.
much of the code for processing the lencomp and agecomp expected values are in doing the tail compression which happens separately for males and females.