Using data where three age-classes are marked

questions concerning analysis/theory using program MARK

Using data where three age-classes are marked

Postby B.K. Sandercock » Tue Aug 02, 2016 6:48 pm

I'm working with a dataset for a tropical bird where 3 age-classes were marked: second-year (SY), third-year (TY), and after-third-year (ATY). Technically, there is a fourth age-class of hatch-year (HY) birds but they were censored because the kids all disappear after natal dispersal. I wanted a model that included annual variation, the effects of age-class at banding, but pooled transitions for the same age-classes within the same year.

The PIMs are kind of weird so posting to the forum in case anybody else has a similar question in the future. The oddness arises for how to match up the years for the first couple of transitions because they are orphaned in a model with full time-dependence (see parameters 16 to 18 in the PIMs). The relevant section of the Mark manual is Section 7.3 Using data where both young and adults are marked. The example on page 7-27 of the manual shows an example of coding for 2 age-classes and 4 transitions. The PIMs in the example below have 3 age-classes and 6 transitions for apparent survival. Both models are ignoring possible time-since-marking effects.

Code: Select all
Marked as second-year SY (transitions are SY to TY to ATY)
 INPUT ---    group=1 Phi rows=6 cols=6 Triang;
  INPUT ---                1   7  12  13  14  15;
  INPUT ---                    2   8  13  14  15;
  INPUT ---                        3   9  14  15;
  INPUT ---                            4  10  15;
  INPUT ---                                5  11;
  INPUT ---                                    6;

Marked as third-year TY (transitions are TY to ATY to ATY)
  INPUT ---    group=2 Phi rows=6 cols=6 Triang;
  INPUT ---               16  17  12  13  14  15;
  INPUT ---                    7  12  13  14  15;
  INPUT ---                        8  13  14  15;
  INPUT ---                            9  14  15;
  INPUT ---                               10  15;
  INPUT ---                                   11;

Marked as after-third-year ATY (all transitions are ATY to ATY)
  INPUT ---    group=3 Phi rows=6 cols=6 Triang;
  INPUT ---               18  17  12  13  14  15;
  INPUT ---                   17  12  13  14  15;
  INPUT ---                       12  13  14  15;
  INPUT ---                           13  14  15;
  INPUT ---                               14  15;
  INPUT ---                                   15;
B.K. Sandercock
 
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Re: Using data where three age-classes are marked

Postby cooch » Tue Aug 02, 2016 8:29 pm

Nice -- but you chickened out on posting the corresponding DM. ;-)

In general, building multi-age models using PIMs is relatively straightforward, with some thought. Building the corresponding DM is generally harder -- the main effects are easy enough, but interactions among the various age classes are 'more challenging'. I usually give the 3 age-class DM problem out as an exam question (which is why it isn't in the book -- that would spoil the fun).
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Re: Using data where three age-classes are marked

Postby B.K. Sandercock » Wed Aug 03, 2016 1:04 pm

A better solution to this problem came to me this morning, as often happens, while I was walking my dogs. The order of the three groups for the different age-classes is arbitrary when they are imported into Mark. If the three groups are ordered in descending order with the oldest age-class first and the youngest age class last, then the PIMS for the same model simplify to the following structure. I think this format would make it easier to keep track of different age-classes for fitting annual covariates, plotting the real estimates or using the variance components procedure. Or setting up the appropriate design matrix...
Code: Select all
PIM for ATY birds
 INPUT ---    group=1 Phi rows=6 cols=6 Triang;
  INPUT ---                1   2   3   4   5   6;
  INPUT ---                    2   3   4   5   6;
  INPUT ---                        3   4   5   6;
  INPUT ---                            4   5   6;
  INPUT ---                                5   6;
  INPUT ---                                    6;
PIM for TY birds
  INPUT ---    group=2 Phi rows=6 cols=6 Triang;
  INPUT ---                7   2   3   4   5   6;
  INPUT ---                    8   3   4   5   6;
  INPUT ---                        9   4   5   6;
  INPUT ---                           10   5   6;
  INPUT ---                               11   6;
  INPUT ---                                   12;
PIM for SY birds
  INPUT ---    group=3 Phi rows=6 cols=6 Triang;
  INPUT ---               13   8   3   4   5   6;
  INPUT ---                   14   9   4   5   6;
  INPUT ---                       15  10   5   6;
  INPUT ---                           16  11   6;
  INPUT ---                               17  12;
  INPUT ---                                   18;
B.K. Sandercock
 
Posts: 28
Joined: Mon Jun 02, 2003 4:18 pm
Location: Norwegian Institute of Nature Research

Re: Using data where three age-classes are marked

Postby cooch » Sun Sep 03, 2017 4:33 pm

I was re-visiting the basis for this discussion recently (for adding some related material to Chapter 7 in the book), when I realized the missing comment to Brett's final post is that...his approach absolutely makes good sense, *if* you assume that survival of the second and third age classes is the same among 'marking groups'. In other words, if you assume (say) that survival over an interval of a (say) age class 3 individual is the same, regardless of what age it was markeds at. Look again at the PIMs brett posted (below). Notice that the same indexing is used for intervals on (3, 4, 5, 6), for all three groups of birds. If you're willing to make that assumption, then Brett's approach does simplify things nicely.

Code: Select all
PIM for ATY birds
 INPUT ---    group=1 Phi rows=6 cols=6 Triang;
  INPUT ---                1   2   3   4   5   6;
  INPUT ---                    2   3   4   5   6;
  INPUT ---                        3   4   5   6;
  INPUT ---                            4   5   6;
  INPUT ---                                5   6;
  INPUT ---                                    6;
PIM for TY birds
  INPUT ---    group=2 Phi rows=6 cols=6 Triang;
  INPUT ---                7   2   3   4   5   6;
  INPUT ---                    8   3   4   5   6;
  INPUT ---                        9   4   5   6;
  INPUT ---                           10   5   6;
  INPUT ---                               11   6;
  INPUT ---                                   12;
PIM for SY birds
  INPUT ---    group=3 Phi rows=6 cols=6 Triang;
  INPUT ---               13   8   3   4   5   6;
  INPUT ---                   14   9   4   5   6;
  INPUT ---                       15  10   5   6;
  INPUT ---                           16  11   6;
  INPUT ---                               17  12;
  INPUT ---                                   18;


However, if you're *not* willing to make that assumption, then you're left with a fairly complex model -- period -- that modifying which age comes first in the PIMS won't necessarily solve. The question, then, becomes, whether or not the explicit assumption being made in these PIMs is reasonable. We're all clever enough to come up with situations where it might be, and, on the other side of things, where it might not (e.g., if you suspect 'adults' of individuals marked as adults are an unknown mixture of 'residents' and 'transients', whereas adults from the 'marked as young' group are (by defnition) 'resident). So, it might be quite reasonable in such a case to use different indexing for adults as a function of the age of marking. Which is more or less the starting point for the current examples in Chapter 7.
cooch
 
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Re: Using data where three age-classes are marked

Postby cooch » Sun Sep 03, 2017 9:12 pm

cooch wrote:I was re-visiting the basis for this discussion recently (for adding some related material to Chapter 7 in the book)...


Some of which I've just finished, and uploaded - section 7. has been largely re-worked. I'm planning in working up an example similar to Brett's, where 3 different age-classes are marked, but that will take a bit more time (mostly, because working out all the interactions is truly a pain in the butt. One reason alone for assuming 'adults are adults', or some such, is that it mitigates this issue to a large degree. But assumptions are assumptions....).
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