Parameter count question

[birdman]

Quick question about parameter counting. I'm analyzing sparrow survival over 10 years (occasions) for birds banded as adults and those banded as young (2 groups). I've run the model Phi(age*t)p(t).

Does the fact that I've got time specific but not age related survival in recapture mean that the estimate of p(10) keeps the last intervals for each age from being confounded parameters? I'm thinking it should since the p estimate will allow separate identifiability of the phi parameters, and it appears that way in the output. However, due to data sparseness in a few places, I'm getting 20 parameters estimated and I want to make sure I correct to the right number.

If the last intervals are confounded, I count

phi p Beta
Adult 8 8 1
juv 8 0 1

thus 26 parameters

but if not confounded,

phi p Beta
Adult 9 9 0
juv 9 0 0

thus 27 parameters.

Thanks for any input. Just want to make sure I'm not overly confounded myself...

Have a great December however you do or don't celebrate it.
S.P.

[cooch]

Quick question about parameter counting. I'm analyzing sparrow survival over 10 years (occasions) for birds banded as adults and those banded as young (2 groups). I've run the model Phi(age*t)p(t).

Your description of your model isn't informative enough as is to know exactly what model you fit, but I'll hazard the guess that it is 2 attribute groups - banded as young having 2 TSM classes (year after marking, and adult), and banded as adult as the second attribute group - full time-dependence in both.

If so, then the final phi for juveniles in the marked as young group is not estimable, the final phi for the second TSM class (adults) in the marked as young group is not estimable, the final phi for the marked as adults group is not estimable, and the final p is not estimable.

So, if you had 7 occasions, phi(my: a2 t/t, ma: t)p(t), you would have 23 structural parameters, of which 19 would be estimable.

Does the fact that I've got time specific but not age related survival in recapture mean that the estimate of p(10) keeps the last intervals for each age from being confounded parameters? I'm thinking it should since the p estimate will allow separate identifiability of the phi parameters, and it appears that way in the output. However, due to data sparseness in a few places, I'm getting 20 parameters estimated and I want to make sure I correct to the right number.

If the last intervals are confounded, I count

phi p Beta
Adult 8 8 1
juv 8 0 1

thus 26 parameters

but if not confounded,

phi p Beta
Adult 9 9 0
juv 9 0 0

thus 27 parameters.

Thanks for any input. Just want to make sure I'm not overly confounded myself...

Have a great December however you do or don't celebrate it.
S.P.

Again, not knowing exactly what your model is makes it difficult to say. I'd suggest you have a careful read of Appendix F of the MARK book.

[birdman]

Thanks Evan, this cleared up my thinking considerably after structuring the model you suggested. I just wasn't sure about intrinsic indentifiability of parameters estimated across groups, such as the last p which is confounded with terminal phis for each group. Much clearer now. I have been working through the examples in Appendix F for a few days now and most of it seems pretty clear, though I have one related question.

The dipper and AFS Monog examples both deal with parameters being estimated at the 1.0 boundary. In my current data, one issue of concern is estimation of a single p parameter at the lower bound. I know by looking at the data structure that recapture at this occasion is very low, so a low estimate makes intuitive sense. However, I can't get a reasonable estimate or SE, and thus can make no sense of that parameter in the model.

What is your (or others') advice concerning such a situation. Should I fix the parameter at the low level or include it as is? Should such a non-estimable parameter be included in the parameter count when I adjust? i.e. if the model, with sufficient data, should have 27 parameters, but I know this one cannot be estimated, should I make the parameter count (for AIC inference) 26 or 27?

Thanks again, and cheers.
SP