estimable parameters and link functions in POPAN formulation

[whitmere]

Hello all
I am using the POPAN formulation to estimate abundance from a dataset with four capture occasions. I have two questions:

1) In A Gentle Introduction Chap 13, it states that a log or identity link function should be used for the super-population size (N) parameter. Are there particular situations where one of these link functions is more appropriate than the other? From the MARK help file, I read that the log link function constrains the parameter to be positive, whereas the identity link function does not. Would it therefore be more appropriate to use the log link function for N?

2) I am unsure whether I am counting estimable parameters correctly. For the fully time dependent model p(t)phi(t)pent(t) with four capture occasions, there are 12 parameters. From what I understand, five of these are confounded (final phi, initial and final p and initial and final b) and MARK won't estimate b0. Therefore I calculate that there are six estimable parameters. Is this correct?

Thank you for your help!

[cschwarz@stat.sfu.ca]

Either the log-link or the identity should work with N. The only problem that you may run into is if you have a very large population and so the identity link may numerically overflow.

For counting parameters, see bottom of page 6.
There are a total of 3k parameters.
With 4 capture occasions there are
4 p's
3 phi's
4 pents
1 superpopulation size
------
12 parameters

But not all parameters are separately estimable. This is where you have to be careful about counting. Even though phi(3) and p(4) are not separately estimable, the product phi(3)p(4) is a "parameter" that can be estimated and needs to be counted.

You can estimate separately
p(2), p(3)
phi(1), phi(2)
b(2)

Plus the confounded parameters:
phi(3)* p(4)
b(0)*p(1)
b(3)/phi(3)
b(1)+b(0)(1-p(1))phi(1)
+ superpopulation parameter that is a weird confounding

Less 1 parameter because b(0)+b(1)+b(2)+b(3)=1

This gives a total of 9 parameters or 3K-3 in general.

[whitmere]

Thank you for the help!