estimating f from N and phi (S)

[sixtystrat]

I have a set of CMR data and I am using the RD with Huggin's p and c with Random Effects. That model provides estimates of phi (with temporary immigration) and N is a derived parameter. I can of course estimate lambda from the N's and calculate the SEs with the delta method. My question is whether lambda and phi can then be used to calculate f (lambda-phi=f)? The problem comes with estimating the variance. I assume it is not as easy as just adding the variances because lambda and phi are clearly not independent for a given year. Is there a solution to this? Thanks!
Joe

[cooch]

You might consider using RD Pradel models - specifically, data type 163 ("Robust Design Pradel Full Likelihhood p and c with lambda from ratio of N's"). That, in combination with either the Delta method (somewhat painful), or using a numerically intensive approach (MCMC in MARK being my go-to at this point -- see the
section/example starting on p. 41 in the Delta method appendix B). You can use this approach (in conjunction with R, or SAS) to create whatever derived parameter you want, and then evaluate uncertainty directly from posterior. This is *exactly* what JAGS lets you do. The only difference is that JAGS calculates the derived parameter(s) at each step of the chain, whereas using MARK requires post-processing the chains. Its actually not particularly difficult.

And no, the 'robustified Pradel models' are not documented in the book.

[sixtystrat]

Very helpful; thanks Evan!