Hi,
I'm trying to figure out how to construct p(t)=c(t) in the design matrix for closed population mark-recapture
I started with a DM using a common intercept for p(t),c(t) (6 trap sessions, huggins with full heterogeneity)
1 0 0 0 0 0 0 0 0 0 0 0 0 pi
0 1 1 1 0 0 0 0 0 1 0 0 0 p
0 1 1 0 1 0 0 0 0 0 1 0 0 p
0 1 1 0 0 1 0 0 0 0 0 1 0 p
0 1 1 0 0 0 1 0 0 0 0 0 1 p
0 1 1 0 0 0 0 1 0 0 0 0 0 p
0 1 1 0 0 0 0 0 0 0 0 0 0 p
0 1 0 0 1 0 0 0 0 0 0 0 0 c
0 1 0 0 0 1 0 0 0 0 0 0 0 c
0 1 0 0 0 0 1 0 0 0 0 0 0 c
0 1 0 0 0 0 0 1 0 0 0 0 0 c
0 1 0 0 0 0 0 0 0 0 0 0 0 c
But I'd like to constrain p so that the parameters are estimable, and would therefore like to construct p(t)=c(t) using the design matrix, but I'm having some problems.
My first thought is to follow a p(.)=c(.) model, so make all p=1 and all c=1 and delete the intercept because it is redundant, but keep in the time variation. The model then looks like this:
1 0 0 0 0 0 0 0 0 0 0 0 pi
0 1 1 0 0 0 0 0 1 0 0 0 p
0 1 0 1 0 0 0 0 0 1 0 0 p
0 1 0 0 1 0 0 0 0 0 1 0 p
0 1 0 0 0 1 0 0 0 0 0 1 p
0 1 0 0 0 0 1 0 0 0 0 0 p
0 1 0 0 0 0 0 0 0 0 0 0 p
0 1 0 1 0 0 0 0 0 0 0 0 c
0 1 0 0 1 0 0 0 0 0 0 0 c
0 1 0 0 0 1 0 0 0 0 0 0 c
0 1 0 0 0 0 1 0 0 0 0 0 c
0 1 0 0 0 0 0 0 0 0 0 0 c
But this model has a different deviance than the p(t)=c(t) model derived from the PIMs (reference page 14.14).
Can anyone help point me in the right direction with regards to this?
Much appreciated,
Stephanie