Multi-season Multi-state design matrix

[Sunday]

I am working on a very simple multi-season, multi-state occupancy problem (specifics: 2 seasons, 3 surveys in each season, states = 0, 1 or 2). I am using the psi, R, delta p parameterization. I had a question about how delta is coded in the design matrix. The default (what shows up when the design matrix pops up) is as follows:

-,e1,e2,e3,
dlta(1-1) 1 0 0
dlta(1-2) 1 0 0
dlta(1-3) 1 0 0
dlta(2-1) 1 0 0
dlta(2-2) 1 0 0
dlta(2-3) 1 0 0
p1(1-1) 0 1 0
p1(1-2) 0 1 0
p1(1-3) 0 1 0
p1(2-1) 0 1 0
p1(2-2) 0 1 0
p1(2-3) 0 1 0
p2(1-1) 1 0 1
p2(1-2) 1 0 1
p2(1-3) 1 0 1
p2(2-1) 1 0 1
p2(2-2) 1 0 1
p2(2-3) 1 0 1
The setup window’s default label for this is the p(.,.) model. To me, this is the p(state) model rather than the p(.) model.
My thought for the p(.) model was as follows:
dlta(1-1) 1 0
dlta(1-2) 1 0
dlta(1-3) 1 0
dlta(2-1) 1 0
dlta(2-2) 1 0
dlta(2-3) 1 0
p1(1-1) 0 1
p1(1-2) 0 1
p1(1-3) 0 1
p1(2-1) 0 1
p1(2-2) 0 1
p1(2-3) 0 1
p2(1-1) 0 1
p2(1-2) 0 1
p2(1-3) 0 1
p2(2-1) 0 1
p2(2-2) 0 1
p2(2-3) 0 1
I also wanted to test p(state, year) which I specified in the design matrix as:
-,e1,e2,e3,e4,e5,
dlta(1-1) 1 0 0 0 0
dlta(1-2) 1 0 0 0 0
dlta(1-3) 1 0 0 0 0
dlta(2-1) 1 0 0 0 0
dlta(2-2) 1 0 0 0 0
dlta(2-3) 1 0 0 0 0
p1(1-1) 0 1 0 0 0
p1(1-2) 0 1 0 0 0
p1(1-3) 0 1 0 0 0
p1(2-1) 0 0 1 0 0
p1(2-2) 0 0 1 0 0
p1(2-3) 0 0 1 0 0
p2(1-1) 0 0 0 1 0
p2(1-2) 0 0 0 1 0
p2(1-3) 0 0 0 1 0
p2(2-1) 0 0 0 0 1
p2(2-2) 0 0 0 0 1
p2(2-3) 0 0 0 0 1

I wanted to double check with the forum that these were correct and make sure that I didn’t have to stack the p2’s with the deltas as is done with the default.
Thanks in advance...
Cheers,
Trevor

[Sunday]

Also...a curious aside. When you first change the parameterization from Psi (R,s) p(o,t) to Psi R p delta, the betas for the p's are labeled as "d1, d2, d3...". However, if you recall any previous models, the labels for the betas are "e1, e2, e3...". I'm guessing this is unimportant but just thought I'd make a note for those who keep track of such things (say perhaps Jim Hines?).

[darryl]

Hi Trevor
These models are newer so haven't been trialled as much as the other ones which means there's still a certain amount of 'quirkiness' in how they're set up.

It's hard to think of a meaningful reason why there would be 1's in the first column of the default design matrix for the p2's. I always just delete them out and guessed it was a small oversight on Jim part.

Model names are just labels and the important thing is you know what it means relative to the model you're fitting. I'm sure Jim knew what he meant at the time, but I' agree it could perhaps be clearer. Personally I'd probably call this part of the default model p1(.),p2(.),delta(.), or p(state),delta(.).

delta is also a detection probability (of a sorts), so you may want to consider putting a year effect on that too. The design matrix you've given says the year effect is different for the different state (ie an interaction between year and state effects of detection) and an intermediate model that says the effect of year on detection is the same for the different states (if that makes sense to your situation) is:

p1(1-1) 0 1 0 1
p1(1-2) 0 1 0 1
p1(1-3) 0 1 0 1
p1(2-1) 0 1 0 0
p1(2-2) 0 1 0 0
p1(2-3) 0 1 0 0
p2(1-1) 0 0 1 1
p2(1-2) 0 0 1 1
p2(1-3) 0 0 1 1
p2(2-1) 0 0 1 0
p2(2-2) 0 0 1 0
p2(2-3) 0 0 1 0

[Sunday]

Right Darryl....that makes sense. Indeed, that intermediate model is applicable to my situation and I will run it as well.

Regarding delta, I predict that it will be very high (i.e. about 1) and likely would not vary so I've decided to keep it simple and not test a year effect.

Thank you so much for your response. Your insights, not only in the threads that I started but also in other threads, have been very helpful for me. Thanks for your time.

Trevor