Same Fixed Var for PSI and p in Repeated Count Model: valid?

[ferny]

Hi guys - first post, hope you can help me.

Model:
I'm running abundance models, which in presence are called Repeated Count Data (Royle Biometric). From the online tutorials it's Chapter 8.

Question 1:
Can you use the same covariable for PSI and p in the same model?

Question 2:
Can you use a fixed variable for p (i.e. one which does not and cannot change between survey visits)?

Context:
Specifically I'm using pond Area, which I have coded as a category variable with three levels (2+reference category). Area is a fixed value - it does not change between surveys. This makes it an ideal candidate for a PSI covariable. Initially I was simply asking "What effect does Area have on abundance (PSI)" - this is (part of) my research question. But one of my supervisors requested that I ask the following question: "What effect does Area have on abundance (PSI), having controlled for any effect Area has on detection rates". This is easy enough to code - I simply took each of my two (non-reference) PSI categories, and copied them into a p tab 5 times each, once for each survey. Therefore, when you look at the data entry sheet each of the columns (representing a survey) are identical. This is a unique situation with my dataset and there wasn't an example covering this possibility in the tutorials (which rightly kept things more simple!). But of all the variables I've used, this is the only one which *cannot* change between surveys as surveyor, temperature, turbidity, wind or the like could. It's also the only one where I've 'doubled up' and am looking at the same variable on both parts of the model...and I'm not 100% convinced this is a valid approach.

This also has a big impact on the results which the model set gives me so unfortunately it's not just a hypothetical question...and I'm not sure where else to look for information to answer it.

I've tried search but my search terms were a bit awkward. For reference, the entirety of my Presence knowledge comes from the online tutorial courses 1-5+8 and a year of working on these models for my Masters - so if the answer is in there please could you signpost me to the relevant bit and I hang my head in shame and apologise for having missed it, or if it is written simply elsewhere any signposting gratefully received!

[ferny]

In case anyone comes across this same question in the future and finds this post, it looks like pre-2008 people were cautious about doing this, but then along came Kery 2008 and it looks like we can:

Estimating Abundance From Bird Counts: Binomial Mixture Models Uncover Complex Covariate Relationships
The Auk 125(2):336-345. 2008
doi: http://dx.doi.org/10.1525/auk.2008.06185

(Also, I think this question ought to have gone in the general questions (viewforum.php?f=34) forum rather than here - my apologies)