Relation between RSPF and Mackenzi occupancy/detection model

[northernbio]

My question is about deriving an RSPF from an occupancy/detection model. Imagine that I am point sampling a forest bird (brown creeper) using a random stratified sample design, have multiple detections (recordings) from each site and have continuous habitat covariates. With this sample design I can validly estimate the intercept, and hence absolute probability (RSPF) rather than just relative selection (RSF). My single-season, multiple-visit, occupancy/detection model produces something like:

Estimate:
A1 psi : -0.703729
A2 psi.dense_conifer : 0.236967
A3 psi.young_forest : -0.906724
B1 p1 : -0.564892
B2 p1.recording_quality : 0.267717

What is the relationship between this model and an RSPF (as say, defined by Manly et al.)? My first thought is that the occupancy model component (see below) is equivalent to a simple logistic regression (but where the coefficients have been derived after correcting for detection error), and is hence the RSPF. Am I being overly simplistic here (see example calculation below)? Am I violating assumptions?

Brown creeper (BRCR)
Estimate:
A1 psi : -0.703729
A2 psi.dense_conifer : 0.236967
A3 psi.young-forest : -0.906724

so...

logit_brcr = -0.703729 + (dense_conifer * 0.236967) + ( young-forest * -0.906724)
odds_brcr = 2.718 ^ logit_brcr
prob_brcr = odds_brcr/(1 + odds_brcr)


Rob

[darryl]

Nope, that's exactly how I think it could be done. Although, you do have to think about exactly what a 'presence' is this case given your field sampling protocols and so therefore what the probability actually means biologically.
Cheers
Darryl

[northernbio]

Thanks Darryl.

Okay, so I don't need to carry over the detection coefficients to the RSPF.

My focal species all have defended territories during the 6 week breeding period, with a radius less than the detection radius of the microphones (territories of about 0.25 ha with a 30 m radius, where microphones detect 100 m), and sampling occurs over a 3-5 day period... so I feel relatively confident about the closure assumption. For wide ranging species, like pileated woodpecker, a presence (or especially absence) may mean something different.

Rob