Hi all,
I'm working on a single-season occupancy model with covariates, and I wanted to pose a question about the interpretation of the real estimate for 'p' in MARK. A while back I learned that the 'real estimate' for 'psi' only reflects the first site and used CH 21 of the MARK book to generate an overall psi estimate, so I wanted to also make sure my interpretation of the real estimate for 'p' was correct.
Going off the spotted owl/barred owl example in CH 21, I see that the text reports a p-hat=0.36 when BAOW=1 and p-hat=0.71 when BAOW=0. My question is, does the p-hat (i.e., the 'real estimate' for p) reflect the daily detection probability (i.e., probability of detecting the species on one survey event), or the overall detection probability (i.e., probability of detecting the species on all n=J survey events: (1-(1-p)^J). Typically I've seen daily detection probability reported as p, and overall detection probability reported as p-hat to reflect p-hat= (1-(1-p)^J), so I was a bit confused by the annotation in CH 21. It seems like the chapter is referring to the real estimate of p-hat = 0.36 as the daily detection probability, as I see in the sidebar on conditional site occupancy that part of the equation includes (1-phat)^J, making me think that p-hat is just the daily detection multiplied by the number of survey events, J.
My detection models are similar to the example in CH 21, and my top detection model has two covariates: session (June = 0, July = 1) and duration (# days stations were active), and the number of survey events J = 5. When I hold duration constant at the average # days stations were active, the 'real estimate' for p when session = 0 is 0.24, and the 'real estimate' for p when session = 1 is 0.51, indicating detection probability is higher in the month of July. What is the best way to report daily detection probability (p), and overall detection probability (phat) for my 5 surveys based on my top model? I know I can generate p and phat from the raw data of detection histories, and from manually calculating it from the raw data I get an average daily detection probability of 0.4125 and an overall detection probability of 0.93 (i.e., 1 - (1-0.4125)^5), but I am curious if there is a way to get a daily and overall estimate from the top model, or if it's best to report that value separately as reflecting the change in month of June vs July.
Any advice would be greatly appreciated, thank you so much!
~Holly