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Greetings:
I am running a 32 year occupancy data set for spotted owls, which has 1 group and 14 surveys per year (448 enc) using the robust occupancy formulation with psi(1), gamma, and epsilon. When I run the data WITHOUT an IC in the file I get reasonable occupancy estimates that are greater than the naïve estimates.

However, when I append ICs to the file (there are 448 IC, each representing whether there was reproduction noted on each visit) I get different lower estimates. These estimates are less than the naive estimates, which is not correct. Note that I used the global model psi0 e(yr) g(yr) p(year*survey) for both cases (so I did not use an IC in the model).

I also tried the psi, epsilon formulation, but got the same results.

To determine if the problem were too many ICs, I created 1 dummy IC and attached it to the data file and re-ran the same global model (not using the IC). Again the estimates were lower than the run without an IC in the file, and lower than the naive estimate.

There are lots of missing values in the data (dots for not surveyed), but no missing values for the IC (it was noted for every survey that occurred).

Thanks for your consideration of this issue (I hope I'm being myopic and it's something easy). Mary

I just realized what I did not specify, is that this is not an individual covariate (IC) problem per se. I know MARK reports estimates for a particular encounter history when there are ICs. The issue is weird (very low) estimates for models WITHOUT the IC. That was the disturbing thing.

Sorry, I didn't see this post until now. If you're still interested, here's my take. For a single season occupancy model, it should be impossible to get occupancy estimates which are lower than the naive estimates, since you are just dividing the naive estimate by detection probability to get the occupancy estimate. With multi-season occupancy, you are trying to estimate initial occupancy and colonization and extinction for each interval between seasons. If you allow all parameters to vary by season, then I think the occupancy estimates should be greater than or equal to the naive estimates. However, if you put any constraints on the model, then it is possible for the occupancy estimates to be lower than the naive estimates for some cases. It is similar to the case where you do a regression line on 3 or more points... some points will fall above the line and some below.

Jim H.