Unusual Psi and Confidence Intervals

[SBB]

Hello,

I'm working on a single season POM using false positive detections to estimate wolf pack occupancy and I'm getting odd derived Psi estimates. The individual psi, p, p10, and b estimates, SE's, and 95% CI's look fine for every model I run (with and without covariates) but the final psi (derived) estimates are consistently having issues. See the example below.

DERIVED parameter - Psi-conditional = [Pr(occ | detection history)]

Site psi-cond Std.err 95% conf. interval
1 site 1 1.0000 0.0000 0.0000 - 0.0000
2 site 2 1.0000 0.0000 1.0000 - 1.0000
3 site 3 1.0000 0.0000 1.0000 - 1.0000
4 site 4 1.0000 0.0000 0.0000 - 0.0000
5 site 5 1.0000 0.0000 1.0000 - 1.0000
6 site 6 1.0000 0.0000 1.0000 - 1.0000
7 site 7 1.0000 0.0000 0.0000 - 0.0000 initi
8 site 8 1.0000 0.0000 1.0000 - 1.0000
9 site 9 1.0000 0.0000 1.0000 - 1.0000
10 site 10 0.0306 0.0343 0.0033 - 0.2331
11 site 11 0.9880 0.0434 0.0595 - 1.0000
12 site 12 1.0000 0.0000 1.0000 - 1.0000
13 site 13 1.0000 0.0000 0.0000 - 0.0000
14 site 14 1.0000 0.0000 0.0000 - 0.0000
15 site 15 1.0000 0.0000 1.0000 - 1.0000
16 site 16 0.9871 0.0387 0.1625 - 1.0000
17 site 17 0.0000 0.0001 0.0000 - 0.1907
18 site 18 1.0000 0.0000 1.0000 - 1.0000
19 site 19 1.0000 0.0000 1.0000 - 1.0000
20 site 20 1.0000 0.0000 0.0000 - 0.0000
21 site 21 0.0000 0.0001 0.0000 - 0.1679
22 site 22 1.0000 0.0000 0.1969 - 1.0000
23 site 23 1.0000 0.0000 1.0000 - 1.0000
.....
44 site 44 1.0000 0.0000 0.0000 - 0.0000
45 site 45 1.0000 0.0000 0.0000 - 0.0000
46 site 46 1.0000 0.0000 0.0000 - 0.0000
47 site 47 1.0000 0.0000 1.0000 - 1.0000

I have two questions. 1. Why are some of the 95% CIs 0.00-0.00 when psi = 1.0? and 2. I don't believe for one second that almost the entire study area is 100% occupied. So what's going on here?

I've run similar models with previous years' data and not has this issue. To give you a little background on my data and models: I'm working in a fairly small study area (47 sites total) with 9 sampling occasions. The 1st occasion is based on sign surveys and the other 8 are based on hunter surveys. Although both survey methods can have false positives the sign survey happens to only have certain detections this year (based on how we defined certain/uncertain detections) so I've fixed p10 = 0 and b = 1 for these surveys (otherwise the betas and SE's blow up).

Thank you,
Sarah B.

[jhines]

The conditional Psi's are probability of occupancy for each surveyed site, given it's detection history. So, if a site has any detections over all surveys, we know it's occupied, so it's conditional Psi = 1.0). The std. error should be zero or undefined, and conf. interval should be (1.0 - 1.0) or undefined. I'll look into why the program is printing 0.0 - 0.0 in some of those cases, but you can ignore the conf. interval if the conditional Psi = 1.

For sites where no individuals of the species were detected in any survey, the conditional Psi should be less than 1.0. So, the unconditional Psi (1st psi in output) is the probability that a site in your study area is occupied (not knowing which site we're referring to). This would be the same value for all sites if you don't have any covariates. The conditional Psi refers to specific sites, where we know the detection history. This will be 1.0 for sites with detections, and something else for sites with no detections. Another way of saying it is that 100% of sites with detections are occupied.

Jim

[SBB]

For sites where no individuals of the species were detected in any survey, the conditional Psi should be less than 1.0. So, the unconditional Psi (1st psi in output) is the probability that a site in your study area is occupied (not knowing which site we're referring to). This would be the same value for all sites if you don't have any covariates. The conditional Psi refers to specific sites, where we know the detection history. This will be 1.0 for sites with detections, and something else for sites with no detections. Another way of saying it is that 100% of sites with detections are occupied.

Thanks. This makes sense.

I'm just confused about the sites where I have no detections or only "uncertain" detections but the model is still reporting psi = 1. However, I took a closer look at my detection histories compared to the derived psi estimates and noticed the suspicious psi's and 95% CI's (0.00-0.00) all correspond to sites were we did not conduct our sign survey (so there's a missing value in the detection history) and there were either no detections or only "uncertain" detections from the hunter surveys. Could there be an issue related to the missing values? If there's a "certain" detection this problem would obviously be overridden and the 95% CI's look more reasonable (1.0-1.0).

Thanks,
Sarah B.

[jhines]

Hi Sarah,

I should have thought about it a little more before responding. I don't think you can use the conditional psi's when there are false positives. When there are false positives, the sites with detections shouldn't have a psi=1.0, since the sites could be unoccupied with false detections. So, please ignore the conditional psi's for the false positive model until I can think of a way to compute them.