Occupancy Estimation output problem

[Sarah Reed Hurteau]

Hi All,
I am using the occupancy estimation models on avian survey data, with 3 visits to each site, and sites scattered across 3 mountain ranges (which I'm using as groups). I also have multiple covariates such as canopy cover, and GIS derived elevation. I have standardized all covariates prior to importing into MARK.

My problem is when I use elevation as a covariate there seems to be some weird interaction with my range groups, so that my beta estimates are between 900-2500 and the number of parameters in the results browser shows 3 when there should be 7. Has anyone seen this before?

I ran into this problem with another species and a different covariate, but the problem resolved itself when I standardized the covariate. Do you think I have my data set up incorrectly or is it my design matrix? Any suggestions? Examples below.

Thanks,
Sarah

Example of design matrix: where top 9 rows are p and next 3 are psi,
Z = elevation

1000000
1000000
1000000
0100000
0100000
0100000
0010000
0010000
0010000
000100Z
000010Z
000001Z

Example data input
/*History Range1 Range2 Range3 Canopy elevation*/
001 1 0 0 0.432 -1.0575;
100 1 0 0 0.233 -0.7834;
000 1 0 0 -0.760 -0.1622;
001 1 0 0 1.623 0.06111;
000 1 0 0 -0.958 0.59455;

[gwhite]

Sarah:
You never said whether you standardized the elevation covariate to be standardized within each mountain range (so that you have 3 means and SDs), or across mountain ranges. However, I would not standardize elevation (because MARK takes care of the range of values now -- didn't a year or so ago).

Gary

[Sarah Reed Hurteau]

Hi Gary,
Thanks for the advice. I had originally standardized across ranges, but I just tried it standardizing within range, not standardizing range, and using the standardize individual covariates, and I still get the same problem. It shows up in the 3 beta estimates for psi. Any new suggestions?

Sarah

[darryl]

Sarah,
How many sites do you have? It sounds like MARK is trying to make the occupancy probability to be either 0 or 1 based upon the elevation covariate. Sometimes I've seen this when sample sizes are smallish.
Darryl

[Sarah Reed Hurteau]

Hi Darryl,
I have 178 sites. Your correct MARK is trying to push the occupancy probability to 1, at least that is what is on the output.
Sarah

[darryl]

Sarah,
Do you have sites evenly spread across the elevational gradient, or are they clumped around a few values?

When there are covariates in the model, the value of psi reported by MARK is calculated for a single site. There are about 3 options that you can select when running the model for what covariate values are associated with that site; 1) and 'average' site where the average covariate values are used; 2) the covariate values associated with the 1st site in the input file; and 3) something else. However I've sometimes found people can find this misleading. What I suggest you do in a spreadsheet is list out the elevations for all sites, take the beta estimates associated with the psi parameters (the last 4 according to your design matrix) and build the logistic regression equation. You can then estimate psi for each of your sites. What I'd be interested to know is whether the estimates tend to be either 0 or 1, or do you get a good spread of values?

Finally, what is your estimate(s) of psi without the elevation covariate?

Darryl

[Sarah Reed Hurteau]

Darryl,
The sites are spread evenly across the elevational gradient (as part of the sampling design).

When I ran the logistic regression, the estimates tended toward 0.

When you mention the third option for covariates, the 'something else', what does it do?

The psi estimates for p(R) psi(R) where R is range (without elevation)
Range 1 0.231
Range 2 -0.908
Range 3 -0.395

and for the best model p(R) psi(Canopy cover)

Range 1 -0.573
Range 2 -0.338
Range 3 1.356

Sarah

[darryl]

Sarah,
The 'something else' was me not being able to remember what the third option is. I think it's something like user specified covariate values. Next time you run a model in MARK the options are down in the lower right-hand corner of the run window.

When you say logistic regression are you talking about just running a simple logistic regression in some other stats package, or taking the beta values from MARK and use the logistic regression EQUATION (or logit link) to calculate the values of psi for each site? Another option is to use PRESENCE that will report the estimates of psi for each site by default....

I don't understand those values of psi you've given me; they should be between 0 and 1.

Darryl

[gwhite]

Sarah:
There were no occupied sites above an elevation of 2558, and there is apparently a uninteresting optimum of the likelihood with psi = 1 until elevation reaches 2400 or so, and then a very sharp decline to 0 after 2600 or so. However, I was also able to get a solution with the simulated annealing algorithm that fit a more reasonable line to the data, with a gradual decline with elevation. But, the AICc for this model was higher than the uninteresting solution. Darryl guessed correctly that if you were to plot your solution, you would have seen the sudden drop from psi = 1 to psi = 0.

I'll send you via a private email the solutions that I got, plus an Excel spreadsheet that shows the interesting solution. If you paste in the beta values for the uninteresting solutions, you will also see the sudden sharp decline.

I've not seem this type of behavior before, definitely never in a logistic regression unless there were all successes at one end of the scale and all failures at the other end, with no overlap in the values of the predictor variable. I wonder if the uninteresting solution is something that might be characteristic of the occupancy model where both p and psi are being estimated, and there is only a small amount of overlap in values of the Z variable. The second group is particularly suspect.

Gary

[darryl]

Sarah,
After looking at your data I think your problem is a combinations of things, most of which Gary has already alluded to.

Firstly, above a certain elevation for each group, you never had any detections but you do have detections right down to the lower elevations. I think MARK is picking up on this so giving you this uninteresting solution.

Secondly, detectability is estimated to be pretty low. From models without the elevation covariate, then p-hat is about 0.3 or lower. With only 3 surveys per site then there's a pretty good chance that the species may have been there, but undetected. This makes it harder for the methods to tease apart psi and p, leading to unreliable estimates. From some of the work we've done on study design you probably should have done 5 or more surveys per site; cutting back on the total number of sites if need be because of logistics (I know, easy for me to say from my office chair).

I hope this helps.

Darryl