Hey Joe, a few thoughts inline below.
jCeradini wrote:Goal: estimate probability of occupancy and detection, while accounting for multiple survey methods (method specific detection estimates would be nice too), double observers, and unequal sampling effort (oh my).
All surveys were done in the same "season" and closure is assumed based on the ecology of the species.
- A Sites (n = 170): 2 ground surveys per site
- B Sites (n = 80): 2 ground surveys/site plus one additional aerial survey/site
- C Sites (n = 80): one aerial survey/site only
The 2 ground surveys/site were 2 observers independently surveying the same site ~simultaneously. They should be independent (in the sense that what one tech observes doesn't influence what the other tech observes).
The encounter history thus has 3 occasions. I will fix occupancy/detection to 1 for sites that have missing occasions (e.g., only the B sites were surveyed 3 times). This approach is briefly discussed in the Mackenzie et al. occupancy book as the "double sampling design" (p. 173), which suggests modeling all the data within one framework.
I don't have MacKenzie in front of me to reference (will check later), but what you are suggesting does not sound correct re. setting sites with missing sampling events to 1. If I understand (and maybe it comes down to what 'fix' means above) you are talking about taking all the survey locations (sites) that were missing occasions (unsurveyed; typically denoted at a ".") and changing them to a '1', so you could have a encounter history that was say ..1(unsurveyed in t=1, unsurveyed in t=2, surveyed and observered in t=3), and changing that history to "111"?
As I see it, you have 3 possible structures for your ch based on the above:
-11x
-111
-xx1
where 1st is your double observer, 2nd is your double obs + aerial, and 3rd is your aerial survey
Now, I don't have an issue with sharing the data to estimate parameters, but you are going to have to use a fairly reduced model set for the analysis (e.g., no g*t or even full t models will work). Based on what I see, you cannot separate method of survey here easily (you only have 1 event of method aerial on one site), so I don't think it can be teased out easily and without some pretty strong assumptions being made (maybe someone smarter will jump in)
What I'm confused about:
1) How to take advantage of the aerial detection information from the B sites to correct detection for the C sites (one aerial survey only): If I model all the data within one framework, do I need to correct the B Sites' aerial surveys before modeling? So, if a B site was occupied based on the ground survey, the flight encounter history for that site must be a 1 (even if it was recorded as a 0). Then model the effect with a time-varying covariate for detection method, or just a time model on p (same thing, assuming the encounter history is ordered correctly?).
What do you mean 'correct'? If you mean make a survey value a 1 because a different survey value was a 1, then you are missing the point of occupancy modeling in general and moreover you are making up data so you can estimate the effect of time, which as I indicate above, you likely cannot do.
2) Should I use the multimethod model (e.g.,
Nichols et al. 2008. Multi-scale occupancy estimation and modelling using multiple detection methods) to account for potential lack of independence between detection methods or is a regular single-season model, with a detection method covariate, appropriate (if I need to use the former, can I convince Jeff Laake to add the model to RMark
)? I'm confused about how ground surveys and aerial surveys (done at separate times but within the same "season") would be dependent. I am not interested in occupancy at multiple scales.
I don't think you have the data for the multi-method approach, and I seem to remember a couple of papers that were published critically evaluating that model you should dig for. But, even just to look at method differences, you don't have any methods that overlap sample periods in your data set, your method 1 and method 2 are separated by time, and you have 1 survey attempt, so how will you separate the effect of the method from effect of a different sampling period and estimate a parameter based on a single attempt of the method?
3) Do I need to do anything special to account for the double observer survey or, assuming I'm confident in independence, simply treat them as separate/independent occasions?
No, you treat them as 2 separate occasions in you ch. If you wanted to look at any possible dependence in p between observers/occasions, then I supposed you could use MARK's bootstrapping routine.
Overall, I think you need to rethink what is actually possible with these data. It seems that you might be able to estimate some simple models for detection, but stretching it out much farther than that requires some pretty significant assumptions and data twisting based on what you described here.
\bret