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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.

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?).

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.

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?

Thanks!
Joe

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

Thanks for the reply Bret!

Sorry for my potentially confusing use of "fix". I definitely will not be treating missing occasions as real 1's in the CH. What I meant was that I will fix the estimates for missing occasions to 1's (or maybe 0 is more appropriate?) so they're not being estimated. Similar to using a "dot" for missing occasions (but maybe fixing is better: viewtopic.php?f=1&t=2528&p=8002&hilit=missing+data+dot+fix#p8002).

Mackenzie et al. occupancy book just states that, detection probs can be estimated...from the data collected at sites where repeated surveys were conducted, and that information is then applied to sites only surveyed once....occasions when surveys were not conducted could be considered as missing values. (p. 173).

That seems somewhat straightforward to me. But I guess my problem is that I have the added complication of unequal effort and multiple detection methods.

I understand that time and detection method may be confounded, as you said, since the detection methods were not implemented simultaneously. But, in theory, could I not include time-varying covariates likely to affect detection (like abiotic factors, e.g.) to partially control for time effects and then what's leftover is the detection method effect?

Primary issue/question:
If the potential time-method confounding issue doesn't stop me in my tracks, I'm still trying to wrap my head around how to properly use the information from the ground plus aerial survey sites to estimate detection for the aerial survey only sites. It seems like I should take advantage of the fact that for the ground + aerial sites I know whether the aerial survey mis-classified an occupied site as unoccupied.
EDIT: after some more thought, it seems the time-varying covariate for survey method is exactly what I need. The variation in the CH for the ground + aerial sites is exactly what will allow me to model the flight effect (with the caveat discussed previously), and that information can be "shared" with aerial survey only sites. I don't need to "adjust" anything beforehand which, as Bret pointed out, is antithetical to occupancy modeling.

Also, in case this wasn't clear in my 1st post, the sample sizes I listed for each type of site represent the number of sites that were surveyed following the described method(s). For example, there are 80 independent sites that had a double observer ground survey plus one aerial survey.

Thanks again.
Joe