MacKenzie et al occupancy models

[jjulian]

I am using MacKenzie et al.'s occupancy models (in MARK) to estimate detection probability (p) and the proportion of sites occupied (psi) in pond breeding amphibians. With these models, investigators have used individual covariates to model detection probability as a function of time of day, habitat type, precipication events, etc. However, has anyone seen any refs for folks who have used search technique as an individual covariate of detection probability? Would this violate some of the model's assumptions?

Using search technique as a covariate would be most useful in cases where someone switches their search technique during the year from egg mass visual encounter surveys in the spring, to larval dipnet surveys in the summer as the study species hatches and becomes free swimming. Using search technique as a covariate of p would then be used to estimate detection probability for the entire length of the sampling year.


Jim

[bmitchel]

Jim -

If your search technique switches for all sites at the same time (i.e. same occassion), I don't think it makes sense to use technique as a covariate. This is because you can't separate technique from other factors that may be changing between occasions. Instead, I would probably model different p's for each occasion where the method changes. In other words, if occassion 1 and 2 used method 1, 3 through 5 used method 2, and occassion 6 and 7 used method 3, my PIM for p would look like:

1 1 2 2 2 3 3
1 2 2 2 3 3
2 2 2 3 3
2 2 3 3
2 3 3
3 3

[bmitchel]

Jim -

[Please ignore the earlier post from me... a draft was inadvertently submitted]

If your search technique switches for all sites at the same time (i.e. during any given occasion only one method was used), I don't think it makes sense to use technique as a covariate. This is because you can't separate technique from other factors that may be changing between occasions. Instead, I would probably model different p's for each occasion where the method changes. In other words, if occasion 1 and 2 used method 1, 3 through 5 used method 2, and occasion 6 and 7 used method 3, the PIM for p would look like:

1 1 2 2 2 3 3

Mathematically, this might amount to the same thing as using method as a covariate... but I think that using different p's when techniques changes is more straightforward, and makes it clearer that technique may not be the only thing changing. This approach also allows you to easily model the other covariates (temp, rainfall, etc...) differently for each search technique.

Where I think you should use technique as a covariate is in the situation where multiple techniques were used during one trapping occassion. It does not sound to me like this is the case in your situation.

Brian

[cooch]

Jim -

Mathematically, this might amount to the same thing as using method as a covariate...
Brian

Not entirely equivalent. Using the PIM approach is strictly analogous to a single-level ANOVA - all you ask is the basic 'heterogeneity' question. Suppose you anticipated that one technique was (say) twice a likely to detect something as another technique - you'd then want to build this sort of 'rank structure' into the constraint. You could do this in any number of ways (for example, by using some 'guesses' as to relative efficiency, and using ordinal covariates, or perhaps more generally using the cumulative logic link). However, you still would not be able to separate temporal effects on p from methodological effects on p (since they would be effectively collinear).

[darryl]

If your search technique switches for all sites at the same time (i.e. during any given occasion only one method was used), I don't think it makes sense to use technique as a covariate. This is because you can't separate technique from other factors that may be changing between occasions. Instead, I would probably model different p's for each occasion where the method changes. In other words, if occasion 1 and 2 used method 1, 3 through 5 used method 2, and occasion 6 and 7 used method 3, the PIM for p would look like:

1 1 2 2 2 3 3

I think I'd use a more general PIM structure than Brian and have a seperate p parameter for each survey, then apply any constraints though the design matrix and with covariates (in fact I think you need to do this in MARK if you want to make detection probability a function of something like air-temp that may vary at each site, each survey).

I half agree with Brian's inital point that you may not be able to seperate out the effect of 'method' from other stuff on p, but it depends how many surveys you've done it the year. For example, if you only did 2 surveys, and used different methods in each, then you would not be able to tease out 'method' from other things that may have been different. But if you used the same method for 3 surveys, then a different method later in year for another 3 surveys, then I imagine that you should be able to tease out 'method effects' from other other factors. Really it comes down to how much replication and how 'balanced' your study design is with respect to the factors you want to include in your model for p and/or psi.

However another point you might want to consider is that you're comparing apples with apples in the first place. Is the manner is which 'occupancy' is defined in spring also hold for summer? Is the closure assumption likely to be (badly) violated?

Cheers
Darryl

[jjulian]

Thanks for the feedback thus far, here’s a little more detail on my surveys.

There are 8 sampling occasions – occasions 1-3 are done with method V (visual encounter survey), and occasions 4-8 are method D (dipnet surveys). However, for half of our sites we did not sample them on occasions 2, 6, and 8 (each site has at least 2 method V visits, and 3 method D visits).

Occupancy is defined as the detection of any life stage (egg, larval, or adult) of the species of interest. Egg masses are around during occasions 1-3, but generally absent in occasions 4-8. Larvae are around during occasions 3-8, and generally absent from 1 and 2. Adults can be seen or heard during all occasions. Thus, not all life stages are present at each sampling occasion. Since method V is effective at detecting egg and adult stages, and Method D is effective at catching larvae would I be grossly violating the assumption of closure?

Another assumption is that a “false” presence is not recorded, but what about the opposite situation? If you cannot id every captured individual to a species, is this a violation of the model? The id of the larvae of some species do not become evident until they mature.

As far as my original question, this is what I’ve taken from comments:

If there are temporal changes between occasions that could affect p that weren’t quantified when sites were visited, it would be best estimate a separate p for each occasion, use method as a covariate (of p), and include any other site specific covariates (i.e. temperature) that I feel may be appropriate. I assume the advantage of this approach would be that it would separate “temporal” effects on p from “methodological” effects.

If there aren’t temporal changes between occasions that affect p, a less general PIM structure like 1 1 1 2 2 2 2 2 would be appropriate, and I would include site specific covariates to explain other sources of variation in p.

Have I misinterpreted what folks have been getting at?


Jim

[darryl]

Occupancy is defined as the detection of any life stage (egg, larval, or adult) of the species of interest. Egg masses are around during occasions 1-3, but generally absent in occasions 4-8. Larvae are around during occasions 3-8, and generally absent from 1 and 2. Adults can be seen or heard during all occasions. Thus, not all life stages are present at each sampling occasion. Since method V is effective at detecting egg and adult stages, and Method D is effective at catching larvae would I be grossly violating the assumption of closure?

As you're defining occupancy as the presence of any life-stage of the species then the closure assumption is probably ok provided the species is either always present or always absent from your sites from the first to last survey.

Another assumption is that a “false” presence is not recorded, but what about the opposite situation? If you cannot id every captured individual to a species, is this a violation of the model? The id of the larvae of some species do not become evident until they mature.

The assumption of the models in MARK is that you don't misatkenly say the species was there when it wasn't. A few of us have talked about extending the models to situations where you might be unsure about whether you've detected the target species, but haven't really had a chance to take a serious look at it yet though.

If there are temporal changes between occasions that could affect p that weren’t quantified when sites were visited, it would be best estimate a separate p for each occasion, use method as a covariate (of p), and include any other site specific covariates (i.e. temperature) that I feel may be appropriate. I assume the advantage of this approach would be that it would separate “temporal” effects on p from “methodological” effects.

Ok, although I would have temperature would be a covariate that is varying al the time hence would be a survey-specific covariate (measured with each vist) rather than a site-specific one.

If there aren’t temporal changes between occasions that affect p, a less general PIM structure like 1 1 1 2 2 2 2 2 would be appropriate, and I would include site specific covariates to explain other sources of variation in p.

Ok, but you couldn't inculde any survey-specific covariates (eg temperature or observer) using this PIM structure

Darryl