Resightings in multi-state models?

questions concerning analysis/theory using program MARK

Resightings in multi-state models?

Postby ardr » Tue Feb 01, 2011 3:02 pm

Hi everyone,

I’m trying to use multi-state models to answer the simple question of whether survival in state A differs from state B, but I have data that are best described as “live capture and release” plus “resight” data.

Example:
Summer breeding (state A) and summer non-breeding (state B) birds
Sampled twice per year for 5 years, in breeding and in wintering season (same geographic location)
Winter captures coded as a “resight” because breeding state cannot be coded during winter but these captures offer information about survival
Want survival estimates for breeding and non-breeding states (SA and SB)

After much RTFM (and primary lit and forum posts) and many analysis forays, I selected a multi-state Barker model as the best choice for my particular dataset. However, I immediately got the error that this model is restricted to “AB01” data and does not accept “2” as a resight code, as the other Barker models do.

Is there really no way to include my out-of-season “resight” data in a multi-state model? Is there a workaround? A better model class choice? Any and all suggestions are welcome and appreciated.

Reducing the dataset to only “in-season” observations results in giant error estimates, but the only other workaround that I can even halfway justify is coding out-of-season captures as “non-breeding” and hoping that allowing time variation in transition probabilities will take care of the uneven distribution of states among sampling encounters (but unfortunately I can’t use a primary/secondary setup in a robust design because that produces the error that you can’t have both states A and B within a single primary).

I’m sure that someone out there has dealt with a similar situation before - any advice from you wise experts is greatly appreciated, and a giant thank you in advance!

Cheers,
ardr

P.S. More specifics on my sampling design/dataset/study organism (which is not actually a bird, or breeding, but was nicely analogous to this example used in the MARK book) happily given upon request.
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Re: Resightings in multi-state models?

Postby krgrayson » Tue Feb 01, 2011 3:18 pm

Hi Ardr -

When do the transitions between states occur? Using the example you gave, if you can justify that the "decision" between breeding or not breeding occurs in the spring (as is common in birds and amphibians for example), you can make only one transition possible between states (in the spring prior to the summer sampling). Thus individuals coded as "A" in the summer are also "A" in the winter, but can transition to the "B" state in the spring. So you would have separate summer and winter survival probabilities for "A" and "B", which can be useful. Not sure if this applies to your organism or its states.

Kristine
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Re: Resightings in multi-state models?

Postby Bill Kendall » Tue Feb 01, 2011 4:41 pm

Your idea for using a multistate model with incidental observations (like a Barker model) would have high potential, but as you discovered, there is no such model in MARK. I'm not sure which model you were trying (maybe the MS model with recoveries?).

Anyway, it sounds like you have a specific sampling period in the winter. You could get at what you are trying to do with a multistate model with state uncertainty. If you just have one sampling period per spring and one sampling period per winter, you could use ESURGE, which is set up for this kind of problem. MARK also offers this kind of model, although it is not yet published. It is set up for robust design data, but could be tricked into accommodating just one sampling period (by setting up dummy sampling periods with all zeroes). Here is how you might view the model structure. You set up two states, just as you've envisioned it (breeder A and non-breeder B). You have two primary occasions per year (spring and winter). If an individual is captured in the summer, I believe you've stated its state is known, so you will enter an 'A' or 'B' into the history for that time period. In the winter, you never know its breeding status from the capture itself (although you might know its state circumstantially from capture the previous spring). No matter. For winter captures you enter a 'u' if you're using MARK. If you use ESURGE, its documentation would tell you how to enter this 'event'. In any case, the probabilities of correctly assigning state given detection would be set to 1.0 in the spring and 0 in the winter. If you captured the individual the previous spring, the multistate structure (fixing transition probabilities to keep the individual in the same state until the next spring) will acknowledge the known state implicitly.

There are still some "devils in the details" here, but that is the general idea. Admittedly, the MS and RD chapters of the book need to be updated to present these possibilities. Stay tuned.

Bill Kendall
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Re: Resightings in multi-state models?

Postby cooch » Tue Feb 01, 2011 7:09 pm

Bill Kendall wrote:<snip>

You set up two states, just as you've envisioned it (breeder A and non-breeder B). You have two primary occasions per year (spring and winter). If an individual is captured in the summer, I believe you've stated its state is known, so you will enter an 'A' or 'B' into the history for that time period. In the winter, you never know its breeding status from the capture itself (although you might know its state circumstantially from capture the previous spring). No matter. For winter captures you enter a 'u' if you're using MARK. If you use ESURGE, its documentation would tell you how to enter this 'event'. In any case, the probabilities of correctly assigning state given detection would be set to 1.0 in the spring and 0 in the winter. If you captured the individual the previous spring, the multistate structure (fixing transition probabilities to keep the individual in the same state until the next spring) will acknowledge the known state implicitly.


What Bill is describing seems analogous to a state uncertainty problem -- Paul Conn has done some nice work with this using E-SURGE applied to a disease system, where an individual on encounter is classified as either 'diseased', or 'healthy', or 'unknown'. This seems analogous to 'breeder', 'nonbreeder', or 'unknown breeding status' in the system you're describing. Paul discusses the relative merits of treating 'U' individuals as a separate state, versus an approach based on a misclassified state where true state is 'unobserved', coded in E-SURGE. Might be worth looking at Paul's paper -- (2009) Multistate capture-recapture analysis under imperfect state observation: an application to disease models. Journal of Applied Ecology, 46, 486-492.
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