multi-strata model with missing data

[roodbergen]

Dear people,

I have colour marked Black-tailed godwits to estimate survival. To check whether nest success is of influence on survival and/or recapture rate, I created multi-strata models with three strata: S (nest hatched), F (nest failed to hatch) and O (unknown=missing data).

The problem is that the last stratum is a combination of the first two, and possibly birds that did not breed at all.
In addition, the outcome of a nest is usually known at banding (godwits are captured on the nest), but is often unknown in subsequent years, which will affect psi.

Is this a valid solution to my problem of missing data?
Are there better ways to deal with it?

All the best,

Maja Roodebrgen

[darryl]

Maja,
Check out the paper:

Kendall, Hines and Nichols. 2003. Adjusting multistate capture-recapture models for misclassification bias: Manatee breeding proportions. Ecology 84: 1058-1066

Sounds like there's some simularites with their situation (can only identify a breeding female if calf is also detected) although from memory I think they had robust-design type data.

I don't think this can be done in MARK, but there's other options.

Cheers
Darryl

[gwhite]

Darryl:
The robust-design multistrata model is in MARK, including all 12 different closed population estimators for each primary occasion. The open robust-design model of Kendall is also available in MARK. Further, the robust-design version of Barker's model is in MARK, but with only 6 closed population estimators (no mis-identification), because mis-identification in the Barker model doesn't make sense with the p parameter (but would makes lots of sense with the R and R' parameters.
Gary

[Bill Kendall]

It's not completely clear from the original description whether Darryl's or Gary's response is more pertinent. If the reason that animals in that third state are difficult to define is that they were there but not captured, then the usual multistate model will take care of that probabilistically.

If, in addition, they are skipping and are therefore unavailable, then a 3-state model (one unobservable) is appropriate. It is best to have robust design or telemetry data in this case. There are a number of papers out on estimability issues in this case when there is only one observable and one unobservable state. However, there is little out yet on multiple observable states. An exception is a recent paper by Marc Kery. In either case, as Gary points out, MARK could be used.

If you capture animals in that third state but cannot determine success, then you can treat it as a misclassification problem. As Darryl pointed out, our Ecology paper, along with a 2004 paper in Marine Mammal Science, adjusts for this problem when you have robust design data. In the absence of this type of data, or other supplemental data to inform you, leaving that third state in place as a state for unknowns makes some sense. The only problem there is that you know that mixture could induce heterogeneity in capture, survival, and transition probabilities. This problem is described for the case where sex is sometimes unknown, by Nichols et al. (2004, Ecology December issue)

Cheers,
Bill

[darryl]

My apologies Gary.

I was meaning that I wasn't sure whether the parameterization suggested by Kendall et al. could be done easily within MARK as I was under the impression that it was different to the standard likelihood given you have this combination of possible 'true' states caused by the misclassification/misidentification. I've never tried applying their approach withn MARK before, but if anyone else has I'd be interested in seeing an example at some stage to relieve me of my ignorance.

Cheers
Darryl