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Dears
I am trying to simultaneously model survival of the bird and survival of the coloure ring for a joint data set of resightings and recaptures. I have many individuals marked with new colour rings at recaptures because the colour ring felt off. Thus, I have a mark-resighting history of every bird and and a resighting-history of every colour ring, and I try to fit both models in one integrated model making the resighting probability dependent on whether the colour ring still is on the bird. However, it looks like there are some circularities in the model - or I just did not manage to correctly collate the data. Does anybody have experience with such a model. Any hint is welcome!
Thanks a lot!

Thanks to Jeff Laake, I solved the problem - thanks Jeff!

here is the solution:

Laake, J. L., Johnson, D. S., Diefenbach, D. R. Ternent, M. A. (2014). Hidden Markov Model for Dependent Mark Loss and Survival Estimation. Journal of Agricultural, Biological, and Environmental Statistics, 19(4), 524–540. https://doi.org/10.1007/s13253-014-0190-1

In my specific case the birds have a metallic ring that does not fall off but cannot be read by scopes in addition to the plastic alpha-numeric color ring that can be read by scope but falls off after a few months. Therefore, I include two different detection probabilities (resighting and recapture probability for birds that still have their plastic rings) and recapture probability only for those that do no longer have the plastic ring. Birds that get new plastic rings on a recapture, are treated as new releases, i.e. new capture histories whereas the "old" capture history ends at a recapture.