Confounded parameters in MSORD with transients and residents

questions concerning analysis/theory using program MARK

Confounded parameters in MSORD with transients and residents

Postby violetblue » Thu Oct 06, 2022 9:54 pm

Hello,

My questions concerns confounding in an MSORD with transient and resident survival.
My aim is to get an msord as time varying as possible to obtain an estimate of sample variance.

I know the final Psi should be constrained to the second-to-last so that all the S can be estimated.
However I'd like to know if Psi needs to be further constrained in a model with 2 classes of survival?

In this model;
a. MSORD:Two states, nest and skip.
a. S: 2 ageclass survival (transients & residents), time-varying.
b. Psi: time-varying 'nest to skip' and time-varying 'skip to nest', with the final Psi constrained to the second last.
c. p, pent & phi probability of zero in the skipped state.
d. p: time*session
e. pent: time*session
f. Phi: time since arrival i.e. Time-Cohort

This model has 3 beta singularities which result in real parameters being estimated at or close to 1 and with SE=0 (i.e. 3rd last transient S, last transient S and last resident S).

I have cloned their profile likelihood CIs but as this hasn't improved their estimates I think they are not being estimated correctly at the boundary.

Any help would be greatly appreciated,
violetblue
 
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Re: Confounded parameters in MSORD with transients and resid

Postby violetblue » Mon Oct 10, 2022 3:24 am

Just an update on progress; on re-reading
Kendall, W. L., Nichols, J. D., and Hines, J. E. (1997). Estimating temporary emigration using capture–recapture data with Pollock’s robust design. Ecology 78, 563–578.

I realised that Psi in all time intervals need to be constrained so that all S can be estimated, not just the last and second-to-last.

Therefore in this example I constrained Psi 'skip to nest' so that they were all equal (constant) and only
then was I able to estimate time-varying Psi 'nest to skip' as well as both time-varying transient and resident Survival in the same MSORD.

I will now estimate sampling variance with this constrained model, unless anyone has any better ideas?
violetblue
 
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Re: Confounded parameters in MSORD with transients and resid

Postby Bill Kendall » Thu Oct 13, 2022 4:04 pm

You've raised a good question with regard to transience when trying to account for an unobservable state. Let me first clarify a slight misunderstanding. In Kendall et al. (1997) we didn't say one needed to constrain the last transition probabilities to the one before it. We said they need to be constrained to some parameter that is estimable, for example the second to last transitions. Schaub et al. (2004, Ecology) showed specifically that the last transition probabilities are both confounded with the last survival parameter. For further reading on this issue, Langtimm (2009) evaluated the impact on survival estimates when the constraint on transitions was not a good one. Penaloza et al. (2014, Ec Apps) and Kendall et al. (2013, MEE) discussed how to mitigate for this.

In thinking about the question of the effect of transience on this, I went to my standby: simulation. A useful simple approach for these estimability issues with the robust design and unobservable states is to simulate a two-state multistate model, with one state unobservable (p=0) and for the other state assume p is known (this is optimistic but the within-season sampling provides detection probability information separate from the MS structure). By fixing the value of p instead of estimating it you produce underestimates of variance, but it should give an idea of what's estimable.

Using this, indeed even with the assumption of each of the last two psi's being equal, there is some bias when there is transience. Also, as you discovered, if psi(skip) or psi(return) is constant over time, then the bias appears to go away. For this model I am often dealing with sea turtles, in which case the skipping probability tends to be very high (~97%), and therefore a model with constant skipping but time varying return is a reasonable a priori candidate.

I'm happy to provide the simulations I did if interested (William.Kendall@colostate.edu).
Bill Kendall
 
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Re: Confounded parameters in MSORD with transients and resid

Postby violetblue » Mon Oct 17, 2022 8:47 pm

Thank you for your clarification on exactly what parameters are confounded in this model.
I am definitely interested in the results of your simulations so I'll email you offlist about that.

With my data both skipping and returning probability are quite variable. I've chosen to constrain skipping probability because that is what has been done historically for the monitoring of this data. This obviously places some limitations on the estimation of sampling variance but I think we just have to consider the results in that context.

I'll look forward to reading further the references you've provided, and once again thanks for considering my question.
violetblue
 
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Joined: Tue Nov 06, 2018 11:16 pm

Re: Confounded parameters in MSORD with transients and resid

Postby violetblue » Wed Oct 26, 2022 12:31 am

I just wanted to make a final comment.

The parameters in this model (with the proper constraints) are now being estimated correctly, but the final resident survival is very low.

It occurred to me that survival in the final time period is really just the probability of 'being seen' from K-1 to K and that individuals who are skipping in K will appear to have died or permanently emigrated. This is unlike survival estimates in earlier time periods where there is a chance for a couple of years to go by for an individual to appear again and reveal that it really was alive all this time but just skipping breeding seasons. The closer to the end of the sampling period the more chance there is for skipping to be interpreted as lower survival.

So it seems that a very low survival estimate in the final time period could be expected, but it doesn't indicate an imminent population crash.

This brings me back to what would be the best model for estimates without sampling variance. Should it be one with further constraints on survival?
violetblue
 
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Re: Confounded parameters in MSORD with transients and resid

Postby violetblue » Tue Nov 01, 2022 8:29 pm

Update: I now think the problem was an incorrect interpretation of the survival design matrix, so I updated my R script which seems to have fixed it.

Thanks.
violetblue
 
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Joined: Tue Nov 06, 2018 11:16 pm


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