SE/variance for transition parameter at boundary

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SE/variance for transition parameter at boundary

Postby lgallenberg » Thu Apr 07, 2022 4:58 pm

Hello all,

I am working on a multistate analysis with 9 capture occasions and 2 geographical states ("T" or "E"). Each occasion was in one of 2 seasons: Winter or Spring. I am interested in investigating how season and size of the individual affected transition probabilities, but am having issues with transition probability estimates near 1.The estimates near 1 are E -> E from Spring to Winter and T -> T from Winter to Spring. Looking at the capture histories, from Spring to Winter there were a few instances of E -> E transitions and no instances of E -> T transitions. Looking from Winter to Spring, there were quite a few instances of T -> T and no instances of T -> E. So it makes sense that these transition probabilities are being estimated at 1. The issue I'm having is with obtaining accurate standard error/variance estimates.

If I do not consider the individual covariate of size, I can utilize the sin link. My variable in that case was defined as:
Psi.season = list(formula=~-1 + stratum:tostratum:season, link="sin")
Using that approach, I obtained reasonable standard errors and confidence intervals (and found that transition probabilities did vary significantly with state and season).

However, if I want to consider the individual covariate of size as well, I can only use the logit link and am left with standard errors and confidence intervals that cannot be estimated for the E -> E Spring and T -> T Winter parameters. My variable in that case was defined as:
Psi.season.size = list(formula=~-1 + stratum:tostratum:season + stratum:tostratum:size)

In the second case considering the individual covariate, I have tried simulating annealing (options="SIMAANEAL") and refitting with new starting values (retry = 1) but am still left without accurate standard errors for the two transition parameters near 1.

Are there any suggestions for obtaining better standard error estimates for those two parameters while considering the individual size variable?

Thank you!
lgallenberg
 
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Re: SE/variance for transition parameter at boundary

Postby jlaake » Fri Apr 08, 2022 9:09 am

viewtopic.php?f=21&t=3584

See discussion above. You can use profile intervals.
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Re: SE/variance for transition parameter at boundary

Postby lgallenberg » Fri Apr 08, 2022 2:32 pm

Hello,

When I include the individual covariate of size and "profile.int = T" (or specify the real parameter indices for the ones related to Psi) I get the following warning for each Psi parameter:

" * * WARNING * * Real Parameter 12:Psi sE toE g1 c1 a0 is modeled with an individual covariate and cannot have a profile likelihood confidence interval.
12:Psi sE toE g1 c1 a0 1.0000000 0.0000000 1.0000000 1.0000000 "

Is there a way to obtain profile likelihood confidence intervals when individual covariates are considered?

Also, if I do not include the individual covariate and only consider the variables state and season for the transitions, use "profile.int=T", and a logit link, I still get standard errors that are either huge or 0. If I do the same but with a sin link, the estimates are reasonable.
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Re: SE/variance for transition parameter at boundary

Postby jlaake » Fri Apr 08, 2022 2:46 pm

Profile intervals are confidence intervals. Won't change std error. Did you get better intervals? I guess you can't get profile intervals with individual covariates covariates. This is a question for Gary. RMark simply passes request to MARK. Seems like you are trying to squeeze something from your data where there is no information given that you have no transitions for those Psi values.
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Re: SE/variance for transition parameter at boundary

Postby jlaake » Fri Apr 08, 2022 2:53 pm

You could try using log link and hope that MARK's restrictions for sum of Psi=1 will work. Should do.
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Re: SE/variance for transition parameter at boundary

Postby gwhite » Fri Apr 08, 2022 3:18 pm

You can get profile likelihood confidence intervals on beta estimates, and for real parameters for a specific combination of individual covariate values.

Gary
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Re: SE/variance for transition parameter at boundary

Postby lgallenberg » Mon Apr 11, 2022 6:27 pm

Profile intervals are confidence intervals. Won't change std error. Did you get better intervals?


Unfortunately, no, I so far have been unable to obtain reasonable confidence intervals when including the individual size covariate. Unless the profile CI's are stored somewhere special? I have been looking at the results with "summary(model)" and/or "summary(model, se=T)."

Seems like you are trying to squeeze something from your data where there is no information given that you have no transitions for those Psi values.


I set the models up so they are estimating the parameters related to those where transitions did occur. Those where transitions did not occur (E ->E in Spring and T -> T in Winter) are estimated by subtraction.

My conclusion for now is to not consider models that include the size variable for the transition parameters. We will have more data soon so perhaps that variable can be better investigated when more data is available.

Thank you for your responses!
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