time varying estimate of Phi is 1

[Bryan Hamilton]

I'm running some CJS models. The time model is heavily supported by AIC. When I run a simplified time model (Phi(~time)p(~1) )with the default logit link, the real estimate of Phi for time 9 (of 14 time intervals), is 1 and I get the message:

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Note: only 14 parameters counted of 15 specified parameters

AICc and parameter count have been adjusted upward

Beta estimate

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Phi:time9       18.1789730 1372.8637000 -2672.6338000 2708.9918000

I then changed the link to sin and reran the model. All the parameters were estimable and the real estimate of Phi for time 9 is still 1.

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Phi:time9      1.5707967 0.5079366  0.5752410  2.5663524

This leads me to believe that real estimate of Phi for time 9 is really 1. Now I am trying to interpret this estimate and understand what it means to have survival estimated at 1 and if it is biologically plausible.

An estimate of Phi=1 implies that no animals died or left the population over that time interval. I feel like this deserves some explanation. Given the variation in survival over the other time intervals, this is hard for me to understand. Are there some ways I can go into the raw data and verify this? Or any methods of model verification that can help me understand?

Thank you.

[jlaake]

I'd be very surprised a model with Phi varying by time and p constant was the best model. If your p model isn't correct it can press Phi estimates to the boundary of 1. That isn't the only reason but is likely in this case with such a simple model for p.

Also, keep in mind that the model estimates are simply the best ones given the data and model. It doesn't mean that survival was truly 1.

--jeff

[Bryan Hamilton]

I was using the simplified model as an example. I also had to remove the individual covariates to use the sin link.

The strongest model was Phi(~LocName + Gender + time + SVL)p(~LocName + Gender + SVL). The high beta in time 9 lead to an estimate of Phi=1 for all the sites at time 9.

[cooch]

I was using the simplified model as an example. I also had to remove the individual covariates to use the sin link.

The strongest model was Phi(~LocName + Gender + time + SVL)p(~LocName + Gender + SVL). The high beta in time 9 lead to an estimate of Phi=1 for all the sites at time 9.

Have a look at Appendix F -- data cloning. Tool to help you determine whether or not a parameter is 'really' estimated at 1.

As an aside, the moment that you start writing some/all of your question using RMark notation (as you'vwe done with this thread), then this should be in the RMark subforum.

[Bryan Hamilton]

Thanks for the advice on data cloning and forum etiquette. With the sin link and capture frequencies of 100, the standard errors did shrink by a factor of 10, suggesting that apparent survival was very close to 1 in year 9.

This seems implausible and I feel like such high annual survival demands some explanation. My study runs over 15 years, with nearly 500 individuals marked. It definitely has left me puzzled.

Thanks again for taking the time to reply.

[cooch]

This seems implausible and I feel like such high annual survival demands some explanation. My study runs over 15 years, with nearly 500 individuals marked. .

Actually, that sample isn't that large (for example, I routinely work with >250K marked individuals over 40 years -- many others do as well).

More to the point, survival is estimated for the marked individuals. 500/15 = 33 per year on average. And, if you have relatively high survival in general, then having 33 survival from (t) to (t+1) is, arguably, quite plausible. The probability of something surviving all 15 years is probably pretty low, but surviving one year,...

[Bryan Hamilton]

I was thinking I had a big sample over a long time frame...

Thanks for the perspective. That's just what I needed.