Pradel models problems with capture probabilities

[dgomez]

I am using Pradel models to estimate seniority probabilities, but the number of parameters of capture probabilities is different (I have 7 encounter occasions) when I selected the model Seniority only (6 recapture parameters) or survival and seniority (7 recapture parameters). I was wondering if someone can help me with that.
Thanks
Daniela

[Doherty]

Hello Daniela,

You probably need to read a little bit more about the Pradel model to get comfortable with what you are doing.

If you have 7 encounter occasions and you ran a normal Recaptures Only (CJS) model then you could estimate 6 survival (phi) parameters and 6 detection (p) parameters. This model is conditional on first capture - so no p can be estimate for the initial capture session. We also know that in a fully time dependent model the last p and last phi are confounded and can only be estimated as a product - so we usually do attach a strong biological interpretation to the last p and phi.

The Pradel model (or reverse time or temporal symetry model) uses the same encounter history, but also uses information from, conceptually, reversing the encounter history. If you were only interested in seniority you would essentially be running a CJS model in reverse. You could estimate 6 seniority (gamma) parameters and 6 detection parameters - except now the data are conceptually reversed - so a detection parameter for the "last" capture session can not be estimated (similar to the CJS being conditional on first capture) and the "first" p and "first" gamma are confounded in the fully time dependent model (similar to the last parameters being confounded in the CJS).

When you choose to run the "seniority and survival" model you are estimating the 6 phi's from going forward and the 6 seniorities from going backwards. But you are now able to estimate 7 p's with the last one being estimated from going forward and the first one being estimated from going backwards. However, in a fully time dependent model you will probably not want to interpret the first and last parameters as the first p is confounded with the seniority and the last p is confounded with the survival.

I hope that helps,

Paul

[dhewitt]

Paul meant to say that we DO NOT attach a strong biological interpretation to the last p and Phi. Indeed, we often don't think anything about them.

Also, you should read Hines and Nichols -- 2002, Journal of Applied Statistics 29:573-587, Investigations of potential bias in the estimation of lambda using Pradel’s (1996) model for capture- recapture data. The confounding of "first" and "last" parameters that Paul refers to is one issue, but there are more and typically it means other parameters must be interpreted with substantial caution. Basically, you need a decently long time series to do much (say, 5 or more occasions).