transience effect in CJS model

[steffen]

Hi,

I am trying to analyse adult survival probabilities of birds using a simple CJS model and live re-captures over 26 encounter occasions. Because many birds were never re-captured, I want to fit a transience effect. I have done that in RMark as follows:

Code: Select all

DATA<-import.chdata("data.inp", header = F, field.names= c("ch","frequency"), use.comments=TRUE)
DATA.proc<-process.data(DATA, model="CJS", begin.time=1969)
DATA.ddl<-make.design.data(DATA.proc)
DATA.ddl<-add.design.data(DATA.proc,DATA.ddl,parameter="Phi",type=c("age", "cohort"),bins=c(0,.5,26),name="transience")

Then I fit two different models with a transience effect, and either constant survival or time-dependent survival:

Code: Select all

Phi.transience<-list(formula=~transience)
Phi.time.transience<-list(formula=~time+transience)
p.time<-list(formula=~time)

model.1<-mark(DATA.proc,DATA.ddl,model.parameters=list(Phi=Phi.transience,p=p.time))
model.2<-mark(DATA.proc,DATA.ddl,model.parameters=list(Phi=Phi.time.transience,p=p.time))


For model.2, the model returns 51 parameters altogether (25 for p, 25 for Phi, and 1 for Phi transience):

>Output summary for CJS model
>Name : Phi(~time + transience)p(~time)
>Npar : 51 (unadjusted=34)

However, for each interval, the first survival estimate for each cohort is different from the remaining estimates for that interval, so there are clearly more than 26 survival parameters that are being estimated. I gathered from this forum and the RMark introduction that the parameter count provided by RMark is full rank, so I am slightly confused why more parameters are estimated than RMark has indicated, and I suspect that I may have coded the transience effect erroneously.

I would appreciate any comments on whether I specified the transience effect correctly, and whether I should expect one additional (transience) survival parameter for each time interval or just one overall for the whole model.

Cheers,
steffen

[jlaake]

Steffen-

You are confusing real parameters and beta parameters. The parameters that are estimated and counted are the betas. The real parameters are computed from the betas. You are using an additive model which means that the number of real parameters that differ can be greater than the number of betas. The full rank comment is in reference to the number of columns in the DM which matches the number of betas. You do have 51 betas in model 2 but it looks like many of them are at boundaries or not estimable. At the very least, the first time parameter is not estimable because it also includes the additive transience effect. Clearly many of the other time parameters are at boundaries so your data does not support that many parameters.

--jeff