phi shouldn't be 1 - overparameterised?

[rexka997]

Hi all,

I'm working on a simple CJS model using dataset of banding and resightings of albatrosses, over yearly visits 2015-2020. Am also exploring Multistrata, but need to get simpler approach working first.

The issue is that when trying to run Phi(t)p(t) in CJS, all signs point to the model being overparameterised (e.g. crazily high se for the beta-hat for Phi:time2018 and real Phi:2018=1). Also occurs with other models eg. Pradlambda.

I tried argument adjust=FALSE in both mark and mark.wrapper functions, and function adjust.parameter.count - neither helps. I clearly don't understand the problem.

RMark resources suggest the issue is improperly specifying the formula. I can't see what needs to be fixed. Formula specified like this:

Code: Select all

do_analysis=function()
{ Phi.dot=list(formula=~1)
  Phi.time=list(formula=~time)
  p.dot=list(formula=~1)
  p.time=list(formula=~time)
  cml=create.model.list("CJS")
  results=mark.wrapper(cml,data=WCA,ddl=ddWCA,output=FALSE,silent=TRUE)
  return(results)
}


I tried using the sine link when specifying the phi formula (formula=~-1+time, link="sin"), which makes the se for beta-hat look more sensible -- but I still get that unreasonable 100% survival for 2018.

Quite stuck - would be very grateful for a pointer on what I'm missing here.
Thanks!
Kalinka

[jlaake]

Couple of things. albatross are very long lived as I understand so a five year data set is quite short for a long-lived species. Correct me if I am wrong. So if you were to fit a time varying annual survival rate I'd expect some of the estimated parameters might hit a boundary of 1. Now with phi(t)p(t) the last pair of parameters are confounded and you cannot estimate separately. Go read the section of Cooch and White on the CJS model. RMark always assumes the design matrix is full rank and phi(t)p(t) is one of the cases where that is not the case.

Second, I have never suggested that a single parameter at a boundary suggests over-parameterization routinely because it has a large se. In your case the large se is due to the parameter at the boundary with the logit link as you found when you switched to the sin link. However, if a whole set of beta's have large se, then that usually suggests over-parameterization. Here is an example where the Phi model is ~Time+time (clearly over-parameterized) for the dipper data. See how all of the time and Time parameters have large se values

Output summary for CJS model
Name : Phi(~Time + time)p(~1)

Npar : 8 (unadjusted=7)
-2lnL: 659.7301
AICc : 676.0754 (unadjusted=673.99803)

Beta
estimate se lcl ucl
Phi:(Intercept) 0.5143903 0.4767797 -0.4200979 1.448879
Phi:Time -0.0263949 39.8592620 -78.1505510 78.097761
Phi:time2 -0.6717454 39.8620500 -78.8013660 77.457875
Phi:time3 -0.5481457 79.7191990 -156.7977800 155.701490
Phi:time4 0.0730793 119.5779700 -234.2997400 234.445900
Phi:time5 0.0298686 159.4367500 -312.4661600 312.525900
Phi:time6 -0.0460881 199.2959500 -390.6661500 390.573980
p:(Intercept) 2.2203956 0.3288850 1.5757809 2.865010

[rexka997]

Many thanks Jeff, you've got my thinking unstuck.

So if I've understood right, we can diagnose that overparameterisation is NOT my problem because a) only a few of the betas for phi had big SEs, rather than the whole set; and b) a sine link sorted out the large SE but didn't change the parameter estimate from boundary at 1. Instead, the parameter estimate hitting boundary simply reflects that the dataset is still too short, given how long the species lives, to fit time-varying annual survival rate. You're quite right that five years is short cf albatross longevity.

I was aware that with phi(t)p(t) the terminal phi and p values are not identifiable, but was led astray by having npar=10 unadjusted=8 (rather than e.g. npar= 8 unadj=7).

It seems the best course is to model constant survival rate for perhaps another couple of years yet.

Thank you for the quick reply, and also (not least) for RMark. I'm sure you've heard it many times, but RMark is a great and rather fun way of accessing all the CMR tools in Mark.