Derived Parameters for Pradel Recruitment Models

[Bryan Hamilton]

When I look at the results for a Pradel recruitment model, results$derived returns NULL. There is also no derived parameters in the MARK output text file. I swear the derived results used to show up. When I re-read chapter 13 of the gentle introduction manual, the derived results are shown.

How do I access those derived results, ie lambda for a Pradel recruitment model?

Thank you.

[jlaake]

Works for me. The models with derived parameters are listed in DerivedPar.txt in the RMark directory of your R library. They are listed by Model # which is given in the MARK Help-Data Types. It is model 17 and the results below show it for a simple model with the dipper data.

Code: Select all

> mod=mark(dipper,model="Pradrec")
STOP NORMAL EXIT

Output summary for Pradrec model
Name : Phi(~1)p(~1)f(~1)

Npar :  3
-2lnL:  1837.612
AICc :  1843.659

Beta
                  estimate        se        lcl        ucl
Phi:(Intercept)  0.1580851 0.1017136 -0.0412735  0.3574438
p:(Intercept)    2.1147235 0.3247464  1.4782206  2.7512264
f:(Intercept)   -0.5398375 0.0578609 -0.6532450 -0.4264301


Real Parameter Phi
         1         2         3         4         5         6
 0.5394392 0.5394392 0.5394392 0.5394392 0.5394392 0.5394392


Real Parameter p
        1        2        3        4        5        6        7
 0.892326 0.892326 0.892326 0.892326 0.892326 0.892326 0.892326


Real Parameter f
         1         2         3         4         5         6
 0.5828429 0.5828429 0.5828429 0.5828429 0.5828429 0.5828429
> mod$results$derived
$`Lambda Population Change`
  estimate        se      lcl      ucl
1 1.122282 0.0283458 1.068086 1.179229
2 1.122282 0.0283458 1.068086 1.179229
3 1.122282 0.0283458 1.068086 1.179229
4 1.122282 0.0283458 1.068086 1.179229
5 1.122282 0.0283458 1.068086 1.179229
6 1.122282 0.0283458 1.068086 1.179229

$`log(Lambda) Population Change`
   estimate         se        lcl       ucl
1 0.1153642 0.02525729 0.06585992 0.1648685
2 0.1153642 0.02525729 0.06585992 0.1648685
3 0.1153642 0.02525729 0.06585992 0.1648685
4 0.1153642 0.02525729 0.06585992 0.1648685
5 0.1153642 0.02525729 0.06585992 0.1648685
6 0.1153642 0.02525729 0.06585992 0.1648685

>


[Bryan Hamilton]

The derived estimates are not available when I include an individual covariate for Phi. This might also be why I don't get standard errors for f when I include individual covariates.

Thank you.

[jlaake]

I just ran this:

Code: Select all

library(RMark)
data(dipper)
dipper$weight=rnorm(294,0,1)
mod=mark(dipper,model="Pradrec",model.parameters=list(f=list(formula=~weight)))
mod$results$derived


and the values of the derived parameters are NULL but there is a results$derived.

Code: Select all

> mod$results$derived
$`Lambda Population Change`
NULL

$`log(Lambda) Population Change`
NULL


There are no derived parameters in the MARK output file for that run but I did get a non-zero SE for f.

Code: Select all

f:(Intercept)   -0.5353296 0.0580896 -0.6491851 -0.4214740
f:weight        -0.0322267 0.0453325 -0.1210784  0.0566251



Same thing happens if I put weight in model for Phi. This is a question for Gary. But I believe Pradel models are essentially a re-parameterization of Jolly-Seber models and there is an issue with individual covariates because you don't know the value for individuals that are never caught. Someone can correct me if I'm wrong on that point.

--jeff

[Bryan Hamilton]

I think you are correct that individual covariates are not used in Pradel Models. The caveat from the mark book is "There are always challenges in modeling parameters that are linear functions of each other-be advised- think carefully."

I'm learning that solving one problem can cause two problems. Thank you for looking into the standard errors. This must be an issue with something other than the individual covariates.

[cooch]

Basic idea is pretty simple -- If phi and/or f are modeled as functions of individual covariates, then the population parameter lambda is also a function of these individual covariates, which generally makes little sense.

As noted in the help file:

Individual covariates can be used to model phi and p in the Pradel models. However, the biological meaning of modeling lambda as a function of an individual covariate is not clear. Intuitively, it makes more sense to model f and gamma as functions of individual covariates, even though these parameters can be combined with phi to provide a derived estimate of lambda.