Modelling heterogeneity in RMark

[lucac1980]

Dear all, 
I'm new to RMark, and this is likely to be a fairly trivial question:
I'd like to use RMark to estimate the abundance of an animal population, and wish to compare the 8 CMR models of Otis et al. (1978): M0, Mb, Mt, Mh, Mbh, Mth, Mbt, Mbth.

So far, I could figure out the Rcodes for the first 6 full-likelihood models:

# Defining parameter models
pdotshared=list(formula=~1,share=TRUE)
ptimeshared=list(formula=~time,share=TRUE)
ptime.c=list(formula=~time+c,share=TRUE)
pdotmixture=list(formula=~mixture,share=TRUE)
pmixture=list(formula=~mixture)
cmixture=list(formula=~mixture)
ptimemixtureshared=list(formula=~time+mixture,share=TRUE)

# Capture Closed models
M0=mark(mydata,model="Closed", model.parameters=list(p=pdotshared))
Mb=mark(mydata,model="Closed")
Mt=mark(mydata,model="Closed", model.parameters=list(p=ptimeshared))

# Heterogeneity models
Mh=mark(mydata,model="FullHet",model.parameters=list(p=pdotmixture))
Mbh=mark(mydata,model="FullHet",model.parameters=list(p=pmixture,c=cmixture))
Mth=mark(mydata,model="FullHet",model.parameters=list(p=ptimemixtureshared),adjust=TRUE)

Are they correct?
Further, I could not figure out the codes for the last 2 models (i.e. Mbt and Mbth).
Any help would be much appreciated,
Thanks a lot in advance!
Luca

[jlaake]

I'm not sure what you are trying to accomplish. Are you trying to duplicate what is in Capture? If so then you are not going to be able to mimic the h models because I believe it uses a jackknife approach. The first 3 simple models M0,Mb,Mt are specified correctly. Once you start mixing b t and h then there are lots of ways to specify the models, so there is no single correct way.

--jeff

[lucac1980]

Dear Jeff,
thanks for your reply. Yes, I am trying to duplicate what is in Capture. As far as I could gather, Capture2 uses different estimators for different models: M0 (null), Mt (Darroch, Chao), Mb (Zippin), Mh (Jackknife, Chao), Mbh (removal), Mth (Chao), Mtb (Burnham), while no estimator is available for Mtbh.
I assume R codes use the null and zippin estimators for M0 and Mb, respectively, right? Not clear what estimator is used for Mt though (Darroch? Chao?).
Just wondering id there is RMark codes for Mh, Mbh and Mth and Mtb using the estimators above.
Finally, it is not quite clear to me why Mtbh is said to have no estimator, but in its model selection output Capture actually provides values for such a model.
Luca

[jlaake]

You are not understanding me. First, what is done in R with RMark is simply to create the input file for mark.exe (MARK) which is what fits the model to the data. Second, all of the models fitted in MARK are maximum likelihood estimators (MLE) that are solved numerically and may or may not correspond to specific estimators (eg jackknife) in CAPTURE that are not MLEs. Thus what you are attempting is not possible for all of the closed estimators. You can create likelihood versions of the various combinations of t.b.h effects by using the FullHet model and including the relevant effects.

--jeff

[lucac1980]

Dear Jeff, thank you for clarifying the issue!
I'll explore more in details the formulas for the closed models! =)
Luca

[crocutalupus]

Dear all,
I am trying to replicate what the Program CAPTURE does in Mark but using R.
If I understand you correctly, Jeff Laake, it is not possible to do it within the RMark package.
Has anyone found a way to do it? lucac1980?

Thanks a lot in advance for your precious help.

[cooch]

Dear all,
I am trying to replicate what the Program CAPTURE does in Mark but using R.
If I understand you correctly, Jeff Laake, it is not possible to do it within the RMark package.
Has anyone found a way to do it? lucac1980?

Thanks a lot in advance for your precious help.

Not possible, I believe, or arguably necessary. The MLE-based closed population abundance estimation models available in MARK (or, via RMark as a front-end to mark.exe) are more robust, and more flexible (especially wrt to modelling heterogeneity, where you can approach heterogeneity in any number of ways) -- and have superceded CAPTURE.