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To start with, I am pretty new to CMR analyses (!) and am just looking for some general advice on the best approach to modelling my data.

I have a long capture-mark-recapture data set (30 years, with >10,000 individuals recorded) which contains time-varying individual covariates (e.g. weight, body condition, parasite load), but using this information is tricky, as values are only available for sampling occasions when the individual was encountered. As far as I can make out, this pretty much makes these data unusable as continuous covariates - is that correct?

It would seem a shame not to use this wealth of information in some way, and I don’t think it is particularly biologically relevant to resort to time-varying population-level summaries of the measured variables, such as mean body condition and parasite load recorded from the entire population for each sampling period. I know that time-varying individual covariates with ‘missingness’ can be included in Bayesian CMR models, but don’t feel that is the best option for me right now, because of time constraints and a serious lack of skills in Bayesian analyses!

Additionally, preliminary analyses suggest that the age of the individual has a large effect on survival (juveniles less likely to survive than adults). So, I need to find a way to include an age structure in the models, and have the individuals move from the juvenile age group to the adult age group over time.

So, having pretty much ruled out Bayesian analyses, I have been mulling over the best MARK-based approach (using RMark). One idea is to use a multistate model, and define discreet levels of, for instance, parasite load (i.e. light/moderate/heavy), as well as defining age states. So I would end up with states that were defined on the basis of age and parasite load, e.g.: juvenile & light, juvenile & moderate, juvenile & heavy, adult & light, adult & moderate, adult & heavy. In this example, I would have 6 states in the model, and individuals can move between them. However I would need to constrain movement from the states, so that individuals couldn’t get younger!

I am just generally interested in whether people think this is a sensible approach, and/or whether there are neater or more appropriate ways to model my data, whilst optimising all the supplementary data available in the form of time-varying individual covariates.

I’m looking forward to getting your input, and thank you in advance for your time.

bootzies wrote:
...I am just generally interested in whether people think this (multi-state discretization) is a sensible approach, and/or whether there are neater or more appropriate ways to model my data, whilst optimising all the supplementary data available in the form of time-varying individual covariates.

I’m looking forward to getting your input, and thank you in advance for your time.

Well, I put said approach in the book (chapter 11), so it must be sensible.

Actually, it is quite sensible, pretty robust, and dead easy to implement in most cases (your 'age effect' issue would complicate things some, but is not insurmountable. Working up sensible DM's can also be a challenge -- see example in the book, for one such situation). The Bayesian tack is more elegant (see lots of good papers by Simon Bonner), but I would tend to agree, somewhat more difficult to implement.

Largely, though, if you don't have too many missing covariates, the methods are fairly convergent. So, in the short run, I'd suggest trying a couple of multi-state approaches, and see how you get on.

If you use the multistate model with RMark, you'll get design data for Psi for transition probabilities. With 6 states, you'll get design data for each state to each of the other states. By default, the prob of staying in the same state is computed by subtraction. If Juvenile strata are 1-3 and adult strata are 4-6, then all you need to do is to create a field called fix in the design data which is assigned NA except for strata 4-6 and tostratum 1-3 will have the value 0 so it will not let it transition from adult to juvenile. All other transitions will be estimated, so you'll have 21 parameters (15 for juveniles and 6 for adults) even with time invariance. Good thing you have a lot of data. This is the new approach to fixing parameters and you'll see many examples showing the old approach using indices. The index approach is most useful when the fixed parameters vary across models. In this case, these parameters are fixed for all models by adding the field to the design data. Make sure you have the most recent version of RMark from CRAN.

--jeff

Thanks very much for your fast responses and the very helpful reassurance and information. It is great just to get a sanity check and ensure I am approaching the analysis in a sensible way. I'm sure I will have further, more specific, queries once I get into the modelling, but will try not to pester you too much!
Thanks again.