Multi-state Models

[ssaps33]

I am a novice user to MARK but am quite familiar with the general CJS models. However, I am running a multi-state model with 3 groups and 2 states and 5 encounters. I conducted a mark-recapture study of 6 populations at 3 different elevations (my groups) and sampled every season for a year to determine transitions between disease states (positive or negative). I have looked at each population seperately to get an idea of what is happening, but want to do a more thorough analysis so I can compare the effects of elevation and season. However, running a complete g*t model gets quite complicated with 6 estimates of S.

This model comes out at the top and is what I expected. However, some of my estimates equal 1 with extremely small SE or I have extremely low estimates (0.38 E-08). This definitely doesn't seem right so I was hoping someone might have some advice on how I can proceed.

Thank you very much.

Kind regards,
Sarah

[abreton]

All of my advice assumes that you've specified the models correctly using the interface provided by MARK. If that's the case then anytime you're fitting multi-state models with real data (i.e., typically sparse) you'll want to apply two 'tricks' often suggested at MARK workshops and described in the MARK Book,

(1) use estimates from simpler models as starting values in more complex models.
(2) for complex models try simulated annealing -- an alternative optimization option in program MARK.

Both of these can help you to overcome the issue that you're describing, in particular poor results for those estimates that are close to 0 or 1 (a boundary). I generally start any analysis by fitting the 'dot' model, that is a model without variation in any parameter -- for example, for a CJS model we might describe this model as phi(.) p (.). At this stage, if data are sparse (nearly always), I gradually increase model complexity and each time use parameter estimates from the previous model as starting values (for the optimization) for the next model. Just before you run a model, check the 'Provide Initial Parameter Estimates' option on the Setup Numerical Optimization Form -- this option allows you to pick any previously run model as a source for the estimates. Using this approach to 'pull yourself up' to the most complex model can be very useful...and it might solve your problem.

Simulated annealing takes LONGER to run than the standard optimization option in MARK. For small datasets, time is not an issue. But for larger datasets, it can take many hours or even days for the sim option to finish. I suggest you run the option on a simple model to assess how long this might take. A good option is to let MARK run overnight for the more complex models -- watch out for that annoying habit for windows to update/restart on its own. Note that trick (2) renders trick (1) potentially not very useful, this is so because simulated annealing jumps around the likelihood surface (multi-dimensional) in order to avoid climbing a false summit (maximum). Imagine that you provide starting values, MARK starts searching for the maximum near this point on the surface, but then jumps to a different location...and then jumps again, etc. This decreases the usefulness of the starting values.

I suggest that you use key words from my post to search the 'entire [MARK] book' which you've obviously been reading. If you search, e.g., on 'simulated annealing' you'll find many helpful sections of text. Similarly, search for 'starting values', also 'estimates on a boundary' or just 'boundary' perhaps. Note -- for a novice you've done well getting this far with multi-state models!

andre

[ssaps33]

Thank you Andre! I will take a look into that and see how it goes.

[ssaps33]

Hi Andre,

I have a quick question - since I have 2 states and 3 groups I have 6 estimates for survival, recapture, and transition. A complete DOT model would have all survival estimates constant across all strata and groups and therefore that model would only produce 3 estimates (one for survival, recapture, and transition)?

I am just a bit confused since now I have the 2 strata to deal with in addition to my 3 groups.

Thank you.

Kind regards,
Sarah

[abreton]

That's right, setting all parameters constant across time (occasions) and identical among groups will result in three estimates, one each for transition, survival and recapture (psi (.) phi (.) p (.)). Of course, since only one transition per state is in the model two additional estimates are available by subtraction, e.g., 1-psi (B to A) = psi (B to B), so technically the dot model will provide five estimates (2 by subtraction) in your case. If you haven't detected this on your own, note that you can specify which state transitions are estimated in the model. This trick allows you to get standard errors for all state transitions (e.g., AA, AB, BB, BA). It might seem silly to even build this no doubt unrealistic model but it's a great way to detect problems with the structure of the input file or the data before you invest time building a complex model. It's also a great way to initiate the process of acquiring starting values for the next complex model -- the dot model is as simple as it gets.

Regarding,

I have 2 states and 3 groups I have 6 estimates for survival, recapture, and transition

How many estimates will depend on the structure of the model.

andre