Unobserved stated in MSCRD or MS models with > 2 states

[Miguel]

The book’s examples that include a unobserved state (e.g., MS_rdsimple.inp, p.550) only have two states. When I included a unobserved state in models with more than two states (e.g., ISLAND.inp, p.310) the parameters for the unobserved state were not estimable.

I also simulated capture histories for three states (unobserved state was not simulated not to include ‘U’ in capture histories) and again the unobserved state parameters were not estimable.

Intuitively it seems to be that a unobserved state should be able to be included in MS models with > 2 states. Am I wrong?

Your comments are greatly appreciated, thank you,
Miguel

[krgrayson]

Hi Miguel -

I am not sure how you are structuring your model, but as far as I know there are no limits to the number of states in multi-state models with an unobservable state. Except, of course, the quality of your data to estimate the number of parameters. The data set I have been working with has ten states, two of which are unobservable.

You need to make sure the parameters you are trying to estimate are both biologically reasonable and statistically identifiable. For example, in MSMR models with unobservable states survival probability for the unobservable state must be assumed equal to an observable state.

I recommend the following papers:
Kendall, W. L. 2004. Coping with unobservable and mis-classified states in capture-recapture studies. Animal Biodiversity and Conservation 27:97-101.

Bailey, L. L., W. L. Kendall, and D. R. Church. 2009. Exploring extensions to multi-state models with multiple unobservable states. Pages 693-709 in D. L. Thomson, E. G. Cooch, and M. J. Conroy, editors. Modeling Demographic Processes in Marked Populations. Springer, New York, New York, USA.

Bailey, L. L., S. J. Converse, and W. L. Kendall. 2010. Bias, precision, and parameter redundancy in complex multistate models with unobservable states. Ecology 91:1598-1604.

Hope this helps!
Kristine

[Miguel]

Kristine,

Thank you for your reply and for the reading list. I spent my day trying to get MARK to work with a unobserved state in MS models with > 2 states to no avail. I'm not using my own data - not yet anyway. I'm using the 3 island example from the MS chapter. I simply added a forth state, unobserved, which makes sense to me that it should be estimable. I'm simply trying to replicate the best fit models for this 3 island MS example with the added unobserved state.

I'm fairly proficient with most MARK models and I'm using simple MS models that are not time-specific. It should be straight forward but I am absolutely stumped. If capture and transition probabilities were very high for the observed states them - maybe - it would make sense if MARK had a hard time with the unobserved state parameters. However, that is not the case here so I cannot think of a logical reason for the failure of MARK to estimate the unobserved state parameters.

I constrained survival of the unobserved state to equal survival for one of the other states and fixed p for unobserved to zero. Am I missing something?

Thanks again for your help,
Miguel

[krgrayson]

Hi Miguel -

Nothing obvious to me pops out from your description. Happy to take a quick look at the file if you email it to me.

KG

[Bill Kendall]

Miguel,
It sounds like you might not have set up the three state example correctly. You say you added a fourth state? If so, that would not work because the simulated system represented by the data includes only three states. In other words there are no individuals transitioning to/from the unobservable state. Instead, pretend one of the three states is unobservable (e.g., delete each 'C' from the .inp file and then run the model with p(c)=0.

Other papers discussing multiple states and unobservability include more than one by Marc Kery, Hunter and Caswell (2009), and Bailey et al.(2010). The last one is in the latest issue of Ecology, but I don't have access to the specifics of the other two right now.
Bill

[Miguel]

Thank you Kristine and Bill for your replies.

At first glance it would seem intuitive that whenever individuals are not captured that there should be a unobserved state. However, I simulated encounter histories with a unobserved state (replaced ‘unobserved’ captures with zeros) and of course this time the unobserved parameters where estimable for the reasons that Bill just gave. I think I now have a better understanding of MS models with a unobserved state.

I will be analyzing 11 years of mark-recap. data that is challenged by seasonal variation, temporary emigration and by a large proportion of transient captures. Before I attempt a MSCRD analysis of my data, I am simulating analyses with the types of problems I expect to encounter. This approach I hope will also reduce the number of silly questions.

Once again, thank you for your assistance, I greatly appreciate it.
Miguel

[cooch]

Miguel,
It sounds like you might not have set up the three state example correctly. You say you added a fourth state? If so, that would not work because the simulated system represented by the data includes only three states. In other words there are no individuals transitioning to/from the unobservable state. Instead, pretend one of the three states is unobservable (e.g., delete each 'C' from the .inp file and then run the model with p(c)=0.

You need to be a bit careful with this approach - if you simulate a full MS data set with 3 states (call them A, B and C), assuming (during the simulation) that all states are observable, and that individuals are captured, marked and released in all 3 states, then if you change all C encounters to '0', you need to remember to eliminate any saturated '0' histories (e.g., for a 6 occasion study, anything looking like '000000'). MARK will warn you if you have the problem of frequencies of individuals never marked and released.

It is actually somewhat easier (and perhaps less error-prone) to simulate 3 states (2 observable, 1 unobservable), but simply have no releases in the unobservable state (which makes sense, perhaps, since if the state is unobservable, it is difficult to imagine a plausible way in which you would have newly encountered and marked individuals in that state). This is trivial to do using the simulation capabilities in MARK (covered in Appendix A in the 'book').

[Bill Kendall]

Evan makes a very good point for avoiding error messages. MARK does not like histories of all 0's. Simulating your own data set with p=0 and no releases for the unobservable state(s) could be less time-consuming than searching for and deleting all null histories.

[Miguel]

Even and Bill,
Thank you for your comments. I tried the approach you suggested in a MS model and it worked great. Could a similar approach be used to simulate permanent immigration?

I would like to generate capture histories for a MSCRD model with both unobserved and permanent immigration states. Could permanent immigration could be simulated by making transitions from other state to a permanent immigration state (i) one way transitions, (ii) fix the probability of remaining in that state to one, (iii) no releases and (iv) fixing p and c to zero. Does this seem like a good approach?

Thanks again,
Miguel

[Miguel]

I just wanted to correct myself - I meant to say permanent emigration.