Multistate transition parameter estimated by substraction

[tgarrison]

I’m working with some radio-telemetry data for fish released in a river in several groups over time. Receivers were placed in downstream locations and so the “time” model in this case estimates river-reach specific estimates of parameters. Typically, reach-specific survival and detection probability parameters are estimated for each release group. In this case, however, I’m trying to account for variable travel-times for fish in each release-group by setting up a Multistate model where the state in this case is the week of detection at a receiver. Hence the model would try and estimate reach-specific survival and detection probability for weekly cohorts of fish instead of by the aggregate release group.

As you can imagine, there’s a large number of transition parameters, many of which either aren’t possible or weren’t observed. Question is, when setting up a Multistate model in RMark and estimating Psi with the mlogit link function, is there a way to allow the ‘tostratum’ that determines the estimate of Psi by subtraction to vary over time?

As a general example, if in the first time period the observed transitions for state A were:
A -> A
A -> B
A -> D
but in the second time period the observed transitions for state A were
A -> A
A -> B
A -> E
and in the third time period the observed transitions for state A were
A -> C
A -> E

Then by setting the ‘totstratum’ that determines one of the estimates of Psi by subtraction to ‘A’, the model would unnecessarily estimate two Psi parameters for the third time period, when in fact, only one Psi parameter needed to be estimated. However, in the above example, there is no natural ‘tostratum’ to specify since there is never a common transition in all three time periods.

Currently, the model is coming up with some sensible parameter estimates, but technically more parameters are being estimated than necessary. Is there any way to get around this ?

Thanks,

Tommy

[jlaake]

Unfortunately not because MARK does not allow that. If you want to do this you can try the multistate model in my marked package on CRAN. There I use a log-link for Psi and enforce the mlogit restriction by dividing by the sum. It is up to the user to use fix in the design data to set one of the cells to 0 to achieve identifiability. That said I've not done a huge amount of testing with the multistate model in marked but I did do some. You'll see in the design data in marked, that all of the transitions are in the data (eg., AA,AB,AC,BA,BB,BC,CA, CB,CC) whereas in RMark one is missing.

regards --jeff

[tgarrison]

Thanks, Jeff. I've been looking for an excuse to try out your 'marked' package.

[jlaake]

You have 2 options:

MSCJS uses ADMB.

HMMMSCJS uses FORTRAN code with a hidden Markov model formulation.

Sorry the documentation is far from what it should be. Just not enough hours in the day.

--jeff