violation of primary assumption in MS models??

[AKJohnM]

I came across an issue that I'm having a hard time understanding in a basic multistate mark-recapture analysis. This issue regards survival across the non-observation period being dependent on state during the following observation period, which is, as you know a violation of a primary assumption for these type of models. I assumed that survival is only dependent on previous state and if all animals start in the same state, they should all have the same survival estimate for the following observation period regardless of transition. However, that is not the case because survival across that non-observation period is also tied with state transition.

My data consist of suckling proportions of juvenile mammals. All are suckling during their first year and I allow state transitions (to independence or continued suckling) to occur just prior to the second observation period (t2). I'm analyzing the data in Program MARK which claims for multistate model calculations, "all mortality takes place before movement" (p. 8 - 5). If that were the case, I would expect to see equal survival rates for juveniles in both states at t2 because they all started in the same state at t1, but when I look at the parameter estimates, survival rates are clearly different depending on which state they were observed in at t2. I experimented with other similar datasets and get basically the same result - differing survival depending on state transition. In a way, this makes sense because survival is tied to state transition between observation periods. However, a certain proportion of those that are transitioning back to suckling are considered to have died. I don't quite understand how an animal that transitions to a state that requires it to be alive, is by estimation, dead - unless it transitions then dies before the next observation period. Yet, this is contrary to what Program MARK claims to calculate - survive then transition, not transition then survive. It seems to me that the MARK calculations take into account survival and state transition regardless of when they occur during the non-observation period - i.e., it doesn't seem they are temporally separable the way things are calculated. As such, survival is, in part, dependent on state in the subsequent observation period (a violation) because it is tied to the transition to that next state. Am I missing something here? Can anyone please help clarify this?

Other things I've tried:

I can force survival to be the same between the 2 groups by setting the PIMs to 1 for all animals during that first time period, but I'm a little uneasy with that because I feel MARK should know this and it doesn't seem to. Also, although the survival estimates for subsequent periods make sense, I don't have the confidence that MARK is calculating them correctly because of the issue I outline above.

Used robust design, multistate modeling but get basically the same results.

Considered a recruitment (to independence) probability analysis but that seems to be more relevant to one state being unobservable - not the case with my data as both states are highly observable but not necessarily equally observable.

Thanks in advance for any thoughts on this question and I apologize if this is just a trivial issue that has a simple explanation.

--John

[cooch]

I came across an issue that I'm having a hard time understanding in a basic multistate mark-recapture analysis. This issue regards survival across the non-observation period being dependent on state during the following observation period, which is, as you know a violation of a primary assumption for these type of models.

Am pressed for time at the moment, but can make one quick comment - what you've stated (above) isn't an assumption of MS models generally - it is an assumption of 'computational convenience' in some software (like MARK, for example, which assumes that an animal survives, then moves). But, there is no reason in principal that you couldn't 'flip it' so that you estimate movement first, then survival as a function of 'where you land'.

Various software (other than MARK) do have different MS parameterizations. For example, program M-SURGE has a parameterization called JMV (which was in fact described by Brownie et al. in 1993) which
differs from the typical Arnason-Schwarz (AS) model in that it permits the capture probability for time (i+1) to depend on the state at periods (i) and (i+1) (whereas the AS model permits the encounter probability to depend only on current state, and time). Thus, the AS model is in fact a special (reduced) case of the more general JMV model.

[AKJohnM]

Thanks for the quick response. It is somewhat helpful. However, I guess my main concern is that Program MARK does not seem to be computing what I think the manual says it is computing. That is, an animal dies (or survives) then moves. If that was the case, then I'd expect no difference in survival for the different states it moved to. That mortality (or survival) would only depend on the previous state. And that is what I'm really interested in estimating. Perhaps I could use a time-varying individual covariate to represent the previous state?

[cooch]

Thanks for the quick response. It is somewhat helpful. However, I guess my main concern is that Program MARK does not seem to be computing what I think the manual says it is computing. That is, an animal dies (or survives) then moves. If that was the case, then I'd expect no difference in survival for the different states it moved to. That mortality (or survival) would only depend on the previous state. And that is what I'm really interested in estimating. Perhaps I could use a time-varying individual covariate to represent the previous state?

MARK does what the manual says - estimates based on first-order Markov process - probability of survival *and* moving from (i) to (i+1) function of state at time (i). Period.

You're misreading. Clearly, and animal has to survive, in order to move. The estimates you get are for state at time (i).

[AKJohnM]

I don't believe they are, because as I stated. All began in the same state. Therefore, all survival estimates should be the same at t+1, but they are very different. You can test this yourself with any legitimate multistate dataset. Just set all the first period states to be the same. Survival to next period will differ depending on transitions during that interval, not on the previous state.

[cooch]

I don't believe they are, because as I stated. All began in the same state. Therefore, all survival estimates should be the same at t+1, but they are very different. You can test this yourself with any legitimate multistate dataset. Just set all the first period states to be the same. Survival to next period will differ depending on transitions during that interval, not on the previous state.

Thats because if you have no individuals in one of the states, your estimate of initial S from the state where you have no individuals is, in fact, not estimable. The estimate MARK reports will be 0.45 (more or less), with a SE of ~0.0. The value 0.45 is the starting value MARK uses for a given parameter.

[AKJohnM]

Ok, thanks. That makes total sense.