Violation of assumption in Multistates model?

[shubhaPAndit]

Hi Researchers,

I was trying to develop a multistate model and while reading the papers about the assumptions of the model, I found that survival and recapture probability of individuals among strata should be equal. I interpreated as: Multistates model can not be used if survival probabilities among the strata are not homogenous.

I am referring the paper of White et al, Multistate Survival Models and Their Extensions in Program MARK, J of wildlife management, pages 1521-1523

The page 1523 the last paragraph says
"....The above example of an encounter history probability demonstrates an arbitrary assumption of the multistate model as implemented in MARK based on the Brownie et al. (1993) formulation: they modeled survival with the survival rate for the stratum where the capture of the animal took place, and then movement to a new stratum takes place. That is, all mortality takes place before movement. An animal cannot move to a new stratum where a different survival rate pertains and then die. If it dies, it must do so on the current stratum. If it lives, then it can move to a new stratum. This assumption is critical if survival rates are different between the strata, with violation of this assumption resulting in estimated survival being a weighted average across strata. If survival is the same across all the strata, then the assumption is not important because survival is the same regardless of the stratum currently occupied. Where geographic areas define strata, as in a meta- population study, this assumption is often difficult to meet or validate, and limits the usefulness of the model in that strata-specific survival estimates are not obtainable unless the transitions between strata take place immediately before an encounter occasion"

Or is it taking about the individuals fitness, i think if it is fitness, we can relax the assumption if we use the individuals of one size or age.
Any suggestions?

[Bill Kendall]

The assumption is that survival probability is homogeneous WITHIN strata, not among strata. Furthermore, this survival probability is associated with the stratum you started from in that period. So, for the case of strata A and B, if at time t an individual is in stratum A, its survival probability between t and t+1 is assumed the same as any other individual that is in A at time t. You can refine this assumption if you have individual covariates. A point of the paragraph you quoted is that with geographic states, this assumption can cause a problem if movements (e.g., from A to B) occur other than at the end of the t to t+1 interval.

[shubhaPAndit]

Thank you Dr. Kendall for your response.
it means that all individuals of our interest group within the strata is supposed to be equal. That is good and it is only possible to meet the assumption if we make the time as a strata (year 1 = A, Year B=starta B , and so on).

If any one want to make the strata based on space (geographic), it is almost impossible to get the equal survival probabilities of the individuals. You mentioned that it would be a problem if there were a survival probabilities different between A and B at the end of the t and t+1 interval. It means to me that, suppose animal moved from strata "A" to "B" between Summer and Winter in order to avoid harsh condition of Strata A. In that scenario, between summer and winter, the survival probabilities are different among A and B. what do you think whether we are violating the assumption so that we can not use the multistate model?
Thanks,

Shubha Pandit, PhD