Open Multi-State Model for Live Recaptures
The muti-state data type was extended to have a robust design by Kendall and Bjorkland (2001). Each primary session is considered to be open, allowing animals to immigrate and emigrate from the study area. However, an animal's state is fixed during a primary session, i.e., it cannot change states during a primary session. Transition between states is only allowed between primary sessions (psi parameter below).
The parameters in the open robust-design multi-state model are:
S(s) - survival rate between primary occasions for state s.
psi(r, s) - transition probability from state r to state s.
The following parameters appear for each primary session.
pent(s, t) - probability of entry onto the study area of state s at time t. The probability of already being present at the start of the primary session is obtained by subtraction, so that the sum of the pent values in a primary session should be constrained to <=1 using the MLogit link function. An example of how to invoke constrains and still use the MLogit link function is also provided.
phi(s, t) - probability of remaining on the study area of state s at time t, given that the animal had previously entered the study area.
p(s, t) - capture probability of the animal on the study area of state s at time t given that the animal is on the study area at time t.
Encounter histories are formatted as LLL..., i.e., only live encounters are needed, because dead encounters are not used in this data type.