I have known-fates data on radio-marked animals, but I also have information on which of two habitat types the animal was in on each sampling occasion. I'm interested in estimating survival for each habitat type, which could be easily done with a known-fates model, but I'm also interested in the transition probabilities between the two habitat types. In the 'Gentle Introduction', it discusses how to use live-dead data in a multi-state model, but in that case entry into the 'dead' state is permanent. I'm wondering if I could do something similar where I had four states:
A = habitat 'A'
B = habitat 'B'
C = dead in habitat 'A'
D = dead in habitat 'B'
I could fix p = 1, and some of transition probabilities to 0 (psiAD, psiBC, psiCA, psiCB, psiCD, psiDA, psiDB, psiDC). Then the resulting estimates would be interpreted as:
psiAA = probability of remaining in A
psiAB = probability of moving from habitat A to B
psiAC = mortality in habitat A (i.e., survival in A = 1 - psiAC)
psiBB = probability of remaining in B
psiBA = probability of moving from habitat B to A
psiBD = mortality in habitat B (i.e., survival in B = 1 - psiBD)
My question is whether this would be appropriate or am I overlooking something?
Thanks!