number of occasions = number of intervals

[SandraChristine]

Hi,
I'm hoping someone can help me to understand why models which include both live recaptures and dead recoveries have the same number of intervals as occasions. This seems to be true for the Burnham(both) as well as the Barker(both) options in MARK. When I run the following: S(time)p(time*group)r(group)R(.)R'(.)F(.)F'(.) as a Barker(both), I get 6 S and 25 p parameters, but was expecting to get 5 and 30, respectively (I have 6 occasions and 5 groups).
Thanks, Christine.

[cooch]

Hi,
I'm hoping someone can help me to understand why models which include both live recaptures and dead recoveries have the same number of intervals as occasions. This seems to be true for the Burnham(both) as well as the Barker(both) options in MARK. When I run the following: S(time)p(time*group)r(group)R(.)R'(.)F(.)F'(.) as a Barker(both), I get 6 S and 25 p parameters, but was expecting to get 5 and 30, respectively (I have 6 occasions and 5 groups).
Thanks, Christine.

Have a read of section 10.2, chapter 10 from the book. In particular, the assumption about dead recoveries being 'encountered' during the interval after the last live capture occasion.

[SandraChristine]

Is there any way to account for recoveries that occur at the same time as recaptures (e.g. I visit the site for the next round of recapture and find several dead individuals)?

[jlaake]

Those should be treated as mortalities that were recovered in the interval prior to the the capture event. Thus, if this is the only way you are getting recoveries then you don't have recoveries from the interval after the last occasion and that recovery probability should be set to zero and you'll have to cope with an unestimable survival for that last occasion.

[cooch]

Is there any way to account for recoveries that occur at the same time as recaptures (e.g. I visit the site for the next round of recapture and find several dead individuals)?

Those recoveries would alter/have different implications for F. As such, you might consider a multi-state live-dead model, treating marking location as a site. This would make the interpretation of F cleaner.

In your post, you say recoveries that occur at the same time as recaptures. In all likelihood, they occurred before the recapture event (i.e., preceding interval), although there are complications, since you'd need to account for possibility that they were in fact there, dead (on the ground say, but not encountered until a particular recapture event). This can be handled.

[SandraChristine]

That helps a lot! just one more point I'm not clear on:
Having read 10.2, I see that I gain an extra S parameter by recovering individuals after the recapture periods (this still holds true with your recommendation to use recoveries from one occasion as deaths for the preceding interval). But I still don't understand how I lose a p parameter... (in a model with only live recapture data you have one more p than S, so if the combination of live and dead data gives me an extra S parameter, wouldn't I expect the same number of S and p parameters?). But I end up with only 5 p parameters when I have 6 occasions.

[cooch]

That helps a lot! just one more point I'm not clear on:
Having read 10.2, I see that I gain an extra S parameter by recovering individuals after the recapture periods (this still holds true with your recommendation to use recoveries from one occasion as deaths for the preceding interval). But I still don't understand how I lose a p parameter... (in a model with only live recapture data you have one more p than S, so if the combination of live and dead data gives me an extra S parameter, wouldn't I expect the same number of S and p parameters?). But I end up with only 5 p parameters when I have 6 occasions.

For a live encounter study with n occasions and (say) two primary structural parameters (say, phi and p for a live encounter study), you end up with 2 x (n-1) parameters, not all of which are separately identifiable. For example, for a 7 occasion live encounter study, you have 6 phi and 6 p estimates, of which only 11 are estimable (first 5 phi, first 5 p, and a function of the terminal phi*p product).

You state that in a live recapture data you have 'one more S than p' - this is incorrect - and suggests you're not fully understanding the larger issue of parameter structure, and identifiability, of even the simpler models. Make sure you understand for live encounters (alone) and dead recoveries (alone) before you tackle combining the two.