groups with varying interval lengths

[jsaracco]

Hi all.

Under the cjs model, I'm looking for advice on the best way (if there is one) to handle groups that differ with respect to interval length between capture occasions. In the past, I have dealt with this by simply setting capture probabilities to zero whenever capture occasions were missed for a particular group.

For example, for one group sampled annually for 4 yrs, I might have a "time-constant" pim for p that would look like:

1111
111
11
1

For another group that was only sampled in yrs 1, 3, and 4, I would have:

1211
211
11
1

I would then set p2=0.

I am now dealing with a data set with many groups that i would like to include in a single analysis (examining various group covariates). These groups, however, have sampling intervals that vary widely from about a couple of wks to 2 months or more. I could take the above-outlined approach, using a capture interval of, say, 2 wks, but that would result in lots of missed capture occasions for many groups. Perhaps this is my only option. But if anyone has other ideas on how to deal with this I'd apreciate hearing about them. Thanks!

Jim

[Jon Runge]

I asked Gary White the same question awhile back, here's response:

"You will have to include the time interval between occasions (call it L) as a covariate in a log link for the parameter. So, assume you are estimating survival, S, across an interval of length L. Then, log(S)=B1*L, and S=exp(B1*L)=exp(B1)^L. So, the unit length of survival (day) is exp(B1), and the interval survival is exp(B1)^L = DSR^L where DSR = Daily Survival Rate."

Just to be complete (ie risk stating the obvious): You model the time interval covariate with a column for L in the design matrix. Then you need to have rows specific to each group and time period to capture the unique interval for each group/time combination. Also, make sure that phi has a log link. Don't constrain any parameters with log link to be 0--that won't work. Finally, note that DSR is just an example. You could use unit length = 1 week, 1 month, whatever you want your survival estimate to mean biologically.
--Jon