time varying indivdual age covariate?

[jclaisse]

My sampling intervals vary between 2 and 4 days over a ~40 day period. I am tying to see if daily survival increases with age (days) but since I was unable to sample everyday or even at the same interval over the given period if I try to fit a general age model

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the same parameter will correspond to fishes from different cohorts which will have different ages because of the unequal sampling intervals.

Can I overcome this by using a different indivudual co-variate for each time period that is the age (days) for each indivdual at the start of that time period?

From reading the section in CH12 of the gentle introduction that deals with this I think I could impliment this as follows:

Start with the time varying pim

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Then in the DM

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and this would yeild the linear model:
Logit(phi)=beta0 + beta1(starting age)

[ganghis]

Hi,

That approach would get you close, but wouldn't allow age transitions to occur between sampling intervals (i.e. only the starting age would be used). Thus some fish would stay a given 'age' for 2 days, while others would stay the same 'age' for 4 days. In some ways, I think you are best off recoding your encounter histories to contain all 40 days (all histories would contain 0's for occasions where you don't sample). Then you can use a general age based model - or individual covariates if they are initially caught at wide variety of ages (such as you describe in the most recent post). You then could set p=0 for the days where you don't sample. That might be the most coherent way to approach things, although your PIMs will be rather large.

Cheers, Paul Conn

[jclaisse]

Thanks Paul. I think coding everyday individually would help make a lot of aspects of this more straight forward.

But setting the days I didn't sample p=0 then brings up another question about what happens to the estimates of Phi for those daily intervals and for the subsequent interval before the day I did sample?

For example, if I didn't sample 2 days and then sampled on the third, is all the mortality that occurs over that whole period accounted for in the Phi estimate for the 1 day interval leading up to the sampling day or is it averaged across the 3 single day intervals?

And if it is the latter, then regardless of which days I didn't sample and set p=0, a full daily age model will still produce an estimate of phi for each day they would just be averages across the days I didn't sample (which I think is the same thing as just setting my sampling interval lengths to different lengths in my origianl approach to this).

[cooch]

Thanks Paul. I think coding everyday individually would help make a lot of aspects of this more straight forward.

But setting the days I didn't sample p=0 then brings up another question about what happens to the estimates of Phi for those daily intervals and for the subsequent interval before the day I did sample?

For example, if I didn't sample 2 days and then sampled on the third, is all the mortality that occurs over that whole period accounted for in the Phi estimate for the 1 day interval leading up to the sampling day or is it averaged across the 3 single day intervals?

And if it is the latter, then regardless of which days I didn't sample and set p=0, a full daily age model will still produce an estimate of phi for each day they would just be averages across the days I didn't sample (which I think is the same thing as just setting my sampling interval lengths to different lengths in my origianl approach to this).

Read the sections of the book that cover unequal time intervals for the answer to one part of your question.

[ganghis]

Parameter identification/estimability will depend on the distribution of sampled age classes as well as the particular sequence of sampling dates you are considering. I'm guessing there may be some issues with estimating a separate Phi for every age class, so you'll probably want to impose a constrained model (linear and quadratic on the logit scale would probably be worth trying).

If you have an entry for every day in each encounter history, you'll be estimating daily survival as a function of age.

Hope this helps. Cheers, paul