Time-Varying Indiv. Covar. - Extrapolating Missing Values

[kthall]

Hello.

I work with snails and would like to use size (length) as a time-varying individual covariate. I have chosen this approach as opposed to an age model because I do not feel comfortable picking arbitrary categorical levels to observe the almost certain effects of size on phi, p, and psi in my multi-strata dispersal model.

The growth rate of these snails is known (and deterministic) so I can confidently extrapolate missing data for each snail on each occasion where it was not encountered. My concern is the effect of having these extrapolated values in my input file for individuals that were either:

1) Not yet born during this study- do I just use 0's for all intervals until the first encounter, or back-track all values towards the birth size and then 0's before that occasion?

and

2) Those that may have long since died (rather than those that were just not recaptured)- will having extrapolated values for a potentially dead animal mess up the likelihood?

Much thanks in advance from a frustrated grad student!

[gwhite]

You don't say what data type you are using, but I'm guessing the CJS live encounters data type. For the CJS (and also dead encounters data type), the survival estimates are conditioned on the first encounter. So, preceeding zeros never enter the likelihood, and hence, the value of the size covariate never enters the likelihood (note that this is NOT true for the Pradel data types, or any of the Jolly-Seber data types).

However, trailing zeros in the encounter history are a bit more problematic. These values are used, even if there is a long string of zeros. So, be careful what values you put here. If the snails grow continuously, and you end up with a gigantic snail for the last zero entry, your are likely to induce a growth effect in your model that may not actually exist in your data.

An approach that avoids the whole issue of interpolating or extrapolating size covariates is to use the multi-state model with 3 or so size classes. Then, you do not have to specify a size class for snails not captured. You may want to try both approaches to be sure you get consistent results.

Gary

[kthall]

Thanks Gary (and others). This has been immensely helpful already.

A quick clarification that may help me get the best advice here: The growth of these snails is deterministic- meaning once they get to ~ 22mm in length at around 4-5 years of age, they stay at this reproductive size until they die (which can be over 15 years later).

So for the trailing zeros in my encounter history (which is CJS live encounters), can I use known growth rates to fill each missing individual covariate time interval up to 22mm, and then use 22mm for each subsequent interval? Just worried that having "actual" data for a potentially dead snail will mess things up in the estimation.

I really hope to be able to use time-variant individual covariates for addressing other effects (percent cover, edge effects, etc.) as well, so really understanding what happens to with values corresponding to trailing zeros would be a tremendous help

[gwhite]

"A quick clarification that may help me get the best advice here: The growth of these snails is deterministic- meaning once they get to ~ 22mm in length at around 4-5 years of age, they stay at this reproductive size until they die (which can be over 15 years later).

So for the trailing zeros in my encounter history (which is CJS live encounters), can I use known growth rates to fill each missing individual covariate time interval up to 22mm, and then use 22mm for each subsequent interval? Just worried that having "actual" data for a potentially dead snail will mess things up in the estimation."

You are correct -- use 22mm for each subsequent interval once a snail should have reached this asymptotic size.

However, I would still advice you to consider the multi-state data type, but your assumptions are much cleaner with that model.

Gary