NestID as a random effect in nestling survival

[Eldar]

Hallo,
I am trying to understand the issue of nest survival modeling in Mark. I have passerine (tree swallow) nestlings with unknown fate date (interval censored), so data perfectly suits for the design of Mark nest survival module. But the problem is that there are several chicks in each nest and their survival, I suggest, is not independent. I would assume that the best option would be to put nest ID into the model as a random effect, but I cannot understand is it possible and how to make such random effects in Mark.
I've seen articles from Jay Rotella and SAS code, but would like to solve this problem in Mark, RMark or R. Any suggestions are welcome.
~ Eldar

[Rotella]

Hi Eldar,
In many studies, nesting success is defined as the probability that a nest will have >= 1 young bird leave the nest. In such situations, nest survival analysis does not deal with fates of different young in the same nest. That said, it doesn't mean you can't consider further details such as you mention on individual young. If you do work with random effects with nest survival data, you will want to carefully consider issues of left truncation that are common in nest-survival data: these issues have been discussed in the Studies in Avian Biology volume 34 published in 2007 ("Beyond Mayfield ...") in papers by Heisey et al. and Rotella et al. Finally, one can run nest survival models in MARK (and through RMark) as shown in various help files for MARK and RMark, but I am not aware of how to run a model with nest ID as a random effect in MARK.
Best!
Jay

[cooch]

This can be done in any one of a couple of ways. The brute force (but totally acceptable) way is to select a check at random from each nest, run the analysis, then repeat multiple times. This is, in effect, a bootstrap on the estimate, and is a fairly common approach to handling such 'non-independence'. This should be easy enough to code up using an interface of some data manipulation tool and calling MARK.

In fact, this general approach is the basis for what is known as the 'individual bootstrap' feature which is currently in MARK, but not documented (documentation will be released by the end of the summer, in all likelihood).

[bacollier]

Eldar,
I don't have any idea on the specifics (and I just learned something from Evan's post, thanks Evan ), but it 'might' be possible to do this in a GLMM using a user defined link function for the logistic exposure approach in the same manner as a glm() by re-defining the link function (I saw some discussion on this a while back on the R lists so you might search there).

(https://stat.ethz.ch/pipermail/r-help/2 ... 03799.html)

Bret

[Eldar]

Thank you so much for all of these ideas.
It seems to me that I really need to treat each nestling not a whole nest because I am going to test a relationship between juvenile death and cold snaps. So each death needs to be incorporated.
So there are two options (that I can try) – glmm-lmer-nlme (R) and individual bootstrapping (Mark). As far as I can understand there are no detailed descriptions for both of the approaches, so it will not be possible just to plug my data into package or module. (Jessi L. Brown did wrote the link function in R (see examples in ?family) but after testing mixed model for overdispersion she switched to MARK : http://www.bioone.org/doi/abs/10.1525/a ... .125.1.105).
Before starting to practice in one (or both) of the approaches I would like to discuss advantages of MARK vs. GLMM. Am I right that the main plus of MARK is that it will estimate real daily survival rate while with Shaffer et al. model we will estimate constant survival for the whole interval between nest checks? In my case the latter is not too interesting because we assume that cold snap but not an average temperature for the interval kills chicks. Please, correct me if I am not right here.
With individual bootstrapping approach I am not sure I understand what are we going to do after getting the distribution for each beta? Are following steps described somewhere? I can imagine that we may take errors (or variances) for each beta and say that this is a random part results, then we can take mean betas as a fixed part. But how can we get errors for the fixed part?
~ Eldar

[Eldar]

Having no responces to the previous post I decided to go for bootstrapping idea that Evan suggested. But I still need some help:
Suppose that we have 5 competing models to test. What level of averaging will be appropriate?
I suggest that model comparison will be better done for models built on the same dataset, so, we generate subset from data (randomly choosing 1 nestling from each nest) then run all 5 models and build results table, then generate next dataset, run same 5 models, build table and so on.
What will be the next step?
1. Can we average real (response scale) parameters or do we need to average at the betas level?
2. Do we need (and can we use) Delta method for conf. intervals?
3. Can we average AIC, AICc, delta AICc, AICc weights from the results table?
I can’t find any documentation on this and I need your advices before running the bootstrap.
~ Eldar

[B.K. Sandercock]

Known fate models in Mark include the known fate procedure and the nest survival procedure, but are also in other software too. It is possible to include individuals as a random effect in Cox proportional hazards models in Program R. Cox PH models are in the survival package, and the function for random effects is cluster(). In the following example, encounter histories would need to be coded similar to the nest survival procedure in Mark with date of entry, date of exit, and fate. var1 and var 2 would be your fixed effects and cluster() would allow you to include NestID as a random effect.

output <- coxph(Surv(entry, exit, event)~ var1 * var2 + cluster(NestID))