Nest Survival

[BStevens]

I have a question concerning estimating c-hat with the nest survival model. It is my understanding that estimating c-hat via deviance divided by deviance df, although biased high, is a conservative way estimate overdispersion for this model. If deviance degrees of freedom is the difference in the number of paramaters between the saturated model and the global model, how does one determine the deviance degrees of freedom for this analysis. In the nest survival model the effective sample size is based on the number of exposure days, not the number of nests. In this case, it seems that the saturated model would have a number of paramaters equal to the efffective sample size. However, the MARK output gives a deviance degrees of freedom as if the saturated model had 1 paramater for each nest, not each exposure day. Am I interpreting this wrong or is there a discrepency here?

Thanks,
Bryan

[gwhite]

Bryan:
You are correct that there is a discrepancy in MARK on the deviance calculation and the effective sample size. The parameter space for this model is the daily survival rate (DSR) of each individual.
For the effective sample size, the number of days that an individual is known to survival is taken as the starting point, and then 1 is added for the interval at the end if the individual died. This is because we don't have the information on the exact day of death.
However, for the deviance, the number of individuals is taken as the sample size -- just because using the effectivve sample size as calculated above will be too large. For known fate and nest survival models, there is no reliable GOF test because the saturated model is a reasonable model to consider, and obviously the deviance of the saturated model is always zero. In other words, you can construct the saturated model in MARK, and get the deviance of zero. But, there is no information left to consider GOF. Further, any model that you construct that has fewer parameters than the saturated model is then just a likelihood ratio test between the saturated model and the model being considered, with the inherent assumption that you made to obtain this model assumed to be true so that the resulting test is strictly from lack of fit.
There is a lot more to all this than meets the eye, but my best example is a single survival interval with n animals in a known fate model. There is only 1 estimable parameter, and this happens to be the saturated model as well. There is no information on GOf. Yet, we publish this type of survival estimate all the time -- e.g., Kaplan-Meier estimates. I think MARK users have been obsessing over GOF tests when in reality there is no reliable GOF test available.

Gary

[BStevens]

Thanks, that was what I was anticipating, I just wanted to make sure I was estimating c-hat correctly.