Correct or Not Correct for Overdispersion in Nest Survival

[mwfrantz]

Hello All,

I will preface my post in that I have read all relevant chapters in the MARK manual related to overdispersion. I have also reviewed the only 2 posts related to this matter for nest survival models which somewhat gave different thoughts.

My main question is does one need to correct for overdispersion in Nest Survival models?

A post by cooch in 2006 said c-hat >1 “isn’t relevant for nest survival” data and shouldn’t be done. However, MARK output still provides a c-hat value, -log2L values, etc. where you could divide the deviance by df by hand and get c-hat as well. There are some very recent nest survival papers published that have corrected for overdispersion (e.g. http://talltimbers.org/wp-content/uploa ... al2015.pdf).
The only options available for Nest Survival are the LRT and reviewing deviance/pearson residuals.
My concern is that according to deviance residual plots and MARK calculated c-hat values, both my standard (general/constant with no covariates) models and saturated model (including all possible covariates) are highly over-dispersed; both have c-hat values around 2.7 and 2.8. Deviance residual plots are all above 0 (so no spread above and below zero) with a few outside the interval.

I recall in the manual that c-hat values <3 can be ok, but my second question is how "relevant" are c-hat values in a nest survival model? Basically, should I be concerned given my data?

All nests were checked/monitored consistently across years following the same standard avian protocols. I have 280 nests over a 6 year period in one group (Year is a covariate modelled as several dummy covs but has no overall support); I have up to 12 covariates but never are all of them in one model if I take a 2-stage modelling approach. Two of these variables are time-within season (linear and quadratic), and a third is Nest Age. Nesting season is 77 days over a 3.5 month period. I'm taking the top temporal covariates from an initial model and using it as a baseline in a second, final model that has habitat covariates (similar to paper listed above).

From forum users’ experience, what is typically the source of overdispersion in nest survival models?
I apologize in advance if I am naive in asking any of these questions and overlooked something.
Thanks for everyone’s time!

[cooch]

Hello All,

I will preface my post in that I have read all relevant chapters in the MARK manual related to overdispersion. I have also reviewed the only 2 posts related to this matter for nest survival models which somewhat gave different thoughts.

My main question is does one need to correct for overdispersion in Nest Survival models?

A post by cooch in 2006 said c-hat >1 “isn’t relevant for nest survival” data and shouldn’t be done. However, MARK output still provides a c-hat value, -log2L values, etc. where you could divide the deviance by df by hand and get c-hat as well.

You should read (or, re-read) section 5.2 of Chapter 5 -- this will give you some insights as you why you shouldn't derive an estimate of c-hat using the deviance/df from the full output. Basically, because it is typically not chi-square distributed for the sorts of data we're using.

Second, there is a fair conceptual connection between nest survival models, and known fate models. Read (or re-read), section 16.8 of Chapter 16 (the known fate chapter). It explains why there is no GOF test for known fate models. My current understanding is that the same logic applies to nest survival models.

There are some very recent nest survival papers published that have corrected for overdispersion (e.g. http://talltimbers.org/wp-content/uploa ... al2015.pdf).

Not that I can see - they only mention of 'overdispersion' in the paper is wrt to AICc, where the authors appear to have simply parroted the basic 'description' of what AICc means. In short, I see absolutely nothing in the paper that indicates they did any adjustment for 'lack of fit' at all -- which doesn't surprise me, since I'm not aware of any such GOF test for nest survival models.

The only options available for Nest Survival are the LRT and reviewing deviance/pearson residuals.
My concern is that according to deviance residual plots and MARK calculated c-hat values,

See above -- the c-hat you are using is apparently basied on dividing the deviance from the full output by the df. Don't, it is (generally) wrong, and if that is the basis for your concern - stop now.

[Rotella]

You might take a look at:
Sturdivant, R.X., J.J. Rotella, R.E. Russell. 2007. A smoothed residual based goodness-of-fit statistic for nest-survival models. Studies in Avian Biology 34:45-54.

and at various SAS code I provide for nest-survival goodness-of-fit testing at:
http://www.montana.edu/rotella/nestsurv/

Although I'm sure some users would appreciate being able to implement these tests in R, I only have code for implementing these GOF tests in SAS for mixed-effects or fixed-effect-only models.

[cooch]

You might take a look at:
Sturdivant, R.X., J.J. Rotella, R.E. Russell. 2007. A smoothed residual based goodness-of-fit statistic for nest-survival models. Studies in Avian Biology 34:45-54.

and at various SAS code I provide for nest-survival goodness-of-fit testing at:
http://www.montana.edu/rotella/nestsurv/

Although I'm sure some users would appreciate being able to implement these tests in R, I only have code for implementing these GOF tests in SAS for mixed-effects or fixed-effect-only models.

Jay -- perhaps time to add a short section on same in your chapter?

[mwfrantz]

To summarize, given the potential bias in the deviance calculation MARK uses if your data don't follow a chi-square distribution, my fears of overdispersion may not be true since I have been basing it on those output values. At least built into MARK, there are not any reliable GOF tests for known-fate models (and nest survival by extension) since the saturated model is suppose to fit the data "perfectly" (CH.16-26).

My follow-up question to clarify then is that I shouldn't put any "salt" into interpreting the visual deviance/pearson residual plots either (i.e. the visual appearance of residuals follows the same wrong set of assumptions for this model type)?

Thanks Rotella for the paper reference. I have used everything but SAS but will look into it! Thanks everyone for their input on this subject.