Hi Joe
c-hat is estimated with error. David Fletcher advises against applying a correction unless the calculated c-hat lies outside the range expected by chance. In the coming release of secr that can easily be checked by simulation (new argument 'nsim' in chat.nk() triggers simulations). Release is a week or two off; otherwise get the development version from GitHub.
If some sessions have significant overdispersion and others don't then my preference is to base the decision on biological judgement: adjust if it makes sense because you can see a biological explanation for the difference. At least we are just talking about CI width - not like the bad old days where CAPTURE had people jumping between 'preferred' estimators, with different biases.
QAIC: a very good question, and one I've asked David to think about. Possibly c-hat pooled (averaged) across sessions, but what should be the weights? Similar sample size would argue for equal weights.
As an early adopter you may have to be patient as we sort out the wrinkles!
Murray
[apologies if you receive multiple copies of this - the software has been playing up for me]