Multi-season Models + Overdispersion

[Bird Counter]

Hello,

I am a Presence user, but this is a general question that is relevant to users of other software types.

Recently, I saw a thesis in which the author proposed using c-hat values from single-season models to adjust standard errors in model-averaged, multi-season model estimates. I had never heard of this. He did not find evidence of overdispersion in his two single-season models so he made no adjustments. It is not clear whether he would have adjusted the SEs of psi1, gamma and eps using the sqrt(c-hat) value he calculated from the single-season models. It also was not discussed how he would have dealt with different estimates of c-hat that > 1 in the single-season models.

I have assessed GOF in single-season models and have found some evidence of overdispersion (mean c-hat <1.7) in one year. However, I did not use this information when constructing multi-season models. This approach does not seem to be the right way to deal with this issue, but I cannot find other ways to deal with it in the applied literature. I am only talking about situations where overdispersion is not excessive.

Any thoughts from the experts in the field?