I created a global model in Presence for a single species multi season analysis. I have 4 seasons, 46 sites and 44 surveys total (11,13,13,7) . I ran the MacKenzie Bailey goodness of fit test using 10,000 parametric bootstraps. My results show a very underdispersed c-hat value of .08 but a P value of .5. According to chapter 4 of Occupancy Estimation and Modeling(2nd Edition) MacKenzie et al 2018 (in reference to Burnham and Anderson 2002) , underdispersion can be ignored. Burnham and Anderson 2002 seem to put an emphasis on the p value even if c hat is not close to 1. However I have read elsewhere that a c hat value this low should indicate that this model should not be used to make inferences. Could I still use this global model to continue fitting models?
My second question is about my real parameter gamma being 0 with a SE of 0. Would this also indicate that a model is a poor fit?
Thanks