GOF/c-hat

[grey pendleton]

I'm using PRESENCE to estimate site occupancy and, more importantly in this case, covariate effects on p. Sites are divided into 5 groups with psi allowed to vary among groups (this part is the same for all models considered). I'm modeling p as a function of covariates, beginning with simple models (1 covariate) and proceeding to add additional covariates. As I increase complexity, c-hat (based on bootstrapping) gets larger; ~1.3 for simpler models increasing to ~3.5 for complex models -- enough to make a difference. The GOF chi-square generally declines with increasing model complexity, but not as fast as the mean chi-square from the bootstrap samples, hence the increasing c-hat. AIC decreases substantially with increasing model complexity, oposite from the c-hat estimates. So AIC suggests that complex models are better, while c-hat suggests they don't fit as well.

Any comments on the possible source of this pattern and suggestions for which c-hat to use in adjusting s.e., AIC, etc. would be appreciated.

[darryl]

Hi Grey,
Sorry, no flashes of inspiration from me here, I haven't noticed this behaviour before. Generally you'd hope the opposite would happen if the simpler models are receiving a lower ranking. How many bootstrap samples have you been using? I generally recommend about 10,000. What are your sample sizes like (sites and number of surveys)?
Darryl