Conditional Co-Occurrence Over-Dispersion and GOF adjustment

[MBroadway]

Hello to the forum,

I'm currently trying to understand how best to move forward with an occupancy analysis after running into issues of over-dispersion. For some background, my data consists of roadside aural avian point counts at sites spaced ~1.6km apart along 51 routes that were generated in a stratified random design. I have 564 sites, ~1,900 surveys and sites could have been visited up to 6 times. Data was collected during the same seasonal periods in each of 2 years. I've fit single-species single-season occupancy models (MacKenzie et al. 2002) for both species before carrying forward the most supported occupancy and detection structures from both species to parameterize a 2-species conditional co-occurrence model (Richmond et al. 2010).

Explanation: There is some evidence of over-dispersion in both single-species models. Correcting for the extra-binomial noise is trivial in these cases with directions in Chapter 5 of the MARK BOOK. However, I have not been able to identify the source of noise and I suspect it is a structural issue. For each species, the model rankings are fairly robust to incremental changes to c-hat until c-hat ~ 2. However, the c-hat values for both species are ~1.7 and >4.0. The deviance residuals plot shows that in either case, the residuals are constant and horizontally distributed but with all values above zero (perhaps indicating a structural issue). By themselves, these are manageable and a conservative adjustment can be made for either case.

Questions: Even though the single-species models can be corrected for extra-binomial noise, I'm presented with the issue of how to address it when combining the encounter histories for the conditional co-occurrence model. Despite all 12 model structures converging with reasonable estimates that appear biologically aligned with the species, SE may be biased due to noise. The deviance values are even larger and thus the c-hats are larger than either of the 2 single-species models.

1) How does one address lack-of-fit at this stage when two very different over-dispersion estimates are now combined? Would applying the most conservative (i.e., highest c-hat adjustment) also potentially 'shrink' real affects?

2) Is bootstrap GOF an option? This isn't available for this data-type in MARK. However, the MacKenzie and Bailey (2004) approach is implemented in PRESENCE.

3) Would building a random effects model help identify structural issues? This seems plausible but also cumbersome to build in MARK if route or site were treated as random effects.

4) In short, in what way does one proceed, or not, with the conditional co-occurrence modeling framework under these circumstances?

Thanks for any help. I can provide more information, clarification, and background if needed.

Cheers,
Matt