Stack Data Methods for Multispecies Occupancy (Rota Model)

[Jordan Heiman]

Hi All, 

I am working on a rather large data set using the occuMulti method. Our data set spans ~10 years with not all sites and cells being sampled every year. Because we are not interested in the changes in occupancy we are using a stacked data approach and included a categorical covariate for year in our state model. Our main interest is the effects of different covariates on occupancy and how presence of one species is affecting the other (as well as how our landscape covariates play into that effect). We are looking at 2 models for our data, one in the summer and one in the winter. The breakdown of the grid cells sampled for our summer model is approximately 51% of the cells were sampled in only a single year, 41% were sampled in 2-4 of the years, and 8% in more than 4 of the years. And the winter model  is about 52%, 22%, and 26% respectively. 

I'm really struggling to wrap my head around the limitations of stacking the data and how that can affect our results with pseudoreplication since each site-year combintation is not necessarily independent. We did include that year covariate but we did not include a random effect for site as (1) as far as I know it is not currently possible to incorporate a random effect in the occuMulti method, and (2) I'm not sure that enough sites have replication to include a random effect and still have the model converge. 

From what I understand, by not including that random effect one of the main concerns is  running the risk of our SE being underestimated, but not, necessarily, the point estimates themselves. However, I do feel like I have seen a lot of publications using stacked data without including that random effect of site. I also am concerned about how this type of error might propogate through the AIC (which we are using to detemine our top models). 

Do any of you have any suggestions on readings or resources that might help me get a better grasp on how we should move forward? Mainly I am just trying to determine if (1) including a random effect of site is critical, meaning I need to recode everything in JAGS or Nimble. Or if (2) there are other ways that we can account for possible pseudoreplication in the way we interpret or assess our models. And overall it would just be good to get a better understanding of all this too. 

Thank you all for the help.

Jordan