The approach described should work, just make sure to include the interaction between your binary (Y/N) variable and whatever else you think is pertinent. Include 'site' as a random effect. Good luck.

A mixed ANOVA model usually contains repeated measures within groups and differences between groups. But your data is binary, rather than repeated, so you can't use ANOVA. But you can use Chi Square :)

Thanks for the answers so far.

If it helps, my global models look something like this:

Response~eel presence (Y/N) + habitat size + stream sinuosity + % catchment forest cover + 1|site

Responses are food-chain length, total fish biomass, fish size spectra, etc.

Just worried that since eel data are included within the responses that the species presence predictor variable is conflated with the response.

I would have my worries as well. Have you tested eel presence as a response to the model (e.g. eel presence ~ habitat size + stream sinuosity + % catchment forest cover + 1|site)? It is essentially trying to understand what level of influence it may have on the overall model to help interpret the overall model you are postulating.

Ah, I see your dilemma! Remove the eel counts from your response variable. Assuming your question is: Does the presence of eels influence food-chain length, diversity, abundance, etc. ?

Also, the relationships between your other variables (habitat size, stream sinuosity, etc.) and the response variable may be dependent on the presence of eels. Therefor, your model should consider this possibility:

(Response - eels) ~ (habitat size + stream sinuosity + % catchment forest cover)*eel presence + (1|site )

If you're using R, the above model will give you the individual interactions between eel presence and each of your other predictor variables.

I used step-wise linear regression (BMDP) in my research to investigate a binary outcome: nest predated yes/no. The input data included both continuous and discrete variables, both describing various habitat influences. One discrete variable was patch type: 3 size categories of woodlot, riparian, unbroken forest, etc. One continuous varaible was distance from edge. This statistical method worked well when modeling a complex mix of several discrete and continuous variables.

There is plenty you can do with the information. At the core is the relationship between variables. These need to be investigated, as I indicated in my earlier answer, just to allow you to interpret the model. It is important to understand how factors may confound others. Simple correlations could provide valuable insights. It would not be unusual for a meta-factor to evolve from such preliminary investigations (i.e., a compound value that describes a more than one measured variables).

I would investigate your models, as hinted by Riley and Virginia, especially the stepwise addition and removal of variables (the simplest I can think are “add1” and “drop1” in R) to assess relevance to the model.

You may also like to investigate the use of Bayesian techniques. Bayesian statistics will give you the freedom of not having to make the sorts of “deterministic” assumptions of distributions of the data you have collected.

Thank you all, these answers are very helpful and I will give some of your suggestions a try!