Background
I have avian malaria infection data for 723 adult birds of 22 species. I am interested in explaining variation in prevalence at the species level, and have a number of species-level covariates. Initially, I had set this up as a multilevel logistic regression with a Bernoulli response and a random species intercept (723 observations among 22 groups):
y ~ longevity + nest + stratum + group_size + movement + centrality +
(1|species)
(brms syntax)
My thought was that this hierarchical structure was necessary to account for pseudoreplication/non-independence in the samples within species. However, as all of my predictors are measured at the species level, and as species are the target of inference, I'm afraid that the above model might limit my ability to identify species-level effects. I began to consider that a binomial response might be more appropriate (22 observations, 723 total trials):
y|trials(n) ~ longevity + nest + stratum + group_size + movement +
centrality
In that case, it didn't seem as though a random intercept was useful since there was only one observation (albeit with multiple Bernoulli trials) per group. I found a few threads that address similar issues ([1], [2], [3]), but it seems that in those instances only a subset of groups have a single observation (most have multiple observations per group). In my case, each group has only a single observation. This comment by Ben Bolker does seem to suggest that I might be good to go ahead without the random effect.
One concern I have is that the two models differ substantially in where they assign error; in the multilevel Bernoulli model, all 95% credible intervals for the fixed/population effects overlap 0 and all the variation in the response seems to be accounted for by the random/group intercept. That makes sense, as I know that there is considerable variation in infection rates across species. But because I'm trying to explain that species-level variation, I'm tempted to remove the random intercept. If I do that, as by using a non-hierarchical binomial model, then the precision around some of the slope coefficients improves.
Question
Considering that species are the target of inference (and the covariates are measured at the species level) is it a defensible approach to omit the random intercept in this case? On one hand, I'm concerned about my ability to identify species-level effects; on the other hand, I'm worried about presenting overly confident coefficient estimates.
