Why is my random effect down-weighing certain ORs? I'm running a mixed-effect logistic regression using data from 21 different sites. One of my key variables of interest is a six-level factor variable. I've included a random effect of site into the model, as well to account for the clustering of respondents in each site.
I noticed when I remove the random effect, certain ORs for the six-level factor become inflated. When I include the random effect, these same ORs shrink.
I'm wondering if someone can offer a simple explanation for this. Many thanks.
EDIT: Including partial model output below.


It all comes down to your sampling unit.  Using a random site effect changes what you are making inference on.  Without a random site effect you are making inference on a population of respondents who visit these sites.  With a random site effect you are no longer making inference on respondents, you are making inference on a broader population of sites from which your collection of sites were sampled.  The respondents at a site are considered repeated measurements on that site, and the endpoint and odds ratio pertains to sites.
While sites can certainly be heterogeneous, and outcomes on subjects who visit the same site may be correlated, I am not a fan of accounting for this using random effects.  Heterogeneity alone does not constitute a random variable, it is your sampling scheme that determines what is random.
If you have repeated measurements on each subject then you could include subject as a random effect since the subjects were sampled from a population of subjects, and it is this population of subjects that you want to make inference on.
