I'll try and explain where I am getting stuck.
I wish to model delay to treatment. I observe patients nested in hospitals. I have a mixture of patient and hospital level covariates. I suspect that there are unmeasured covariates that induce correlation between patients being treated in the same hospital. This would violate the basic assumptions about independent and identically distributed variables, and to get round this I add a random or fixed effect to the model.
Without this, then the unmeasured covariates will be operating through the measured hospital level covariates and induce bias. If estimate a fixed effects model then I would have an individual mean 'delay' for each hospital, but am I correct in thinking that these would be 'collinear' with any measured site level variable, and therefore not identifiable. Does this also apply to a random effects model? And if it does then is the aforementioned bias completely partioned to the 'random effect' or is some still operating through the measured site level covariates?