I have records of $multiple$ visits from many different patients in several different clinics (i.e. visits nested within patients nested within clinic) and plan to perform an analysis that takes into account the clustered nature of the data (since patients within a clinic are correlated and individual visits within a clinic will be correlated). Patient effects are of no direct interest in the analysis, so I understand that they can be modeled using a random effect (e.g. specifying a random effect on the patient ID). However, I'm confused about the clinic effects which I $am$ interested in. If I include clinics in my model as a fixed effect (so I can say things like, on average we expect clinic A to have an increase of $x$ in the dependent variable for a one unit increase in the independent variable, holding all other variables constant), will the inclusion of this fixed effect address the problem on clustered data in the clinics? I've read that I should include random effects to address the clustering, but if I already have $clinic$ in the model as a fixed effects variable, doesn't this take into account the clustering and non-independence of the patients across clinics?
After some additional reading, I have discovered that as long as I've included the clinic as a fixed effect, it does take the clustering into account. Nearly everything I read did not make this point clear.
In addition to fitting a mixed effects model, I also modeled this data using generalize estimating equations (GEE) in proc genmod, obtaining a marginal model. The parameter estimates and standard errors were nearly identical using both approaches.