 <p>Overdispersion isn't really a useful concept in the normal model because it is already fitting a variance for the variability at the observation level. So the error message is telling you that you can't have a grouping factor at the observation level. In that sense, yes, you are trying to overfit your model.</p> <p>In a poisson (or other glm) model, however, it does make sense, because the variability at the observation level is fixed according to whatever the variance term in the glm is, so it does make sense to add an additional variance term to the model to account for any extra variability at the observation level. Hence <code>glmer</code> does not do the same check that <code>lmer</code> does.</p>