# dependence of error in clustered data

One commonly given reason to use mixed-effects model rather than a fixed-effects model is “the assumption of independence of errors does not hold in a multilevel structure, this will cause the standard errors of regression coefficients to be wrongly estimated”. Is this what is also referred to as “non-sphericity”?

But if groupID variables are included as fixed-effects, haven't we already solved for dependence of error within each observation of a particular group?

If the answer requires further context, consider the following case: I have publisher-campaign binomial data with dependent variable isClick (0/1) and independent variables publisherID, campaignID. 80% publisher-campaign combinations are not observed, 15% have 0-1000 data-points, and 5% have 1000-million data-points. The click rate is of order 10^-4. If I train a logistic regression model with publisherIDs and campaignIDs as fixed-effects, what error independence assumption is violated by the model?