 Then it can be shown that

and

These "expected mean squares" can be used as the basis for estimation of the "variance components" σ2 and τ2.In general, random effects are efficient, and should be used (over fixed effects) if the assumptions underlying them are believed to be satisfied.For random effects to work in the school example it is necessary that the school-specific effects be uncorrelated to the other covariates of the model.