I have read many times that random effects (BLUPs/conditional modes for, say, subjects) are not parameters of a linear mixed effects model but instead can be derived from the estimated variance/covariance parameters. E.g. [Reinhold Kliegl et al. (2011)][1] state: > Random effects are subjects’ deviations from the grand mean RT and > subjects’ deviations from the fixed-effect parameters. They are > assumed to be independently and normally distributed with a mean of 0. > It is important to recognize that these random effects are *not* > parameters of the LMM – only their variances and covariances are. > [...] LMM parameters in combination with subjects’ data can be used to > generate “predictions” (conditional modes) of random effects for each > subject. Can someone give an intuitive explanation how the (co)variance parameters of the random effects can be estimated without actually using/estimating the random effects? [1]: https://www.frontiersin.org/articles/10.3389/fpsyg.2010.00238/full