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