[R-sig-ME] Does the “non-independent" data structure defined in mixed models follow the “independency” defined by probability theory?

[David Duffy]

> In practice having correlation across groups seems to distort the
> distribution of the random effect causing some groups to be clustered. In
> extreme cases the random effect can become multimodal.

Further to this, there are nonparametric maximum likelihood (and Bayesian) mixed models that might be useful for this kind of situation -  the distribution of the random effects is modelled as a finite mixture (of eg normals) to be estimated. The npmlreg package implements Murray Aitkin's approach.