[R-sig-ME] literature suggestions regarding residuals in mixed models

[Juliet Hannah]

Hi List,

I have a general question regarding mixed models.

Consider ordinary regression.

If we have a model y ~ x1 + x2. We can fit this in stages
by regressing y on x1, and x1 on x2, and then regressing
the first residuals on the second.

And if x1 is unrelated to other covariates, we can approximate
the regression by removing the effects of all covariates, and then
regressing the residuals on x1.

My question is, I would like to understand what I
can remove in the mixed model setting (as an approximation) --
any fixed or random effects?

Does anyone know of any specific references? I haven't had any
luck in my search.

Thanks for your time.

Regards,

Juliet