Dear list members,

I have a dataset with crossed random effects. I am interested in describing
how variation in the response variable is attributable to each RE.

The only worked examples I have found involve nested, rather than crossed,
REs. My own dataset is large and unbalanced, but the issue can be
illustrated easily using the Assay dataset from MEMSS.

library('MEMSS')
data(Assay)
(rmod <- lmer(logDens~1 + (1|Block) + (1|sample) + (1|dilut), Assay))
vc<-VarCorr(rmod)
vars <- c(unlist(vc), attr(vc,'sc')^2)
100*vars/sum(vars)

I conclude that most variation (91%) is attributable to the different levels
of dilution (dilut), most of the rest (6%) to the different wells (sample),
hardly any at all (0.2%) to the different replicates (Block)and the
remainder (3%) to residual error.

I would be greateful for a second opinion on whether this approach is
appropriate.

Best wishes, Nick

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