Please pardon an extremely naive question. I see related earlier
posts, but no responses which answer my particular question. In
general, I'm very confused about how to do variance decomposition with
random and mixed effects. Pointers to good tutorials or texts would
be greatly appreciated.
To give a specific example, page 193 of V&R, 3d Edition, illustrates
using raov assuming pure random effects on a subset of coop:
> raov(Conc ~ Lab / Bat, data=coop, subset = Spc=="S1")
I realize ('understand' would be a bit too strong) that the same analysis,
resulting in identical sums of squares, degrees of freedom, and residuals
can be generated in R by doing
> op <- options(contrasts=c("contr.helmert", "contr.poly"))
> aov(Conc ~ Lab + Error(Lab / Bat), data=coop, subset = Spc=="S1")
However, as shown in V&R, raov also equated the expected and observed
mean squares, to solve for and display the variance components associated
with the random factors, \sigma_\epsilon^2, \sigma_B^2, and \sigma_L^2 in
a column labeled "Est. Var.". Given the analytical forms of the expected
mean squares for each stratum, I can obviously do this manually. But is
there way to get R to do it automatically, a la raov? This would be
particularly useful for mixed cases in which the analytical formulations
of the expected mean squares may not be immediately obvious to a novice.
Thanks in advance!
Regards,
-jh-
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