R help - Nov 2008 - aov help

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-

Rather than estimating the variance components via the
method-of-moments estimators, have a look at the 'nlme' and
'lme4'
packages, which provide likelihood-based tools for estimating random
and mixed models (and in the case of nlme, gls models too).
Advantages of the likelihood-based approaches include working with
unbalanced data, not producing negative variance estimates when the
MS_{error} is larger than the MS_{between groups}, and providing a
great deal of flexibility in structuring both the random effects and
error covariance matrices.

hth,

Kingsford Jones

On Thu, Nov 13, 2008 at 7:14 PM,  <john_heumann at agilent.com>
wrote:
> 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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