R help - Oct 2006 - Once again: aov vs. lme/lmer

First of all, I apologize for asking a question that has appeared
recurrently in this mailing list.  However, I have googled for it, have
looked at the mailing list archives, and also looked at Pinheiro & Bates
book
(although not very thoroughly, I must confess), to no avail.

Here is the question: I am trying to obtain with lme or lmer the same exact
numerical results (p-values) that I obtain with aov.  Consider the following
data:

  d <- data.frame (a = factor (rep (c (1, 2), c(10, 10))),
                   b = factor (rep (rep (c (1, 2), c(5, 5)),2)),
                   s = factor (rep (1 : 5, 4)),
                   v = rnorm (20))

Let us say that this comes from a repeated measures experiments where all
five subjects (factor s) were tested in all combinations of the two fixed
factors a and b.

With aov, for a model were s, s:a, s:b and s:a:b are random, and a*b
are fixed terms, I would use:

  aov (v ~ a*b + Error (s / (a*b)), data = d)

Is there a way to get the same results using lme or lmer? How should I write
my "random" argument in lme or the "(...|...)" terms in
lmer?  Please notice
that I am not interested in philosophical discussions about whether I am
trying to do wrong things.  I would only like to know whether a given R
function could be used in place of another R function.

Thanks in advance for your help,

-- 
Rafael Laboissiere

I believe the short answer to your question is no:  I don't 
believe it's possible to get the exact same answer from 'lme' or
'lmer'
as from 'aov' for your example. 

      Without a philosophical discussion, I can't tell you why.  I 
almost never use 'aov', because it tests everything using an 'F'
test,
the particular 'F' is really relevant to what we want to know or not.  
With 'lme' and 'lmer', I have more confidence that I know what
I'm doing
and that I'm testing the hypotheses that are likely to be of greatest 
interest for my problem.  The 'aov' algorithm was wonderful half a 
century ago, and was still the best procedure easily available to most 
people a quarter century ago.  We have better tools available today.  In 
case someone reading this reply wants more information on this, I 
suggest they start with the discussion of 'Conservative ANOVA tables in 
lmer' in the R Wiki. 

      Hope this helps. 
      Spencer Graves

Rafael Laboissiere wrote:
> First of all, I apologize for asking a question that has appeared
> recurrently in this mailing list.  However, I have googled for it, have
> looked at the mailing list archives, and also looked at Pinheiro &
Bates book
> (although not very thoroughly, I must confess), to no avail.
>
> Here is the question: I am trying to obtain with lme or lmer the same exact
> numerical results (p-values) that I obtain with aov.  Consider the
following
> data:
>
>   d <- data.frame (a = factor (rep (c (1, 2), c(10, 10))),
>                    b = factor (rep (rep (c (1, 2), c(5, 5)),2)),
>                    s = factor (rep (1 : 5, 4)),
>                    v = rnorm (20))
>
> Let us say that this comes from a repeated measures experiments where all
> five subjects (factor s) were tested in all combinations of the two fixed
> factors a and b.
>
> With aov, for a model were s, s:a, s:b and s:a:b are random, and a*b
> are fixed terms, I would use:
>
>   aov (v ~ a*b + Error (s / (a*b)), data = d)
>
> Is there a way to get the same results using lme or lmer? How should I
write
> my "random" argument in lme or the "(...|...)" terms in
lmer?  Please notice
> that I am not interested in philosophical discussions about whether I am
> trying to do wrong things.  I would only like to know whether a given R
> function could be used in place of another R function.
>
> Thanks in advance for your help,
>
>