R help - Mar 2009 - specifying repeated measures model in lmer

Dear Colleagues,
I have what Roger Kirk (Experimental Design: Procedures for the Behavioral
Sciences, 1968) refers to as a randomized block factorial design.  The anova
table would look like this:

                      df
A                     3
Subj/A          103 (error term for A)
B                   23
A*B                69
B*Subj/A     2369 (error term for B and A*B)

Subjects are nested within A and give a response for each B.  If y is the
dependent variable, is this the correct lmer specification for the above,
where ID is the variable name for Subj:

lmer(y ~ A + B + A*B + (A|ID))

Am I barking up the right tree?  I can also fit:

aov(y ~ A + B + A*B  + ID)
then I have to do some hand calculations to use ID as the error term for A.
 The residual (really B*ID) is the correct error term for B and A*B.

Thanks,

Larry

	[[alternative HTML version deleted]]

On Mon, Mar 23, 2009 at 2:35 PM, Lawrence Hanser <lhanser at gmail.com>
wrote:
> Dear Colleagues,
> I have what Roger Kirk (Experimental Design: Procedures for the Behavioral
> Sciences, 1968) refers to as a randomized block factorial design. ?The
anova
> table would look like this:
>
> ? ? ? ? ? ? ? ? ? ? ?df
> A ? ? ? ? ? ? ? ? ? ? 3
> Subj/A ? ? ? ? ?103 (error term for A)
> B ? ? ? ? ? ? ? ? ? 23
> A*B ? ? ? ? ? ? ? ?69
> B*Subj/A ? ? 2369 (error term for B and A*B)
> Subjects are nested within A and give a response for each B. ?If y is the
> dependent variable, is this the correct lmer specification for the above,
> where ID is the variable name for Subj:
> lmer(y ~ A + B + A*B + (A|ID))
If, as you say, subjects are nested within levels of A, then I don't
think you want a random effects term of the form (A | ID).  I
understand what you say to mean that each subject is exposed to one
and only one level of factor A so trying to fit a random effect for
the levels of A within each subject doesn't make sense.

Trying to understand model specifications for lmer according to the
degrees of freedom for each term is probably not the best approach.
> Am I barking up the right tree? ?I can also fit:
>
> aov(y ~ A + B + A*B ?+ ID)
> then I have to do some hand calculations to use ID as the error term for A.
> ?The residual (really B*ID) is the correct error term for B and A*B.
>
> Thanks,
>
> Larry
>
> ? ? ? ?[[alternative HTML version deleted]]
>
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