[R] Nested and repeated effects together?

Spencer Graves spencer.graves at pdf.com
Wed Jun 7 03:01:05 CEST 2006

	  1.  Am I correct that you are asking for a 4-factor interaction 
without a full set of 2- and 3-factor interactions?   SAS may let you do 
that, but I'm not certain what that means.  The standard treatment of a 
factor with k levels is to code it as (k-1) linearly independent 
"contrasts" that are also linearly independent of the constant term and 
then use ordinary least squares.  As long as standard rules of hierarchy 
are observed, the resulting analyses of variance are independent of the 
specific set of contrasts chosen.  However, when rules of hierarchy are 
broken, the answers may change with different choices for contrasts, and 
it's far from obvious what one is even testing.

	  2.  For these kinds of problems, I usually use "lme" in the "nlme" 
package.  The function 'aov' is older, and its answers may not be as 
good if the design is not balanced.  I've seen only one case where 'aov' 
produced an answer that I couldn't get out of "lme", and that was a 
saturated model in a perfectly balanced experiment where the noise was 
estimated from higher order interactions.  For your case, I would 
consider variations on the following:

	  lme(y~(Gr+Hemi+Region+Gender)^4, random=~1|ID)

	  This assumes that each level of ID is unique.  If not, I suggest you 
make it unique by pasting it together with Region and Gender.

	  The construct (Gr+Hemi+Region+Gender)^4 indicates all main effects 
and interactions up to the fourth order.  If you want, say, all main 
effects plus the three factor interaction Gr*Hemi*Region, I believe you 
could get that from "Gr*Hemi*Region+Gender":  the term 'Gr*Hemi*Region' 
will force all the main effects an subordinate two-factor interactions 
into the model.

	  If you don't already have Pinheiro and Bates (2000) Mixed-Effects 
Models in S and S-Plus (Springer), I suggest you get a copy.  Bates is 
one of the leading contributors in nonlinear estimation and mixed 
models.  The book contains numerous examples.  Also, R script files are 
available for virtually everything discussed in the book.  This will 
allow you to work the examples yourself one line at a time as you read 
the accompanying discussion in the book.  To access them, find where R 
is installed on your hard drive, then find "~\library\nlme\scripts".

	  Hope this helps,
	  Spencer Graves

Stephan Kolassa wrote:
> Dear R people,
> I am having a problem with modeling the following SAS code in R:
> Class ID Gr Hemi Region Gender
> Model Y = Gr Region Hemi Gender Gr*Hemi Gr*Region Hemi*Region 
> Gender*Region Gender*Hemi Gr*Hemi*Region Gender*Hemi*Region 
> Gr*Gender*Hemi*Region
> Random Intercept Region Hemi /Subject = ID (Gr Gender)
> I.e., ID is a random effect nested in Gr and Gender, leading to 
> ID-specific Intercept, Region and Hemi means. We have repeated 
> measurements within each ID (one measurement each for the different 
> combinations of Hemi and Region, i.e. 2 levels in Hemi: L vs. R; 4 
> levels in Region: F vs. C vs. T vs. PO).
> I have been trying things like
> aov(y~Gr+Region+Hemi+Gender+
>     Error(ID/(Gr+Gender))
> and do get results, but I am very unsure whether this implements the 
> right model. An Error term like
>     Error((1+Region+Hemi)/(ID_Vp/(Gender+Gr))), data=daten))
> in the above model looks intuitively better to me, but (1) again: I'm 
> unsure about this, (2) this crashes my R.
> Of course, I have been googling for all permutations of "Nested 
> effects", "repeated effects", "random effects" and digging through the 
> R-help archives, but I can't seem to locate a similar question having 
> been answered before.
> Thank you all for your time!
> Best regards,
> Stephan
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