R help - Jul 2004 - doubly multivariate analysis in R

20 subjects were measured in 5 conditions (thus repeated measures) and
for each subject in each condition there are 4 response measures (thus
multivariate as it is a combined score that needs to be compared across
the conditions).
 
So, using a multivariate approach to repeated measures this is a doubly
multivariate analysis.
 
I would appreciate any suggestions as to the best way to do such a
doubly multivariate analysis in R (I have done it in SPSS and SAS but
would like to see what it takes to do the same in R).
 
Thank you in advance for any help.
 
Ludo

On 07/04/04 16:06, Ludo Max wrote:
>
>20 subjects were measured in 5 conditions (thus repeated measures) and
>for each subject in each condition there are 4 response measures (thus
>multivariate as it is a combined score that needs to be compared across
>the conditions).
>
>So, using a multivariate approach to repeated measures this is a doubly
>multivariate analysis.
>
>I would appreciate any suggestions as to the best way to do such a
>doubly multivariate analysis in R (I have done it in SPSS and SAS but
>would like to see what it takes to do the same in R).
This is the format of most of what I do.  You might find it
useful to look at our "Notes on R for psychology...", reachable
through the R page in my signature.

But the real answer depends heavily on what you want to find out.
I use the same basic format for most of what I do - experiments
on the Web using Javascript to generate items and questions - but
the data analysis varies greatly from study to study, so the
format does not determine the analysis.

I do put all my analysis scripts and experiments in my web page
under "Public archives...."  If you go back and forth between the
experiments and the R scripts, you can even get some idea of the
relation between the two, although probably not much.  (Also,
some of these are pretty old and I've found much better ways to
do things in both R and JavaScript.)  At least you might find
these helpful for getting started.

Now, I usually use an array with the dimensions: subjects,
conditions, and questions.  A lot of what I do involves
calculating within-subject correlations and regressions.  I used
to do that entirely with loops, but lately I've found that R's
mapply() function can do some of it, as well as apply().

Jon
-- 
Jonathan Baron, Professor of Psychology, University of Pennsylvania
Home page:            http://www.sas.upenn.edu/~baron
R search page:        http://finzi.psych.upenn.edu/

If your subjects share similar settings (and therefore may not be ind.), you may
consider performing this analysis in nlme. However, imagine for a moment that
you allow for random intercepts and slopes for each individual. You would be
required to fit a model with 8 fixed effects (a mean and slope for each
response), an 8x8 covariance matrix along with 4 residual variances. Things are
getting rather large.
 
A colleague and I have a paper currently under review for an educational
audience showing how to fit a host of lme models, including a
doubly-multivariate model. We show how to structure the data matrix, model a
covariance structure, and estimate the individual variance terms. I would be
happy to share the code we use and show the structure of the data matrix if you
like. We devote a lot of space to this model, so answering your question here is
difficult.
 
However, structuring the data matrix is rather simple, with a small trick. To
estimate, one needs to stack the individual response variables into a single
column with a dummy code used to flag the individual response variables. We then
create a separate variable for time for each response variable to estimate the
linear rate of change for each response individually (although this need not be
the case). In the modeling function, you then need to remove the overall
intercept from the model (-1) such that the main effect for each response are
interpreted directly as subject-specific means, and then use a few small tricks
to estimate to residual variances through use of the weights() function.
 
If interested, you might check out a paper we published in the R Newsletter in
Dec. showing how to fit longitudinal models in lme with a single response
variable and then go from there. Of course, Pinhiero and Bates is the
authoritative source on models in lme and I would start there. The link below
will take you to a software review page and has a small paper on R showing to
fit a model with 2 response variable, but are not repeated measures.
 
http://multilevel.ioe.ac.uk/softrev/
 
Harold
 
 

	-----Original Message----- 
	From: r-help-bounces@stat.math.ethz.ch on behalf of Ludo Max 
	Sent: Sun 7/4/2004 4:06 PM 
	To: r-help@stat.math.ethz.ch 
	Cc: 
	Subject: [R] doubly multivariate analysis in R
	
	


	20 subjects were measured in 5 conditions (thus repeated measures) and
	for each subject in each condition there are 4 response measures (thus
	multivariate as it is a combined score that needs to be compared across
	the conditions).
	
	So, using a multivariate approach to repeated measures this is a doubly
	multivariate analysis.
	
	I would appreciate any suggestions as to the best way to do such a
	doubly multivariate analysis in R (I have done it in SPSS and SAS but
	would like to see what it takes to do the same in R).
	
	Thank you in advance for any help.
	
	Ludo
	
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