R help - Nov 2007 - Why can repeated measures anova with within & between subjects design not be done if group sizes are unbalanced?

Dear R people:

I wish to switch from SPSS to R, but there is one particular type of
ANOVA design that cannot be done in R.  Or more likely, it can be
done, but it is nowhere documented.

The problem is typical for psychologists:
You have a repeated measures design with different groups of subjects.
 Now, this can be done with the aov command, but the number of
subjects in both groups must be equal (i.e., balanced design).  SPSS
allows for unbalanced designs as well.

If you are still with me, let me just give you an example of what R
can and cannot do so far.  Imagine I have a 2x2 within subjects design
and I have 2 groups (e.g., group healthy and patients, which is stored
in MyGroup).  And imagine I measure reaction time RT in four
conditions, say, in a color condition (red vs green) and in a shape
condition (square vs circle).

Now, in R you would have something like, as anybody who does balanced
repeated measures anova's might know:

aov( RT ~ color * shape * MyGroup + Error( Subjects/( color*shape) )

In spss you would have something like this (of course with the data
organized slightly differently :

GLM
x1 x2 x3 x4 BY MyGroup
 /WSFACTOR = color 2 Polynomial shape 2 Polynomial
 /METHOD = SSTYPE(3)
 /CRITERIA = ALPHA(.05)
 /WSDESIGN = color shape color*shape
 /DESIGN = VAR00001 .

Ok, the question is.  If the group sizes are different (say 10 people
in one group and 12 people in the other group) R is going to give the
wrong answer.  Of course that is not R's fault.

BUT MY QUESTION IS: HOW TO GET THE UNBALANCED REPEATED MEASURES ANOVA RIGHT?

Thanks for the answer!

'nowhere documented' ??

As the posting guide suggests, you could perform a search using
> RSiteSearch("repeated measures", restric="functions")

say.

That generates an inventory of functions that pertain to repeated 
measures designs.

And once you have browsed through that you might focus on

> library(nlme) # load a library with nifty mixed model stuff
> ?lme          # find out how to fit linear mixed models 
> example(lme)  # run some examples
If that is not enough to get you started, the book

J. C. Pinheiro and D. M. Bates (2000), Mixed-Effects Models in S and 
S-Plus., Springer, ISBN 0-387-98957-0

documents all the stops and whistles of the nlme library.

Chuck


On Sun, 4 Nov 2007, Gilbert G wrote:
> Dear R people:
>
> I wish to switch from SPSS to R, but there is one particular type of
> ANOVA design that cannot be done in R.  Or more likely, it can be
> done, but it is nowhere documented.
>
> The problem is typical for psychologists:
> You have a repeated measures design with different groups of subjects.
> Now, this can be done with the aov command, but the number of
> subjects in both groups must be equal (i.e., balanced design).  SPSS
> allows for unbalanced designs as well.
>
> If you are still with me, let me just give you an example of what R
> can and cannot do so far.  Imagine I have a 2x2 within subjects design
> and I have 2 groups (e.g., group healthy and patients, which is stored
> in MyGroup).  And imagine I measure reaction time RT in four
> conditions, say, in a color condition (red vs green) and in a shape
> condition (square vs circle).
>
> Now, in R you would have something like, as anybody who does balanced
> repeated measures anova's might know:
>
> aov( RT ~ color * shape * MyGroup + Error( Subjects/( color*shape) )
>
> In spss you would have something like this (of course with the data
> organized slightly differently :
>
> GLM
> x1 x2 x3 x4 BY MyGroup
> /WSFACTOR = color 2 Polynomial shape 2 Polynomial
> /METHOD = SSTYPE(3)
> /CRITERIA = ALPHA(.05)
> /WSDESIGN = color shape color*shape
> /DESIGN = VAR00001 .
>
> Ok, the question is.  If the group sizes are different (say 10 people
> in one group and 12 people in the other group) R is going to give the
> wrong answer.  Of course that is not R's fault.
>
> BUT MY QUESTION IS: HOW TO GET THE UNBALANCED REPEATED MEASURES ANOVA
RIGHT?
>
> Thanks for the answer!
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901

On 11/04/07 16:34, Gilbert G wrote:
> Dear R people:
> 
> I wish to switch from SPSS to R, but there is one particular type of
> ANOVA design that cannot be done in R.  Or more likely, it can be
> done, but it is nowhere documented.
> 
> The problem is typical for psychologists:
> You have a repeated measures design with different groups of subjects.
>  Now, this can be done with the aov command, but the number of
> subjects in both groups must be equal (i.e., balanced design).  SPSS
> allows for unbalanced designs as well.
> 
> If you are still with me, let me just give you an example of what R
> can and cannot do so far.  Imagine I have a 2x2 within subjects design
> and I have 2 groups (e.g., group healthy and patients, which is stored
> in MyGroup).  And imagine I measure reaction time RT in four
> conditions, say, in a color condition (red vs green) and in a shape
> condition (square vs circle).
At the risk of getting in trouble, let me suggest another approach.
Compute the relevant terms for each subject, then do a t test
comparing your two groups.  The t test does not assume equal sized
groups.  Yuelin Li, in our "Notes on the use of R ..." shows how to
use a t test to check a design very similar to what you suggest:
http://www.psych.upenn.edu/~baron/rpsych/rpsych.html (section 6.10, I
think, perhaps elsewhere too).

You can do this either with a loop or with the lmList() function in
the lme4 package (which is not discussed yet in our "Notes...").

For example, with a loop, you would compute
CS[i] <- RTredsquare[i] - RTbluesquare[i] - RTredcircle[i] +
 RTbluecircle[i]
and then do t.test(CS ~ Group) to see if your two groups differ in the
interaction effect.  It is easier with lmList.  You don't need the
loop.

I do think that nlme is going to replace a lot of standard approaches
in psychology.  (I am almost to the point of understanding it.)  But I
don't think it is necessary for the kind of design you describe.

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

Charles C. Berry <cberry <at> tajo.ucsd.edu> writes:
> As the posting guide suggests, you could perform a search using
> 
> > RSiteSearch("repeated measures",
restric="functions")
> 
> say.
> 
> That generates an inventory of functions that pertain to repeated 
> measures designs.
The problem I noted in practice with researcher is that  nlme is not among those
associated with "repeated measurements", with the exception of the
citation of

Davidian, M. and Giltinan, D.M. (1995) "Nonlinear Mixed Effects Models for
Repeated Measurement Data", Chapman and Hall.

somewhere in the nlme documentation. And as far as I remember, the word
"repeated measurements" cannot be found in text of Pinheiro &
Bates; which
otherwise is the most worn-out book on my shelf.

I may be slightly off with both statements, but the association (mixed model)
<=> (repeated measurements) is not at all obvious. 

For the record: forget repeated measurements. It definitively pays to be fluent
in mixed models. Once you have your data in the "long" form, most work
is done.
And if lme tells you it cannot solve your problem, it has damned good reasons
for it.

Dieter

Hope I am not too late joining this thread.  I believe the difference
between R and SPSS is because SPSS adjusts the Type III SS by the
harmonic mean of the unbalanced cell sizes.  This calculation is
discussed in Maxwell and Delaney (1990, pp. 271-297).

In short, the best explanation I can offer (details see below) is that
SPSS and R produces the same output if you tell SPSS to do SSTYPE(1)
or SSTYPE(2) instead of the default SSTYPE(3).  As discussed in
Maxwell and Delaney, the calculations of SS1 and SS2 do not involve
the harmonic mean.  Maxwell and Delaney discussed the pros and cons of
each type of Sums of Squares.  Apparently SPSS thinks that the
harmonic mean SS3 is the *right* analysis.  Like people who responded
before me, I'd also suggest the use of lme() in unbalanced designs.

Yuelin.

---- details -------
I used the Hays.df data:
http://www.psych.upenn.edu/~baron/rpsych/rpsych.html
And I added one between-subject variable:

Hays.df$grpuneven <- c(1,1,1,1,1,1,1,1,2,2,2,2) # n=8 in grp 1; 4 in grp 2

I ran aov(rt ~ grpuneven*color*shape + Error(subj/shape+color), data=Hays.df) 
which gives you the same output as SSTYPE(1) and
SSTYPE(2) using this syntax in SPSS.

GLM
  Sh1Col1 Sh2Col1 Sh1Col2 Sh2Col2 BY grpuneven
  /WSFACTOR = color 2 Polynomial shape 2 Polynomial
  /METHOD = SSTYPE(2)
  /CRITERIA = ALPHA(.05)
  /WSDESIGN = color shape color*shape
  /DESIGN = grpuneven .






-- Gilbert G wrote --|Sun (Nov/04/2007)[04:34]|--:

   Dear R people:
   
   I wish to switch from SPSS to R, but there is one particular type of
   ANOVA design that cannot be done in R.  Or more likely, it can be
   done, but it is nowhere documented.

   [... snip ...]
   
   Now, in R you would have something like, as anybody who does balanced
   repeated measures anova's might know:
   
   aov( RT ~ color * shape * MyGroup + Error( Subjects/( color*shape) )
   
   In spss you would have something like this (of course with the data
   organized slightly differently :
   
   GLM
   x1 x2 x3 x4 BY MyGroup
    /WSFACTOR = color 2 Polynomial shape 2 Polynomial
    /METHOD = SSTYPE(3)
    /CRITERIA = ALPHA(.05)
    /WSDESIGN = color shape color*shape
    /DESIGN = VAR00001 .
   
   Ok, the question is.  If the group sizes are different (say 10 people
   in one group and 12 people in the other group) R is going to give the
   wrong answer.  Of course that is not R's fault.
   
   BUT MY QUESTION IS: HOW TO GET THE UNBALANCED REPEATED MEASURES ANOVA RIGHT?
   

 
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