Anova in 'car': "SSPE apparently deficient rank"

I have design with two repeated-measures factor, and no grouping  
factor. I can analyze the dataset successfully in other software,  
including my legacy DOS version BMDP, and R's 'aov' function. I would  
like to use 'Anova' in 'car' in order to obtain the sphericity tests  
and the H-F corrected p-values.   I do not believe the data are truly  
deficient in rank. I followed the methods for this kind of analysis  
outlined in Bennett's excellent handouts for his Psychology 710 course http://www.psychology.mcmaster.ca/bennett/psy710/lectures/maxwell_chp12.pdf 
    I am trying to convert my own similar course to R for my students  
for next fall.  I have been successful at analyzing a segment of the  
data as a 2-way repeated measures design.

Here is my code:

 > your.data=read.table(pipe("pbpaste"),header=T)
 > your.data

   partic A1B1 A1B2 A1B3 A1B4 A2B1 A2B2 A2B3 A2B4 A3B1 A3B2 A3B3 A3B4
1     p1    1    1    2    3    1    2    4    7    1    3    7   10
2     p2    2    2    3    3    2    2    5    6    2    4    6    9
3     p3    1    2    2    3    2    3    2    6    1    4    7    9
4     p4    1    1    2    2    1    2    3    6    2    3    8   10
5     p5    2    2    3    3    2    3    5    7    2    3    7    9

 > attach(your.data)
 > multmodel=lm(cbind(A1B1, A1B2, A1B3, A1B4, A2B1, A2B2, A2B3, A2B4,  

A3B1, A3B2, A3B3, A3B4)~1)

 > poke.idata=read.table(pipe("pbpaste"),header=T)
 > poke.idata

    Afac Bfac
1    A1   B1
2    A1   B2
3    A1   B3
4    A1   B4
5    A2   B1
6    A2   B2
7    A2   B3
8    A2   B4
9    A3   B1
10   A3   B2
11   A3   B3
12   A3   B4

 > attach(poke.idata)
 >  

pokeAnova 
=Anova(multmodel,idata=poke.idata,idesign=~Afac*Bfac,type="III")
Error in linear.hypothesis.mlm(mod, hyp.matrix, SSPE = SSPE, idata =  
idata,  :
   The error SSP matrix is apparently of deficient rank = 4 < 6

Thanks for any help or advice. And thanks for the 'car' package, which  
is a great asset to my course. I'm just stuck on this one example.

anova(multmodel, M = ~ Afac*Bfac, X = ~Afac + Bfac, idata=poke.idata)

anova(multmodel, idata=poke.idata, X=~Afac+Bfac)

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]

Behalf Of Peter Dalgaard
Sent: January-03-10 5:32 AM
To: Colleen F. Moore
Cc: r-help at r-project.org
Subject: Re: [R] Anova in 'car': "SSPE apparently deficient rank"

Colleen F. Moore wrote:

I have design with two repeated-measures factor, and no grouping
factor. I can analyze the dataset successfully in other software,
including my legacy DOS version BMDP, and R's 'aov' function. I would
like to use 'Anova' in 'car' in order to obtain the sphericity tests
and the H-F corrected p-values.   I do not believe the data are truly
deficient in rank. I followed the methods for this kind of analysis
outlined in Bennett's excellent handouts for his Psychology 710 course

    I am trying to convert my own similar course to R for my students
for next fall.  I have been successful at analyzing a segment of the
data as a 2-way repeated measures design.

Here is my code:

 > your.data=read.table(pipe("pbpaste"),header=T)
 > your.data

   partic A1B1 A1B2 A1B3 A1B4 A2B1 A2B2 A2B3 A2B4 A3B1 A3B2 A3B3 A3B4
1     p1    1    1    2    3    1    2    4    7    1    3    7   10
2     p2    2    2    3    3    2    2    5    6    2    4    6    9
3     p3    1    2    2    3    2    3    2    6    1    4    7    9
4     p4    1    1    2    2    1    2    3    6    2    3    8   10
5     p5    2    2    3    3    2    3    5    7    2    3    7    9

 > attach(your.data)
 > multmodel=lm(cbind(A1B1, A1B2, A1B3, A1B4, A2B1, A2B2, A2B3, A2B4,

A3B1, A3B2, A3B3, A3B4)~1)

 > poke.idata=read.table(pipe("pbpaste"),header=T)
 > poke.idata

    Afac Bfac
1    A1   B1
2    A1   B2
3    A1   B3
4    A1   B4
5    A2   B1
6    A2   B2
7    A2   B3
8    A2   B4
9    A3   B1
10   A3   B2
11   A3   B3
12   A3   B4

 > attach(poke.idata)
 >

pokeAnova
=Anova(multmodel,idata=poke.idata,idesign=~Afac*Bfac,type="III")
Error in linear.hypothesis.mlm(mod, hyp.matrix, SSPE = SSPE, idata =
idata,  :
   The error SSP matrix is apparently of deficient rank = 4 < 6

Thanks for any help or advice. And thanks for the 'car' package, which
is a great asset to my course. I'm just stuck on this one example.

Hmm, this does seem to work with regular anova.mlm:

 > anova(multmodel, idata=poke.idata, X=~Afac+Bfac,test="Sph")

Analysis of Variance Table


Contrasts orthogonal to
~Afac + Bfac

Greenhouse-Geisser epsilon: 0.2880
Huynh-Feldt epsilon:        0.4871

             Df     F num Df den Df    Pr(>F)     G-G Pr     H-F Pr
(Intercept)  1 36.67      6     24 6.164e-11 2.5249e-04 3.3530e-06
Residuals    4


As far as I recall, the epsilon corrections do not have a formal
requirement of a nonsingular SSD of the relevant contrast. Not sure
about the accuracy of the F probabilities in such cases, though.

--
    O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
   c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
  (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907

Dear Peter and Colleen,

I think that Peter realizes this, but what Anova() does in this case is
equivalent to the MANOVA 

anova(multmodel, M = ~ Afac*Bfac, X = ~Afac + Bfac, idata=poke.idata)

Error in anova.mlm(multmodel, M = ~Afac * Bfac, X = ~Afac + Bfac, idata =
poke.idata) : 
  residuals have rank 4 < 6

which in turn is equivalent to

anova(multmodel, idata=poke.idata, X=~Afac+Bfac)

Error in anova.mlm(multmodel, idata = poke.idata, X = ~Afac + Bfac) : 
  residuals have rank 4 < 6

both of which fail for the same reason that Anova() does: Because the
within-subject interaction has 6 df and there are just 5 subjects, the
residual SSP matrix, say SSPE, is of rank 4. The hypothesis of no
interaction has (3 - 1)*(4 - 1) = 6 df, and thus the response-transformation
matrix for this hypothesis, say P, has 6 columns. The error SSP matrix for
the interaction, t(P) %*% SSPE %*% P, is also therefore of rank 4 < 6.

I believe that under these circumstances, it's possible to do the univariate
F-tests but not the multivariate repeated-measures ANOVA. Since Anova()
always computes the multivariate tests, however, I don't see a way around
the problem without entirely changing how Anova() gets the univariate tests.

What's unclear to me is whether the full data set really has just 5
subjects.