[R] Anova in 'car': "SSPE apparently deficient rank"

[Peter Dalgaard]

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 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.
> 

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             Øster 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