[R] Two-factorial Huynh-Feldt-Test

[Bela Bauer]

Peter Dalgaard wrote:

>>The models I use for the anovas are the following:
>>
>>aov(vecData ~ (facWithin + facBetweenROI + facBetweenCond)^2)
>>aov(vecData ~ facBetweenROI + facBetweenCond %in% facWithin +
>>Error(facBetweenROI %in% facWithin))
>>aov(vecData ~ facBetweenCond + facBetweenROI %in% facWithin +
>>Error(facBetweenCond %in% facWithin))
>>
>>SAS seems to calculate the Huynh-Feldt test for the first and the
>>second model. The SAS output is (for the second aov)
>>    
>>
>
>Would you happen to know what logic SAS uses to recognize cases  where
>the corrections apply?  I thought it only did it in the case of
>repeated measurements, as in
>
>proc glm;
>        model bmc2-bmc7=bmc1 grp / nouni;
>        repeated time ...
>  
>

Yes, of course, the entire SAS script is available to me:
PROC GLM;
MODEL col1 col3 col5 col7 col9 col11 col13 col15 col17 col19 col21 col23 
=/nouni;
repeated roi 6, ord 2/nom mean;
TITLE 'ABDERUS lat ACC 300-500';

This script wasn't written by me and unfortunately, I don't know 
anything about SAS scripting, which makes it hard for me to follow the 
script.

>http://www.psych.upenn.edu/~baron/rpsych.pdf
>
Thanks for that link, it seems like a quite useful paper!

Now, I've tried to follow it and apply the steps to my own problem, but 
I came up with a H-F and G-G value that is still slightly different from 
the one that SAS calculates (I'll attach my code at the end of this 
mail). With my old code (see my last email), I get 0.4682799. With the 
new code, I get 0.4494588 as G-G epsilon and 0.6063626 for the H-F 
correction. I think that this corresponds (or should do so, rather) to 
the SAS value of  0.6333.
Now, as you can see, the differences are small, but still there.
The main difference between my two versions of the code are that in the 
old code (based on that book), a covariance matrix is calculcated for 
every condition and then these are averaged for the covariance matrix 
that is used in the H-F formula. The new code, on the other hand, 
averages the data over all conditions and then calculcates the 
covariance matrix for that, which could probably explain the 
differences. There also seems to be a difference between the original 
H-F correction and the algorithm that SAS uses; this is mentioned in the 
PDF, but they don't explain it any further. I suspect that this 
difference could be exactly the difference between my two code versions, 
but I don't know for sure.

Now, with the difference between my value and the one from SAS being so 
small, I suspect that there's only a very slight difference between the 
algorithms. Do you have any hints what these could be, or how I could go 
about investigating it?

Thanks a lot for your help!

Bela Bauer

mtx <- NULL
for (iROI in 1:length(unique( roi )) ) {
  for (iSubj in 1:length(unique (subj )) ) {
    mtx <- c(mtx,
             mean(asa[subj==unique(subj)[iSubj] & roi==unique(roi)[iROI]],
                  aoa[subj==unique(subj)[iSubj] & roi==unique(roi)[iROI]]))
  }
}
mtx <- matrix(mtx,ncol=length(unique( roi )),byrow=F)

S <- var(mtx)

k <- 6
D <- (k^2 * (mean(S) - mean(diag(S)))^2)
N1 <- sum(S^2)
N2 <- 2 * k * sum(apply(S, 1, mean)^2)
N3 <- k^2 * mean(S)^2
epsiGG <- D / ((k - 1) * (N1 - N2 + N3))
epsiHF <- (10 * (k-1) * epsiGG - 2) / ((k-1) * ((10-1) - (k-1)*epsiGG))
print(epsiGG)
print(epsiHF)