[R] How do I compute interactions with anova.mlm ?

[Peter Dalgaard]

Schadwinkel, Stefan skrev:
> Hi,
>
> I wish to compute multivariate test statistics for a within-subjects repeated measures design with anova.mlm. 
>
> This works great if I only have two factors, but I don't know how to compute interactions with more than two factors. 
> I suspect, I have to create a new "grouping" factor and then test with this factor to get these interactions (as it is hinted in R News 2007/2), 
> but I don't really know how to use this approach. 
>
> Here is my current code:
>
> Two Factors: fac1, fac2
>
> mlmfit <- lm(mydata~1)
> mlmfit0 <- update(mlmfit, ~0)
>
> % test fac1, works, produces same output as SAS
> anova(mlmfit, mlmfit0, M = ~ fac1 + fac2, X = ~ fac2, idata = idata, test = "Wilks")
>
> % test fac1*fac2 interaction, also works, also the same output as SAS
> anova(mlmfit, mlmfit0, X = ~ fac1 + fac2, idata = idata, test = "Wilks")
>
>
>
> Three Factors: fac1, fac2, fac3 
>
> mlmfit <- lm(mydata~1)
> mlmfit0 <- update(mlmfit, ~0)
>
> % test fac1, works, same as SAS
> anova(mlmfit, mlmfit0, M = ~ fac1 + fac2 + fac3, X = ~ fac2 + fac3, idata = idata, test = "Wilks")
>
>
>
> Now, I try to compute the interactions the same way, but this doesn't work:
>
> % fac1*fac2
> anova(mlmfit, mlmfit0, M = ~ fac1 + fac2 + fac3, X = ~ fac3, idata = idata, test = "Wilks") 
>
> % fac1*fac2*fac3
> anova(mlmfit, mlmfit0, X = ~ fac1 + fac2 + fac3, idata = idata, test = "Wilks")
>
>
> Both of these above differ quite much from the SAS output and I suspect, my understanding of X and M is somewhat flawed. 
>
> I would be very happy, if someone could tell me how to compute the two interactions above and an interaction of N factors in general.
>
>   
You need to ensure that the difference between the X and M models is the
relevant interaction, so something like

M=~fac1*fac2*fac3
X=~fac1*fac2*fac3 - fac1:fac2:fac3

should test for fac1:fac2:fac3

If the within-subject design is fac1*fac2*fac3 with one observation per
cell (NB!), then you can omit M. X can also be written as
~fac1*fac2+fac2*fac3+fac1*fac3 or ~(fac1+fac2+fac3)^2.

For the next step, use, e.g.,

M=~fac1*fac2+fac2*fac3+fac1*fac3
X=~fac2*fac3+fac1*fac3

to test significance of fac1:fac2 (notice that the main effects are
still in X becaus of the meaning of the "*" operator in R).


> I would also be interested in computing linear contrasts using the T matrix and anova.mlm.
>
> Thank you very much,
>
> Stefan 
>
>  
>
> --
> Stefan Schadwinkel, Dipl.-Inf.
> Neurologische Klinik
> Sektion Biomagnetismus
> Universität Heidelberg
> Im Neuenheimer Feld 400
> 69120 Heidelberg
>
> Telefon:  06221 - 56 5196
> Email:    stefan.schadwinkel at med.uni-heidelberg.de 
>
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>   


-- 
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
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