contrast matrix for aov
Prof Brian Ripley <ripley at stats.ox.ac.uk> writes:
On Wed, 9 Mar 2005, Darren Weber wrote:
How do we specify a contrast interaction matrix for an ANOVA model? We have a two-factor, repeated measures design, with
Where does `repeated measures' come into this? You appear to have repeated a 2x2 experiment in each of 8 blocks (subjects). Such a design is usually analysed with fixed effects. (Perhaps you averaged over repeats in the first few lines of your code?)
Actually, that's not "usual" in SAS (and not SPSS either, I believe)
in things like
proc glm;
model y1-y4= ;
repeated row 2 col 2;
[Not that SAS/SPSS is the Gospel, but they do tend to set the
terminology in these matters.]
There you'd get the analysis split up as analyses of three contrasts
corresponding to the main effects and interaction, c(-1,-1,1,1),
c(-1,1,-1,1), and c(-1,1,1,-1) in the 2x2 case (up to scale and sign).
In the 2x2 case, this corresponds exactly to the 4-stratum model
row*col + Error(block/(row*col)).
(It is interesting to note that it is still not the optimal analysis
for arbitrary covariance patterns because dependence between contrasts
is not utilized - it is basically assumed to be absent.)
With more than two levels, you get the additional complications of
sphericity testing and GG/HF epsilons and all that.
O__ ---- Peter Dalgaard Blegdamsvej 3 c/ /'_ --- Dept. of Biostatistics 2200 Cph. N (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907