# Repeated measures ANOVA in R for non-orthogonal design

I have data from a two-factor within-subjects experiment design where the conditions are not orthogonal. Factor one (Location) has three levels; factor two (Stimulus) has three levels, one of which is "no stimulus".

When multiplying these factors I get nine conditions, three of which are equivalent. All three Location x "no stimulus" conditions are equivalent because of lack of stimulus. As a result I only have observations from 7 conditions (just a single Location x "no stimulus" condition, intended to be used as a control condition). I just chose an arbitrary level of Location for that condition for the sake of coding the data.

My question is - how can I analyse my data in R using ANOVA?

I've tried building a model with the lme() function in the nlme package (following a textbook example for orthogonal designs), but I get an error when trying to build the model (presumably because of missing conditions?):

> model <- lme(Y ~ Location * Design, data, random = ~ 1 | Subject / Location / Design, method="ML")
Error in MEEM(object, conLin, control\$niterEM) :
Singularity in backsolve at level 0, block 1


The lmer() function in the lme4 package also gives an error:

model <- lmer(Y ~ Location * Design + (1|Subject) + (1|Location) + (1|Design) + (1|Location:Design), data, REML=FALSE)
Error in mer_finalize(ans) : Downdated X'X is not positive definite, 8.


The ezANOVA() function in the ez package also gives an error.

Any advice on how I could approach this analysis would be greatly appreciated! Would it be bad to duplicate the "no stimulus" observations for each of the two Location x "no stimulus" conditions which don't have observations?

• It would be easier by viewing (a part of) the dataset. But I am under the impression it could work by considering Location is nested in Design. Does it work if you do Design + Design:Location instead of Location * Design ? – Stéphane Laurent May 18 '13 at 9:03