Repeated-measures / within-subjects ANOVA in R
I'm attempting to run a repeated-meaures ANOVA using R. I've gone through various examples on various websites, but they never seem to talk about the error that I'm encountering. I assume I'm misunderstanding something important.
The ANOVA I'm trying to run is on some data from an experiment using human participants. It has one DV and three IVs. All of the levels of all of the IVs are run on all participants, making it a three-way repeated-measures / within-subjects ANOVA.
The code I'm running in R is as follows:
aov.output = aov(DV~ IV1 * IV2 * IV3 + Error(PARTICIPANT_ID / (IV1 * IV2 * IV3)),
data=fulldata)
When I run this, I get the following warning:
Error() model is singular
Any ideas what I might be doing wrong?
Answer
Try using the lmer function in the lme4 package. The aov function is probably not appropriate here. Look for references from Dougles Bates, e.g. http://lme4.r-forge.r-project.org/book/Ch4.pdf (the other chapters are great too, but that is the repeated measures chapter, this is the intro: http://lme4.r-forge.r-project.org/book/Ch1.pdf). The R code is at the same place and for longitudinal data, it seems to be generally considered wrong these days to just fit OLS instead of a components of variance model like in the lme4 package, or in nlme, which to me seems to have been wildly overtaken by lme4 in popularity recently. You may note Brian Ripley's referenced post in the comments section above just recommends switching to lme also.
By the way, a huge advantage off the jump is you will be able to get estimates for the level of each effect as adjustments to the grand mean with the typical syntax:
lmer(DV ~ 1 +IV1*IV2*IV3 +(IV1*IV2*IV3|Subject), dataset))
Note your random effects will be vector valued.