I ran a computer-based experiment in which there were two within-subject factors, A and B. So all participants got multiple trials in each A*B cell. There was also one between subject factor, C.
I'm trying to predict response time, so initially I did:
> lmer(rt ~ A*B*C + (1|subj)
but was told I should specify random effect interactions as well, e.g.:
> lmer(rt ~ A*B*C + (1|subj) + (1|A:subj) + (1|B:subj)
In that case, shouldn't I also specify the three-way interaction? e.g.:
> lmer(rt ~ A*B*C + (1|subj) + (1|A:subj) + (1|A:B:subj)
I understand the first model, but I'm not quite clear on the other two--though they all provide different results. Can someone clarify what these models do and which one is most appropriate?