I am following-up this and this thread because I found it very difficult to understand the implications of using each of the two types of random-effect correlations. In particular, I fitted model like this
model <- lmer(RT ~ F1*F2 + (F1*F2|subject), data = mydata)
Where F1 and F2 are two binary factors (coded 0 vs. 1) representing manipulations within-subject: each subject does all four experimental conditions defined by F1*F2.
Imagine that F1 is a painful-inducing manipulation (0 = non painful, 1 = painful) and F2 is painkiller (0 = no painkiller, 1 = painkiller). I want to know whether the painkiller is most effective on individuals who are more sensitive to pain without painkillers (i.e., when F2 = 0).
For this reason, I inspected correlations between two random effects: ranef-F1 and ranef-F1:F2. If I got this correctly, a positive correlation implies that individuals who are more sensitive to pain (high ranef-F1) are also those for which the painkiller is most successful (high ranef-F1:F2). What are the implications of testing this hypothesis by inspecting VarCorr(model) versus cor(ranef(model))? Another related issue is: Whereas I can easily get p-values for cor(ranef(model)), I cannot have p-values for VarCorr(model), or can I?
I tried to go through the lme4 paper and through several Questions&Answers, but I could not really understand this point.
Could anyone help me solve this issue?