I have a multilevel problem where I want to have a random intercept and a random slope. However the random slope is the interaction of two predictors. In this case, do I also have to allow random slopes for the individual predictors?
For example, with lme4 is this OK?
lmer(y ~ x + w + x:w + (1 + x:w|group), data=mydata)
Or should i use
lmer(y ~ x + w + x:w + (1 + x + w + x:w|group), data=mydata)
even if I am not interested in either x or w to be random?