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Jul 2, 2014 at 14:37 comment added Adel Yes, I would say so. Remember, that (1) when you add an interaction you are asking whether the effect of x on y changes across the values of w – or alternatively, w changes across the values of x depending on the causal story you want to tell; (2) when you then let any of these terms (x or w) vary at random there is then no good statistical reason why you should constrain the random terms only to xw since the effect on y depends now not only on the fixed effects but also on the random effects of x, z and xz.
Jul 2, 2014 at 12:40 vote accept George Michaelides
Jul 2, 2014 at 12:40 comment added George Michaelides Thanks. So if x or w or both do not improve the model but xw does, it is OK to keep just xw
Jul 2, 2014 at 9:28 history edited Nick Stauner CC BY-SA 3.0
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Jul 2, 2014 at 9:24 review First posts
Jul 2, 2014 at 9:28
Jul 2, 2014 at 9:06 history answered Adel CC BY-SA 3.0