I think that it's helpful to consider what you're telling your model is true. In the case of specifying Item
as a random factor, you are essentially saying that the words used in the study are random selections from a larger body of possible words (which is probably true). You're also telling your model that, right now, each word has its own unique intercept (... + (1 | ITEM)
) but that there is a some shared intercept for reaction time (not specified directly, but assuming you're using something like lme4
, then you model implies the intercept unless specified otherwise). These, to me, seem like reasonable assumptions: there's nothing special about any single word outside of these word traits (i.e., frequency and valence), there is likely some general basal reaction time that people have (i.e., the fixed intercept), and each word does likely have a unique effect on that basal reaction time (i.e., the random intercept assigned to each word).
Now, the question beyond this is whether you're telling your model everything it needs to know. For example, you're observing multiple participants over repeated tests. I would hazard a guess that each participant has their own basal reaction time, so you probably need to add participants as a random effect as well (... + (1 | ITEM) + (1 | SUBJ)
). You may then ask whether or not each person may have their own effect for frequency and valence (e.g., maybe some words are more frequent in a personal lexicon than in the general population, or maybe some people have special emotional associations to some words). If you have reason to believe this, then you may need to add random effects as well.
More directly to your stated question, you actually have to make ITEM
have its own random effect in a model that also includes FREQ
. Since each item has its own unique frequency, the model would become rank deficient if you included both variables together as fixed effects. The only way to avoid that issue would be to treat the words themselves are random selections from a population of possible words and treat specific word traits as having some fixed effect for predicting reaction time. In reality, your model is not dissimilar to an item response theory model: see here (IRT models in lme4), here (additional IRT in lme4), and here (response time IRT in R)