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My data look like this: The dependent variable is score on a language task (numerical). I have $2$ between subject variables:

  1. age (young vs old: categorical)
  2. language (monolingual vs. bilingual: categorical)

Then, I have $3$ within-subject variables (task conditions):

  1. verb type (2 values: categorical)
  2. focus (2 values: categorical)
  3. definiteness (2 values: categorical)

There are two random effects:

  1. subject
  2. item

I run an lmer model in R. I want to include random intercepts and random slopes.

Question: Does it make sense to include random slopes for within-subject (so verbtype, focus and definiteness) factors for RE subject and random slopes for between-subject factor (so age and language) for RE item?

If yes, the model would look like this, so all factors as random slopes for both random effects:

lmer(score ~ age * language * verbtype * focus * definiteness + 
             (1+age+language+verbtype+focus+definiteness|subject) + 
             (1+age+language+verbtype+focus+definiteness|item), 
     data)

Intuitively, I feel like it does not make sense to include between-subject factors (age and language) as random slopes for subject and between-item factors (verbtype, focus and definiteness) as random slopes for item. If this intuition is correct, the model would be:

lmer(score ~ age * language * verbtype * focus * definiteness + 
             (1+verbtype+focus+definiteness|subject) + (1+age+language|item), 
     data)

Which one of these models makes more sense?

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  • $\begingroup$ +1. Your intuition is correct. The second model is correct (assuming that all three within-subject factors are between-item). $\endgroup$ – amoeba Aug 3 '17 at 18:47
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See here. In short, "a model specifying random slopes for a between subjects variable would be unidentifiable." But you can still include within-subject factors as random slopes for subject RE.

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