Should between-subject factors be included as random slopes for item in a mixed effects model?

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?

• +1. Your intuition is correct. The second model is correct (assuming that all three within-subject factors are between-item). Aug 3, 2017 at 18:47

1 Answer

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.