lmer reports "fixed-effect model matrix is rank deficient so dropping 1 column / coefficient" and doesn't show one interaction"

Question

So I'm trying to run a mixed-effects model looking at the relative intensity of Arabic and English fricatives produced by bilingual Arabic-English speakers; for context, I'm looking at /f/ and /v/, Arabic doesn't have /v/ natively so any instances of its production were in English.

I tried to run this model:

lmer(intensity_relative ~ segment * position +
       position * language + segment * language +
       (1|speaker), data = df3_uae)

However, I get the warning: fixed-effect model matrix is rank deficient so dropping 1 column/coefficient and the model doesn't show any interaction results for segment * language. Could this be because in the language column "Arabic", there isn't any recorded instance of /v/ so there's a missing segment? If not, is there a way to fix this?

Thanks!

Answer 1

Could this be because in the language column "Arabic", there isn't any recorded instance of /v/ so there's a missing segment?

Yes, that would explain it. The interaction parameter is allowing the mean for /v/ in Arabic to be different from what you'd expect based on /v/ vs/f/ generally and on Arabic vs English generally. You don't have any data to estimate that difference, so the model drops the parameter.