lme4_fixed-effect model matrix is rank deficient so dropping 1 column / coefficient

I have a dataset consisting of the following: one column language containing five different languages. Two other columns Canonicity and Intrinsic containing either (0, 1). One last column, useOfIntrinsic. You can view the data here.

I would like to test the use of intrinsic as a function of Language, Canonicity and useOfIntrinsic. Thus, I ran the following mixed-effect logistic regression model:

glmer(INT ~ Language * Canonicity + Language + Canonicity + useOfIntrinsic +
(1|Picture) + (1|ID), data = data, family = "binomial")

I also tried:

glmer(INT ~ Language + Canonicity + useOfIntrinsic:Language + Canonicity:CAN +
useOfIntrinsic + (1|Picture) + (1|ID), data = data, family = "binomial")

However, I get this error:

fixed-effect model matrix is rank deficient so dropping 1 column / coefficient

I do not get the error when I exclude the useOfIntrinsic factor. This factor is basically is the count of intrinsic==1 for each Language. I add this factor in order to test whether overall use of intrinsic is a good predictor intrinsic.

There are other post that talk about this error (e.g. What is rank deficiency, and how to deal with it?) but I am still unable to fix the error.

Another related question is whether I should reduce the significance level when running the same model 5 times (or order to change the reference language group)?

• Totally make sense. I instead used the frequency of intrinsic use per subject. The model works fine with that. However, I get the same error if I scaled this factor 'log(data$useOfInt)', I am wondering why is that? Thank you – Aloush87 Apr 1 '17 at 23:33 • I'm not sure i follow what a subject is in this model, or what model exactly is producing the error. If you run the exact same model as above but replacing data$useOfInt with its logarithm, it still has the same problem as before--every language has exactly one value of log(data\$useOfInt) associated with it, so you can't put both that and language in a single model. – Jacob Socolar Apr 2 '17 at 2:09