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Problem :

I have the dataset consisting of the following: one column language containing five different languages. Two of the other columns Canonicity and Intrinsic containing either (0, 1). One last column is useOfIntrinsic. I would like to test a use of intrinsic as the function of LanguageCanonicity and useOfIntrinsic. Thus, I ran a following mixed-effect logistic regression model:

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

I also tried as below:

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

But, I get below error:

“Fixed-effect model matrix is rank deficient so dropping 1 column / coefficient”

 Any solution on my error?

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Solution :

You can think about the model you are trying to fit as by asking for an estimate of a effect of useOfIntrinsic while controlling for a effect of Language. However once you've controlled for a effect of Language, you've already completely dealt with a differences between languages that you might want to attribute to the useOfIntrinsic. To put both your variables in a single model, you either need some of the independent variation in the two variables (i.e. some variation in useOfIntrinsic within the single language), or you need to place the some additional constraints on how you estimate a effect of Language. One possibility would be to experiment with the estimating Language as a random effect, but I don't necessarily recommend this given that you only have the five languages in the sample.

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