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non-singularity with glmer() in a logit mixed model

Hi, and thank you for your idea, David Duffy. I am sorry if I was not clear. My use of the expression "more restrictive definition" was not in the sense of three categories of the same variable. I tried to say that I have two dependent binomial variables and one  them has less ones. The reason I mentioned that is because they are about a similar phenomenon, that is why I want to compmare the results and the reviewer ask us to use the same explanatory variables even if they are not significant. Indeed, variable y.A is "R&D" and y.B is "process innovation". There is all possible combinations of values for the two variables in different firms: firms with 0-0 in both variables, 1-0, 0-1, or 1-1. Therefore, I need to estimate two models and compare the results. I am having troubles with the model for R&D (in a developing country!).

Best regards

Fernando