non-singularity with glmer() in a logit mixed model
The focus of the paper is to compare the results of two dependent variables, Y.A and Y.B for firms nested in 24 regions. I am estimating mixed logit models [...] the definition of Y.A is much more restrictive though more interesting than the definition of Y.B. Therefore, for Y.A there are far fewer ones for firms in the 24 regions.
I don't know if this is helpful, but you might try a multinomial (or even ordinal, if that is appropriate) outcome (no, y-loose, y-strict) GLMM. There are a few suitable R packages (eg MCMCglmm).