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Consider using less stringent convergence tests
Following Doug Bates recommendations, it might be best to disable gradient-based tests in fitted mixed models by using control = lmerControl(calc.derivs = FALSE). It speeds up testing and these tests are rather likely to produce false positives.
@singmann do you have a reference on the false-positives point? (I've seen the speedup recommendation in the lme4 vignette)
Unfortunately nothing citable. Doug Bates said this in person during SMLP 2024.