I am building a mixed effects logistic regression to predict linguistic (corpus) data. I have coded for various factors, some of which do not correspond to a large amount of data. For example, one predictor is Pauses with two levels [present, absent]. Pauses occur in only 11% of my data. When I insert all of my factors in a stepwise regression (using R base step function), the factor Pauses is selected as significant. However, when I put Pauses together with other factors in a mixed effects regression with a participant random intercept and a stimulus random intercept I have noted a strange behavior: Depending on the reference level selected for Pauses (e.g. if I relevel it to "absent"), including this factor in the overall mixed effects model will lead to non-convergence. When I relevel the factor to "present", it converges without a problem (and interestingly the factor turns out significant). I don't understand why this would happen in a binary factor like this. Conceptually, there should be no difference depending on which level this factor is releveled to (the only difference being what hypothesis I am testing with my data). If I understand correctly, all that should change in my regression is the coefficient. Does this indicate a problem with my model building or the data? Does it make sense to report in a paper the model with the factor leveled to the level that led to convergence?
After some looking around, I believe the reason why the model converged (or not) depending on which reference level was chosen is quasi-complete separation (https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faqwhat-is-complete-or-quasi-complete-separation-in-logisticprobit-regression-and-how-do-we-deal-with-them/). I ended up trusting the model results with the factors releveled in the way that made it converge.