Is an unbalanced categorical independent variable a problem for binomial logistic regression? My dependent variable is a yes/no measure; I'm trying to predict the probability of an event to lead to a yes or no. The independent variable is a categorical predictor with 3 levels.
My data is unbalanced; I have an unequal number of events in each of the 3 levels of the independent variable (i.e. 311, 180, 238). Is that okay for a binomial regression or do I need to have an equal number of events across the 3 levels? (I'm not asking about unequal yes/no answers within each level, but about the total number of events in each level). I would appreciate any advice on this.

You have $729$ observations in total. You would have had the most powerful model by allocating $729/3=243$ subjects to each group.
However, despite your imbalance, you still have a large number of subjects ($180$) in your smallest group, so you still have a powerful model.
The way I think about this is that, if I have the funding to collect observations about, say, $51$ subjects on either of two conditions, I would be forced to allocate them unevenly: $25$ in one group and $26$ in the other. If I suddenly found myself with additional funding to collect data on another subject, I would want to balance the groups to $26$ each, not $25$ and $27$.
