I have a dataset of around 120000 (120K) unique individuals. I am fitting a binary logistic regression, where I have around 150 variables to choose from. For the categorical variables, some are very imbalanced. For example, there is a variable that can take on Yes (=1) or No (=0). There are 119K individuals with Yes and the remaining 1K with No.
What are the consequences of having such a variable in the logistic regression?
Can it make my results unstable if I have many of these (say 10-20 similar variables), when using stepwise (forward) or backward automatic selection procedures?
What if the predictor / variable is not binary, but has for example 5 categories where 1 category is largely over or underrepresented?