Situations where a level of a categorical variable occurs very rarely (eg, a rare disease). This can be a problem especially when the variable is the response variable in a model.
In statistics, "rare events" refers to situations where a level of a categorical variable occurs very rarely. Such cases can create special problems. The prototypical situation would be predicting a rare disease with a logistic regression model. However, a particular level of a multilevel categorical variable can also be rare, and there can be adverse consequences even when the variable is a predictor as well.
