Discrete choice models
Count data can be modeled by discrete choice model methods, possibly after some grouping of counts to limit the number of categories. For example, the categories may be 0, 1, 2, 3, and 4 or more if few observations exceed four. Unordered models such as multinomial logit are not parsimonious and more importantly are inappropriate. Instead, one should use a sequential discrete choice model that recognizes the ordering of the data, such as ordered logit or ordered probit.