If the categories for a multinomial response variable can be ordered, then the distribution of that variable is referred to as ordinal multinomial. For example, if in a survey the responses to a question are recorded such that respondents have to choose from the prearranged categories "Strongly agree," "Agree," "Neither agree nor disagree," "Disagree," and "Strongly disagree," then the counts (number of respondents) that endorsed the different categories would follow an ordinal multinomial distribution (since the response categories are ordered with respect to increasing degrees of disagreement).

Specialized methods for analyzing multinomial and ordinal multinomial response variables can be found in the Generalized Linear Models module.