proportional odds logistic regression
Proportional-odds logistic regression is often used to model an ordered categorical response. By "ordered", we mean categories that have a natural ordering, such as "Disagree", "Neutral", "Agree", or "Everyday", "Some days", "Rarely", "Never". For a primer on proportional-odds logistic regression, see our post, Fitting and Interpreting a Proportional Odds Model.
Take a look at the following table. It is a cross tabulation of data taken from the 1991 General Social Survey that relates political party affiliation to political ideology (Agresti, An Introduction to Categorical Data Analysis, 1996).