Models for Ordered Multiple Choices

The ordered multiple choice model assumes the relationship:

where the response of the variable Y is measured in one of k+1 different categories, are k intercept parameters, and b is the slope parameter vector not including the intercept term. By construction, holds. This model fits a common slopes cumulative model, which is a parallel lines regression model based on the cumulative probabilities of the response categories. Ordered logit and ordered probit models are most commonly used.