Chapter 15: Models for ordered choices
Netflix (www.netflix.com) is an Internet company that rents movies to subscribers. After a customer rents a movie, the next time they log on to the website, they are invited to rate the movie on a five-point scale, where five is the highest, most favorable rating. The ratings of the many thousands of subscribers who rented that movie are averaged to provide a recommendation to prospective viewers. For example, from 5 April 2009, the average rating of the 2007 movie National Treasure: Book of Secrets given by approximately 12 900 visitors to the site was 3.8. This rating process provides a natural application of the models and methods described in this survey. The model described here is an ordered choice model. Ordered choice models are appropriate for a wide variety of settings in the social and biological sciences. The essential ingredient is the mapping from an underlying, naturally ordered preference scale to a discrete ordered observed outcome, such as the rating scheme described above. The model of ordered choice pioneered by Aitcheson and Silvey (1957) and Snell (1964) and articulated in its modern form by Zavoina and McElvey (1969), McElvey and Zavoina (1971, 1975) and McCullagh (1980) has become a widely used tool in many fields. The number of applications in the current literature is large and increasing rapidly.
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