Is there a standard name for a multinomial choice model where the observations are in the form of binary questions such as "do you prefer A to B" and "do you prefer B to D"? This seems like a common occurrence, and the likelihood is easy enough to write out by hand, but I'm having trouble searching for references.
Unless I misunderstood the question, this refers to paired preference (1) or pair comparison data. A well-known example of such a model is the Bradley-Terry model (2), which shares some connections with item scaling in psychometrics (3). There is an R package, BradleyTerry2, described in the JSS (2005) 12(1), Bradley-Terry Models in R, and a detailed overview in Agresti's CDA, pp. 436-439, with R code available in Laura Thompson's textbook, R (and S-PLUS) Manual to Accompany Agresti’s Categorical Data Analysis (2002) 2nd edition.
- Thurstone, L.L. (1927). A law of comparative judgment. Psychological Review, 3, 273-286.
- Bradley, R.A. and Terry, M.E. (1952). Rank analysis of incomplete block designs I: The methods of paired comparisons. Biometrika, 39, 324-345.
- Andrich, D. (1978). Relationships between the Thurstone and Rasch approaches to item scaling. Applied Psychological Measurement, 2(3), 451-462.