方法对比

	Unfolding Model	Bradley-Terry 模型	对应分析
领域	统计学	决策	统计学
方法族	Latent structure	Regression model	Latent structure
起源年份	2005	1952	1984
提出者	Clyde Coombs; Borg & Groenen	Ralph Bradley & Milton Terry	Jean-Paul Benzécri; Michael Greenacre
类型	Preference scaling via ideal-point representation	Probabilistic paired comparison model	Exploratory multivariate technique for categorical data
开创性文献	Borg, I., & Groenen, P. J. F. (2005). Modern Multidimensional Scaling: Theory and Applications (2nd ed.). Springer. ISBN: 978-0-387-25150-9	Bradley, R. A., & Terry, M. E. (1952). Rank analysis of incomplete block designs: I. The method of paired comparisons. Biometrika, 39(3/4), 324–345.	Greenacre, M. J. (1984). Theory and Applications of Correspondence Analysis. Academic Press. ISBN: 978-0-12-299050-2
别名	Ideal Point Model, Preferential Choice Scaling, Coombs Unfolding, Katlanma Modeli	BT Model, Bradley-Terry-Luce Model, Paired Comparison Model, İkili Karşılaştırma Modeli	CA, Simple Correspondence Analysis, Reciprocal Averaging, Karşılıklı Uyum Analizi
相关	2	3	2
摘要	The Unfolding Model is a geometric approach to preference analysis that represents both individuals and choice objects (stimuli) as points in a shared low-dimensional space. Originating with Clyde Coombs's foundational 1950 work on preferential choice and rigorously systematized by Borg and Groenen (2005), the model assumes each person prefers the stimulus closest to their personal ideal point, thereby 'unfolding' rank-order preference data into a joint spatial map.	The Bradley-Terry model is a probabilistic model for paired comparisons that assigns a latent strength parameter to each item and predicts the probability that one item beats another in a head-to-head contest. Introduced by Ralph A. Bradley and Milton E. Terry in 1952, it provides a principled statistical framework for ranking items from pairwise preference data, including incomplete comparison designs where not every pair is directly observed.	Correspondence Analysis (CA) is an exploratory multivariate technique for visualizing the association structure of a two-way contingency table. Developed systematically by Jean-Paul Benzécri in France during the 1960s–1970s and brought to an English-language audience by Michael Greenacre in 1984, CA decomposes the chi-square statistic of a cross-tabulation to produce a low-dimensional joint display — called a biplot — in which rows and columns are represented as points whose proximities reflect their associations.