Abstract We introduce a set of models designed to analyze datasets involving responses from multiple subjects on pairwise comparisons from a fixed discrete set of alternatives. These models are part of a greater body of work known as Cultural Consensus Theory (CCT). Like other CCT models, these simultaneously infer each individual’s tendency toward aligning with the group consensus, level of agreement on each item, and also a latent consensus value of each alternative. Two primary models are discussed, referred to as the Strong and Weak Consensus Paired-Comparison Models (SCPCM and WCPCM respectively). The SCPCM works under the assumption that all individuals are answering in accordance to the latent consensus values but with varying degrees of accuracy, while the WCPCM relaxes this assumption and assumes minor deviations from latent consensus values in people’s average valuation of alternatives. The WCPCM also includes inferences on participants’ individual tendencies toward self-consistency (related to their tendencies toward committing violations of transitivity) as well as inferences on the tendency of each item to be evaluated consistently by individuals. The Case III Thurstonian model is used as the backbone for both CPCMs, and inference is conducted under a hierarchical Bayesian framework. Model checks along with applications to both simulated and real data are overviewed.

中文翻译：

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分层配对比较建模，一种文化共识理论方法

摘要 我们介绍了一组模型，旨在分析涉及多个主题对一组固定离散替代方案的成对比较的响应的数据集。这些模型是被称为文化共识理论 (CCT) 的更大工作体系的一部分。与其他 CCT 模型一样，这些模型同时推断每个人与群体共识保持一致的趋势、每个项目的同意程度以及每个备选方案的潜在共识值。讨论了两个主要模型，称为强和弱共识配对比较模型（分别为 SCPCM 和 WCPCM）。SCPCM 的工作假设所有个人都根据潜在的共识值进行回答，但准确度各不相同，而 WCPCM 放宽了这一假设，并假设人们对替代品的平均估值与潜在共识值存在微小偏差。WCPCM 还包括对参与者自我一致性的个人倾向的推断（与他们违反传递性的倾向有关）以及对每个项目被个人一致评估的倾向的推断。Case III Thurstonian 模型用作两个 CPCM 的主干，并且在分层贝叶斯框架下进行推理。概述了模型检查以及对模拟和真实数据的应用。WCPCM 还包括对参与者自我一致性的个人倾向的推断（与他们违反传递性的倾向有关）以及对每个项目被个人一致评估的倾向的推断。Case III Thurstonian 模型用作两个 CPCM 的主干，并且在分层贝叶斯框架下进行推理。概述了模型检查以及对模拟和真实数据的应用。WCPCM 还包括对参与者自我一致性的个人倾向的推断（与他们违反传递性的倾向有关）以及对每个项目被个人一致评估的倾向的推断。Case III Thurstonian 模型用作两个 CPCM 的主干，并且在分层贝叶斯框架下进行推理。概述了模型检查以及对模拟和真实数据的应用。