Abstract We consider a situation in which a group of respondents answers a set of questions and the aim is to identify any consensus among the respondents—that is, shared attitudes, beliefs, or knowledge. Consensus theory postulates that a latent trait determines the respondents’ probability to produce the consensus response. We propose a new version of the variable-response model, which implements consensus theory for numerical continuous responses, ordered categorical responses, unordered categorical responses, or a mixture thereof. The new model also accounts for multiple consensus groups and multiple latent traits underlying the response data. In a series of simulation studies, we identify procedures and conditions that permit an accurate estimation of the number of consensus groups and latent traits. In these simulations, we find that the model recovers the data-generating consensus responses well. We replicate these findings with the empirical data of a memory test.

中文翻译：

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多重潜在特征和共识群体的共识理论

摘要 我们考虑一组受访者回答一组问题的情况，目的是确定受访者之间的任何共识——即共享的态度、信念或知识。共识理论假设潜在特征决定了受访者产生共识反应的可能性。我们提出了一个新版本的可变响应模型，它实现了数值连续响应、有序分类响应、无序分类响应或其混合的共识理论。新模型还解释了响应数据背后的多个共识组和多个潜在特征。在一系列模拟研究中，我们确定了允许准确估计共识群体和潜在特征数量的程序和条件。在这些模拟中，我们发现该模型很好地恢复了数据生成的共识响应。我们用记忆测试的经验数据复制了这些发现。