Consensus theory for multiple latent traits and consensus groups

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.