Incorporating the Luce-Krantz Threshold Model into Cultural Consensus Theory for Ordinal Categorical Data

Cultural consensus theory (CCT), developed by Batchelder and colleagues in the mid-1980s, is a cognitively driven methodology to assess informants’ consensus in which the culturally correct answers are unknown to researchers a priori. The primary goal of CCT is to uncover the cultural knowledge, preferences or beliefs shared by group members. One of the CCT models, calledthe general Condorcet model (GCM), deals with dichotomous (e.g., true/false) response data which are collected from a group of informants who share the same cultural knowledge. We propose a new model, called the general Condorcet-Luce-Krantz (GCLK) model, which incorporates the GCMwith the Luce-Krantz threshold theory. The GCLK accounts for ordinal categorical data (including Likert-type questionnaires) in which informants can express confidence levels when answering the items/questions. In addition to finding out the consensus truth to the items, the GCLK also estimates other response characteristics, including the item-difficulty levels, informants’ competency levels, and guessing biases. We introduce the multicultural version of the GCLK that can help researchers detect the number of cultures for a given dataset. We use the hierarchical Bayesian modeling approach andthe Markov chain Monte Carlo sampling method for estimation. A posterior predictive check is established to test the central assumptions of the model. Through a series of simulations, we evaluate the model’s applicability and find that the GCLK performs well on parameter recovery.