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Cultural consensus theory for the ordinal data case. (English) Zbl 1314.62267
Summary: A Cultural Consensus Theory approach for ordinal data is developed, leading to a new model for ordered polytomous data. The model introduces a novel way of measuring response biases and also measures consensus item values, a consensus response scale, item difficulty, and informant knowledge. The model is extended as a finite mixture model to fit both simulated and real multicultural data, in which subgroups of informants have different sets of consensus item values. The extension is thus a form of model-based clustering for ordinal data. The hierarchical Bayesian framework is utilized for inference, and two posterior predictive checks are developed to verify the central assumptions of the model.

62P15 Applications of statistics to psychology
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62F15 Bayesian inference
Full Text: DOI
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