Model-Based Clustering of Multivariate Rating Data Accounting for Feeling and Uncertainty

Among the models for the analysis of rating data, the CUB (combination of discrete uniform and shifted binomial random variable) is notable because it assumes that the final rating given by a respondent is the result of the joint action of two latent components: the feeling and the uncertainty, which are modelled through a shifted binomial and a uniform random variable, respectively. We propose a mixture of multivariate CUB models for clustering multivariate rating data, estimated using the EM algorithm. The performance of our model was evaluated through simulation studies, which demonstrated its capability to capture the hidden structure of the data. Additionally, we show two case studies which highlight the model’s effectiveness in uncovering latent structures in real-world data and its utility in interpreting the results.