Clustering Multivariate Rating Data Within the CUB Framework

Among the models for the analysis of rating data, the CUB (Combination of discrete Uniform and shifted Binomial random variable) is particularly interesting because it gives an interpretation of the dual latent factors believed to influence the final decision of a rater: feeling and uncertainty. In essence, this model represents the distribution of final ratings as a combination of a shifted binomial and a uniform random variable. Within the framework provided by the CUB model, we propose a mixture of multivariate CUB models to cluster multivariate rating data, whose estimation is performed via the EM algorithm. To evaluate our approach, we conducted two simulations, showcasing the model's consistency in handling complex data structures and capturing underlying patterns. Our findings underscore the potential of this methodology in uncovering hidden structures within multivariate rating datasets, offering valuable insights in various research domains.