A novel model-based biclustering for ordinal data via a URV approach

Abstract We introduce a novel finite mixture model for biclustering ordinal data matrices, simultaneously clustering rows and columns within the Underlying Response Variable (URV) framework. Ordinal responses are modeled as discretizations of latent Gaussian variables, while component-specific covariance matrices are parsimoniously parameterized via a factor analytic structure to capture complex dependence patterns efficiently. To address computational challenges arising from the high-dimensional likelihood evaluation inherent to ordinal data, model parameters are estimated using a Composite Likelihood (CL) approach, which offers significant computational advantages with negligible loss of efficiency. Extensive simulation studies demonstrate the effectiveness of the proposed method in terms of accurate cluster recovery and reliable parameter estimation. We further illustrate the applicability of the methodology through an empirical analysis of two real-world ordinal datasets, highlighting its potential for uncovering meaningful latent bicluster structures.