A Bayesian Model for Co-clustering Ordinal Data with Informative Missing Entries

TL;DR

This paper introduces a Bayesian nonparametric co-clustering model for multivariate ordinal data that treats missing and censored entries as informative, improving data structure understanding.

Contribution

It presents a novel Bayesian model leveraging Dirichlet processes and latent variables to handle informative missingness and high-dimensional ordinal data.

Findings

Model outperforms existing methods in simulations

Effectively identifies subpopulations in real data

Handles high-dimensional data efficiently

Abstract

Several approaches have been proposed in the literature for clustering multivariate ordinal data. These methods typically treat missing values as absent information, rather than recognizing them as valuable for profiling population characteristics. To address this gap, we introduce a Bayesian nonparametric model for co-clustering multivariate ordinal data that treats censored observations as informative, rather than merely missing. We demonstrate that this offers a significant improvement in understanding the underlying structure of the data. Our model exploits the flexibility of two independent Dirichlet processes, allowing us to infer potentially distinct subpopulations that characterize the latent structure of both subjects and variables. The ordinal nature of the data is addressed by introducing latent variables, while a matrix factorization specification is adopted to handle the high dimensionality of the data in a parsimonious way. The conjugate structure of the model enables an explicit derivation of the full conditional distributions of all the random variables in the model, which facilitates seamless posterior inference using a Gibbs sampling algorithm. We demonstrate the method's performance through simulations and by analyzing politician and movie ratings data.