Mixture-based clustering for the ordered stereotype model

• New methodology for clustering rows and columns from a matrix of ordinal data.
• Establishes likelihood-based methods via finite mixtures with the stereotype model.
• Tests the reliability of this methodology through a simulation study.
• Illustrates this new approach with two examples.
• Reviews and compares the performance several model choice measures.

Many of the methods which deal with the reduction of dimensionality in matrices of data are based on mathematical techniques such as distance-based algorithms or matrix decomposition and eigenvalues. Recently a group of likelihood-based finite mixture models for a data matrix with binary or count data, using basic Bernoulli or Poisson building blocks has been developed. This is extended and establishes likelihood-based multivariate methods for a data matrix with ordinal data which applies fuzzy clustering via finite mixtures to the ordered stereotype model. Model-fitting is performed using the expectation–maximization (EM) algorithm, and a fuzzy allocation of rows, columns, and rows and columns simultaneously to corresponding clusters is obtained. A simulation study is presented which includes a variety of scenarios in order to test the reliability of the proposed model. Finally, the results of the application of the model in two real data sets are shown.