Model-Based Clustering Using Adjacent-Categories Logit Models via Finite Mixture Model

• Activity Number: 76 - To Open Source, or Not
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 4:00 PM to 5:50 PM
• Sponsor: Section for Statistical Programmers and Analysts
• Author(s): Lingyu Li* and Ivy Liu and Richard Arnold
• Companies: Victoria University of Wellington and Victoria University of Wellington and Victoria University of Wellington
• Keywords: clustering; finite mixture model; ordinal data; EM algorithm; categorical data analysis

Abstract

This talk presents cluster analysis of ordinal data utilising the natural order information of ordinal data. Three models usually used in ordinal modelling are discussed: the proportional odds model, the adjacent categories model and the ordered stereotype model.

In our research, the data take the form of a matrix where the rows are subjects and the columns are a set of ordinal responses by those subjects to, say, the questions in a questionnaire. We implement model-based fuzzy clustering via a finite mixture model, in which the subjects (the rows of the matrix) and/or the questions (the columns of the matrix) are grouped into a finite number of clusters. We will explain how to use EM (Expectation–Maximisation) algorithm to estimate the model parameters. Specifically, we illustrate the details of using Adjacent-Categories logit model to perform row/column and bi-clustering. This clustering method differs from other typical clustering methods such as K-means or hierarchical clustering, because it is a likelihood-based model, and thus statistical inference is possible.