76 – To Open Source, or Not
Model-Based Clustering Using Adjacent-Categories Logic Models via Finite Mixture Model
Richard Arnold
Victoria University of Wellington
Lingyu Li
Victoria University of Wellington
Ivy Liu
Victoria University of Wellington
This talk presents cluster analysis of ordinal data utilizing 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–Maximization) 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.