# Li, Lingyu

## Fuzzy clustering using adjacent-categories logit model via finite mixture model

#### School of Mathematics and Statistics, Victoria University of Wellington

Traditional analysis of ordinal data treats the outcome either as nominal or continuous variables. The nominal approach ignores the ordinal property whereas the continuous approach introduces assumptions about the ordinal level spacing - thus these traditional approaches can lead to a loss of statistical power, or can introduce bias.

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.

This presentation is eligible for the NZSA Student Prize.