國立政治大學統計學系主講人：劉逸明教授(School of Mathematics and Statistics,
學 術 演 講
學 術 演 講
Victoria University of Wellington, New Zealand)
題 目：Cluster Analysis for Ordered Categorical Data
時 間：民國112年5月8日 (星期一) 下午1：30
Ordinal categorical data can arise in a questionnaire where Likert scale responses to a question might be `better’, `unchanged’ or `worse’. For the identification of groups, patterns, clusters in an ordinal dataset, a common approach uses traditional cluster analysis methods by wrongly treating the ordinal score as a continuous measurement. This approach does not exploit the true ranked nature of the responses, and thus have unreliable results. We have developed likelihood-based models for single mode clustering and co-clustering where the rows (e.g., individuals in a questionnaire) and columns (e.g., questions) of a matrix are clustered simultaneously. It applies fuzzy clustering via finite mixtures to ordinal response models. Model-fitting is performed using the expectation-maximization algorithm and a fuzzy allocation of rows, columns, and rows and columns simultaneously to corresponding clusters is obtained. This talk gives a summary of recent results of our working group on this topic. It includes the development on various ordinal models, Bayesian approaches, alternative correlation structures, and data visualization methods. The application in real datasets is also shown.