title: Biclustering Models for Two-Mode Ordinal Data.
abstract: The work in this paper introduces finite mixture models that can be used to simultaneously cluster the rows and columns of two-mode ordinal categorical response data, such as those resulting from Likert scale responses. We use the popular proportional odds parameterisation and propose models which provide insights into major patterns in the data. Model-fitting is performed using the EM algorithm, and a fuzzy allocation of rows and columns to corresponding clusters is obtained. The clustering ability of the models is evaluated in a simulation study and demonstrated using two real data sets.
authors.affiliation: School of Mathematics, Statistics and Actuarial Science, University of Kent, Cornwallis Building, Canterbury, CT2 7NF , UK. e.matechou@kent.ac.uk.
authors.forename: Eleni
authors.initials: E
authors.lastname: Matechou
authors.affiliation: School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand.
authors.forename: Ivy
authors.initials: I
authors.lastname: Liu
authors.affiliation: School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand.
authors.forename: Daniel
authors.initials: D
authors.lastname: Fernández
authors.affiliation: Centre for Research in Psychology, Behaviour, & Achievement, Coventry University, Coventry, UK.
authors.forename: Miguel
authors.initials: M
authors.lastname: Farias
authors.affiliation: Oxford Mindfulness Centre, University of Oxford, Oxford, UK.|Department of Psychology, University of Oslo, Oslo, Norway.
authors.forename: Bergljot
authors.initials: B
authors.lastname: Gjelsvik
mesh_terms: D000465:Algorithms; D016000:Cluster Analysis; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D016017:Odds Ratio; D011594:Psychometrics; D012067:Religion; D013406:Suicide, Attempted
keywords: EM algorithm; Likert scale; fuzzy clustering; proportional odds