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.
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EM algorithm, Likert scale, fuzzy clustering, proportional odds, Algorithms, Cluster Analysis, Humans, Likelihood Functions, Models, Statistical, Odds Ratio, Psychometrics, Religion, Suicide, Attempted