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.Electronic supplementary materialThe online version of this article (doi:10.1007/s11336-016-9503-3) contains supplementary material, which is available to authorized users.
Highlights
Measurement data with ordinal categories occur frequently and in many fields of application
One motivation for the PO model assumes that the ordinal response has an underlying continuous variable (Anderson & Philips, 1981), called a latent variable, that follows a logistic distribution
Self-classified as religious, replied to 16 questions, shown in Appendix B, all rated on a 6-point Likert scale, (1) “Strongly disagree”, ..., (6) “Strongly agree”
Summary
Measurement data with ordinal categories occur frequently and in many fields of application. A continuous clinical response is often categorised into ordered subtypes based on histological or morphological terms. Likert scale responses might be “better”, “unchanged” or “worse”. When analysing such data, it is of interest to link the ordinal responses to a set of explanatory variables. Despite being introduced more than 3 decades ago, the proportional odds model (PO, McCullagh, 1980) is still frequently employed in analysing ordinal response data in, for example, agriculture (Lanfranchi, Giannetto, & Zirilli, 2014), medicine (Skolnick et al, 2014; Tefera & Sharma, 2015) and socioeconomic studies (Pechey, Monsivais, Ng, & Marteau, 2015). The extensive use of the PO model is due to its parsimony for modelling the effect of covariates on the response, compared to other similar models such as the baseline-category
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