Ordinal Clustering with the flex-Scheme

Abstract

We investigate suitable methods for clustering multivariate ordinal data assuming that the data are collected in surveys with item
batteries on the same ordinal answer format and that respondents are to be grouped to characterize different answering patterns and
tendencies. We consider heuristic partitioning methods and model-based methods which fit within the flex-scheme proposed
by Fritz Leisch for clustering, in combination with different variants of scale handling (numerical coding, nominalization and
respecting the ordinal scale). The performance of the methods to extract the true clustering structure is assessed in an illustrative simulation study using artificial data where the number of observations, the number of variables and the number of response levels as well as the difficulty of the clustering problem are systematically varied to highlight in which situations certain methods might be preferable. By extending the flex-scheme with new methods, which we provide in our R package flexord, we help pave the way for future research on ordinal data clustering with even more complex and diverse data-generating processes.