Finding archetypal patterns for binary questionnaires
This provides a new exploratory tool for researchers in fields like education and psychology to understand binary datasets, though it is incremental as it extends existing methods to binary data.
The authors tackled the problem of analyzing binary data by applying archetypoid analysis for the first time, demonstrating its utility in a simulation study and two applications, including student skill set profiling and item response function description.
Archetypal analysis is an exploratory tool that explains a set of observations as mixtures of pure (extreme) patterns. If the patterns are actual observations of the sample, we refer to them as archetypoids. For the first time, we propose to use archetypoid analysis for binary observations. This tool can contribute to the understanding of a binary data set, as in the multivariate case. We illustrate the advantages of the proposed methodology in a simulation study and two applications, one exploring objects (rows) and the other exploring items (columns). One is related to determining student skill set profiles and the other to describing item response functions.