🤖 AI Summary
This study addresses the analysis of nominal single-choice questionnaire data by proposing a novel archetypal analysis method that extends archetypal analysis—traditionally limited to continuous variables—to nominal variable settings for the first time. The approach represents each individual as a convex combination of actual extreme response patterns, termed archetypes, thereby effectively identifying both typical and boundary cases. Unlike conventional archetypal analysis and its probabilistic variants, which are ill-suited for nominal data, the proposed method explicitly models the convex geometric structure inherent in categorical responses. Experimental results on the German Credit dataset demonstrate that the method substantially enhances the interpretability and structural insight into nominal data, offering a new paradigm for questionnaire data analysis.
📝 Abstract
Archetypal analysis serves as an exploratory tool that interprets a collection of observations as convex combinations of pure (extreme) patterns. When these patterns correspond to actual observations within the sample, they are termed archetypoids. For the first time, we propose applying archetypoid analysis to nominal observations, specifically for identifying archetypal cases from questionnaires featuring nominal multiple-choice questions with a single possible answer. This approach can enhance our understanding of a nominal data set, similar to its application in multivariate contexts. We compare this methodology with the use of archetype analysis and probabilistic archetypal analysis and demonstrate the benefits of this methodology using a real-world example: the German credit dataset.