Archetypal cases for questionnaires with nominal multiple choice questions
Aleix Alcacer, Irene Epifanio
TL;DR
This paper extends Archetypoid Analysis (ADA) to nominal observations from questionnaires with single-choice options by converting nominal variables to binary dummy codes and representing each observation as a convex mixture of actual archetypoids. It argues that archetypoids, being feasible binary patterns, yield interpretable extreme profiles for nominal data, addressing limitations of continuous archetypes from Archetype Analysis (AA) or Probabilistic Archetypal Analysis (PAA). Applying ADA to the German credit dataset demonstrates that ADA uncovering archetypoids aligns with known risk profiles and provides complementary representations, with Hamming-distance analyses reinforcing the extremity and distinctness of the archetypoids. The work suggests ADA as a practical and interpretable method for nominal data, with future work on mixed data, missing values, and scalability for large-scale applications.
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.