Archetypal cases for questionnaires with nominal multiple choice questions

TL;DR

This paper introduces a novel application of archetypoid analysis to nominal questionnaire data, enabling the identification of representative archetypal cases to better understand complex categorical datasets.

Contribution

It extends archetypoid analysis to nominal data, providing a new method for analyzing questionnaire responses with single-answer multiple-choice questions.

Findings

Demonstrated the method on the German credit dataset

Compared archetypoid analysis with archetype and probabilistic archetypal analysis

Showed improved interpretability of nominal data patterns

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.