Modeling Human Responses by Ordinal Archetypal Analysis

This paper introduces a novel framework for Archetypal Analysis (AA) tailored to ordinal data, particularly from questionnaires. Unlike existing methods, the proposed method, Ordinal Archetypal Analysis (OAA), bypasses the two-step process of transforming ordinal data into continuous scales and operates directly on the ordinal data. We extend traditional AA methods to handle the subjective nature of questionnaire-based data, acknowledging individual differences in scale perception. We introduce the Response Bias Ordinal Archetypal Analysis (RBOAA), which learns individualized scales for each subject during optimization. The effectiveness of these methods is demonstrated on synthetic data and the European Social Survey dataset, highlighting their potential to provide deeper insights into human behavior and perception. The study underscores the importance of considering response bias in cross-national research and offers a principled approach to analyzing ordinal data through Archetypal Analysis.