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.

翻译：本文提出了一种专为序数数据（尤其是问卷数据）设计的新型原型分析框架。与现有方法不同，所提出的序数原型分析方法绕过了将序数数据转换为连续量表的两步过程，直接在序数数据上操作。我们将传统原型分析方法扩展至处理基于问卷数据的主观性，承认个体在量表感知上存在差异。我们引入了响应偏差序数原型分析方法，该方法在优化过程中为每个受试者学习个性化的量表。这些方法的有效性在合成数据和欧洲社会调查数据集上得到了验证，突显了其在深入理解人类行为与感知方面的潜力。本研究强调了在跨国研究中考虑响应偏差的重要性，并提供了一种通过原型分析处理序数数据的原理性方法。