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Modeling Human Responses by Ordinal Archetypal Analysis

Anna Emilie J. Wedenborg, Michael Alexander Harborg, Andreas Bigom, Oliver Elmgreen, Marcus Presutti, Andreas Råskov, Fumiko Kano Glückstad, Mikkel Schmidt, Morten Mørup

TL;DR

The Response Bias Ordinal Archetypal Analysis (RBOAA), which learns indi-vidualized scales for each subject during optimization, is introduced, which learns indi-vidualized scales for each subject during optimization.

Abstract

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.

Modeling Human Responses by Ordinal Archetypal Analysis

TL;DR

The Response Bias Ordinal Archetypal Analysis (RBOAA), which learns indi-vidualized scales for each subject during optimization, is introduced, which learns indi-vidualized scales for each subject during optimization.

Abstract

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.
Paper Structure (10 sections, 13 equations, 4 figures)

This paper contains 10 sections, 13 equations, 4 figures.

Table of Contents

  1. Introduction
  2. METHODS
  3. Ordinal Archetypal Analysis
  4. Response Bias Ordinal Archetypal Analysis
  5. Model Optimization
  6. Model Evaluation
  7. Results and discussion
  8. Synthetic study
  9. ESS Round 8 (2016) data
  10. Conclusion

Figures (4)

  • Figure 1: Top panel: Results of the models on synthetic data without response bias. Bottom panel: Results of the models on synthetic data with response bias. The leftmost column represents the loss in terms of cross-entropy and least-squares across different numbers of archetypes. The middle plots provide the NMI, which in the case of the synthetic data are used as an indication of how well the model reconstructs the ground truth structure in terms of how observations are expressed by the archetypes. The left column is the RMSE between the original data and a corrupted reconstruction, $\mathbf{R}_{cor}$ of the original data.
  • Figure 2: Response bias found the the OAA (points) and RBOAA (boxplot) for the synthetic data without response bias (a) and with response bias (b) together with the ground truth. In the case with no response bias the ground truth are evenly spaced between 0 and 1.a
  • Figure 3: The loss and NMI across a different number of archetypes for ESS8 GB data as well as the response bias
  • Figure 4: From left to right: The four archetypes for each of the models; (a) RBOAA, (b) OAA, (c) AA and (d) TSAA. The background is colored after the subjects answer to each question, a darker color indicating that the answer is popular among the subjects. The different archetypes have been visualized for each model as trajectories (vertical lines) across the questions, highlighting their distinct profile. The shared labels of the y-axis have been colored after the questions category according to Schwartz theory of human values Schwartz2012AnValues, Openness to change, Self Enhancement, Conservation and Self Transcendence