A reduced basis decomposition approach to efficient data collection in pairwise comparison studies.

Area of Science:

• Statistics
• Experimental Design
• Machine Learning

Background:

• Comparative judgment studies use pairwise comparisons to assess object quality, often analyzed with the Bradley-Terry model.
• Designing these studies optimally to maximize statistical efficiency is computationally challenging for large numbers of objects.

Purpose of the Study:

• To develop a scalable and computationally efficient method for constructing experimental designs in comparative judgment studies.
• To overcome the limitations of spectral decomposition for large-scale studies.

Main Methods:

• A novel scalable method based on reduced basis decomposition is proposed.
• This method bypasses the explicit construction of a large covariance matrix, reducing computational complexity.
• Eigenvalue bounds are established to guarantee approximation quality.

Main Results:

• The proposed method achieves computational savings of two to three orders of magnitude.
• Simulations show speedup factors over 100 for studies with 64+ objects, with minimal approximation error.
• The method successfully constructed a design for a 452-region spatial study in under 7 minutes.

Conclusions:

• The reduced basis decomposition method offers a computationally feasible solution for designing large-scale comparative judgment studies.
• This advancement enables efficient design construction and real-time updates, as demonstrated in spatial studies and classroom peer assessment.