Community detection in small-sample ordinal regimes: A benchmarking framework for Delphi data

2026-06-18

AI Summary

This study addresses the instability and overfitting of traditional latent variable models when applied to high-dimensional questionnaires with small expert panels. To overcome these limitations, the authors propose a network-centric, structured auto-dimensionality-reduction framework that translates inter-variable covariances into a weighted graph topology. By leveraging community detection and spectral partitioning, the method identifies latent thematic structures, reinterpreting expert-judged collinearity as cohesive topological signals. Validation through synthetic Delphi data simulations demonstrates that the framework significantly enhances structural stability and psychometric consistency under small-sample ordinal data conditions. It effectively circumvents the failure of conventional factor analysis caused by spectral instability and rank deficiency, offering a robust alternative for analyzing complex, sparse expert judgment datasets.

Abstract

The statistical modeling of consensus in Delphi data faces a critical bottleneck: the high dimensionality of questionnaire items relative to the limited sample size of expert panels. This rank deficiency leads traditional latent variable models, such as Principal Component Analysis, to be structurally unstable and prone to overfitting. Addressing this methodological gap, this study proposes a transition from variable-centric covariance models to network-centric connectivity models. By mapping item correlations onto a weighted graph topology, we present a simulation-based benchmark that utilizes community detection algorithms to identify latent thematic structures, effectively addressing the spectral instability and rank deficiency typical of high-dimensional, low-sample-size regimes. The research systematically evaluates the robustness of topological approaches based on structural density, information flow, and spectral partitioning against synthetic datasets designed to replicate the pathological conditions of consensus data, including ordinal scales and systemic noise. The central methodological contribution lies in demonstrating that collinearity among expert judgments - traditionally treated as statistical redundancy to be regularized - can be effectively reinterpreted as a topological signal of cohesion. This framework provides researchers with a structured and automated procedure for dimensionality reduction, ensuring structural stability and psychometric consistency even in small-sample regimes where standard factor analysis breaks down.

Problem

• community detection
• Delphi data
• high-dimensional low-sample-size
• rank deficiency
• consensus modeling

Innovation

• community detection
• Delphi data
• network-centric modeling
• small-sample regimes
• topological signal