Recovering Hierarchical Structures in Psychological Measurement

Abstract

Psychological constructs are often organized hierarchically, making accurate identification of their narrowest dimensions essential to recover broader levels of organization. Existing network methods for this task are limited by either the resolution limit of modularity or the variability introduced by terminating community detection prematurely. We introduce Pairwise Resolution Iteration via Subgraph Modularity (PRISM), a community detection procedure designed to identify dimensions below the resolution limit without requiring a tunable parameter. We evaluated PRISM using 320,000 samples generated from second order factor models across 3,200 conditions that varied the numbers of first and second order factors, factor loadings, indicators per factor, sample size, skew, overlapping dimensions, population error, and correlations among second order factors. PRISM was compared with lower order Louvain and exploratory factor analysis (EFA) paired with several traditional dimensionality methods, many of which set the depth of the bass-ackward estimation procedure. Recovery was evaluated using dimensionality accuracy, bias, and structural accuracy. PRISM generally provided the most accurate and least biased recovery at both levels and maintained strong performance at smaller sample sizes and extreme skew. overlapping dimensions reduced performance across methods, and both network methods performed poorly when overlapping dimensions were combined with few indicators, weak first order loadings, and strong second order loadings. EFA paired with parallel analysis based on principal component eigenvalues was the strongest traditional alternative, particularly in exceptionally large samples. These findings support PRISM as a robust general procedure to recover each level of a hierarchical structure.

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BibTeX RIS

BibTeX

@misc{christensen2026recovering,
  title = {{Recovering Hierarchical Structures in Psychological Measurement}},
  author = {Alexander P. Christensen and Sydney Goldberg and Ashley L. Watts and Luis Eduardo Garrido},
  howpublished = {PsyArXiv},
  year = {2026},
  month = oct,
  doi = {10.31234/osf.io/kjvzu_v1},
  url = {https://osf.io/preprints/psyarxiv/kjvzu_v1/},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Recovering Hierarchical Structures in Psychological Measurement
AU  - Alexander P. Christensen
AU  - Sydney Goldberg
AU  - Ashley L. Watts
AU  - Luis Eduardo Garrido
PY  - 2026
DA  - 2026/10/10
PB  - PsyArXiv
DO  - 10.31234/osf.io/kjvzu_v1
UR  - https://osf.io/preprints/psyarxiv/kjvzu_v1/
AB  - Psychological constructs are often organized hierarchically, making accurate identification of their narrowest dimensions essential to recover broader levels of organization. Existing network methods for this task are limited by either the resolution limit of modularity or the variability introduced by terminating community detection prematurely. We introduce Pairwise Resolution Iteration via Subgraph Modularity (PRISM), a community detection procedure designed to identify dimensions below the resolution limit without requiring a tunable parameter. We evaluated PRISM using 320,000 samples generated from second order factor models across 3,200 conditions that varied the numbers of first and second order factors, factor loadings, indicators per factor, sample size, skew, overlapping dimensions, population error, and correlations among second order factors. PRISM was compared with lower order Louvain and exploratory factor analysis (EFA) paired with several traditional dimensionality methods, many of which set the depth of the bass-ackward estimation procedure. Recovery was evaluated using dimensionality accuracy, bias, and structural accuracy. PRISM generally provided the most accurate and least biased recovery at both levels and maintained strong performance at smaller sample sizes and extreme skew. overlapping dimensions reduced performance across methods, and both network methods performed poorly when overlapping dimensions were combined with few indicators, weak first order loadings, and strong second order loadings. EFA paired with parallel analysis based on principal component eigenvalues was the strongest traditional alternative, particularly in exceptionally large samples. These findings support PRISM as a robust general procedure to recover each level of a hierarchical structure.
ER  -

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