Unidimensional community detection: A monte carlo simulation, grid search, and comparison

Area of Science:

• Psychometrics
• Network Science
• Statistical Modeling

Background:

• Unidimensionality is a core psychometric principle, yet assessing it in network psychometrics is challenging.
• Community detection algorithms, often optimizing modularity, can inaccurately penalize unidimensional structures.
• Modularity's bias towards multiple communities necessitates exploring alternative dimensionality assessment methods.

Purpose of the Study:

• To address the limitations of modularity in assessing unidimensionality within network psychometrics.
• To evaluate the performance of various community detection algorithms and statistical methods in recovering unidimensional and bidimensional structures.
• To identify optimal parameters for community detection algorithms to balance unidimensional and bidimensional recovery.

Main Methods:

• A Monte Carlo simulation was conducted using one- and two-factor models with varying degrees of model error.
• Several community detection algorithms (Leading Eigenvalue, Leiden, Louvain, Walktrap) were compared, with grid searches for optimal parameters.
• Performance was benchmarked against maximum likelihood factor analysis and parallel analysis (PA) using mean and 95th percentile eigenvalues.

Main Results:

• The Leiden and Louvain algorithms, alongside PA methods, demonstrated superior accuracy in recovering both unidimensional and bidimensional structures.
• These methods also exhibited the highest robustness when faced with model error (misfit of the population factor model).
• Optimal parameter settings were identified for community detection algorithms to improve dimensionality assessment.

Conclusions:

• Leiden, Louvain, and PA methods are recommended for accurate dimensionality assessment in psychometric networks.
• These methods offer reliable recovery of underlying structures and are robust to common data imperfections.
• Specific recommendations are provided for applying these methods under different unidimensional and bidimensional conditions.