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Factor Retention in Ordinal Data Under Local Item Dependence: A Monte Carlo Comparison of Correlation Estimators and
1Division of Measurement and Evaluation in Education, Department of Educational Sciences, Trakya University, Edirne, Türkiye.
Educational and Psychological Measurement
|July 20, 2026
Summary
Local item dependence (LID) can distort factor retention methods in ordinal data. Exploratory Graph Analysis with the TMFG method is most resilient to LID, offering reliable dimensionality assessment.
Area of Science:
- Psychometrics
- Statistical modeling
- Data analysis
Background:
- Local item dependence (LID) poses challenges for dimensionality assessment in ordinal data.
- The impact of LID on various factor retention methods is not fully understood.
Purpose of the Study:
- To evaluate the performance of five factor retention methods under different LID conditions.
- To assess the influence of six correlation matrix estimators on factor retention accuracy.
- To determine the resilience of factor retention methods to varying LID structures and correlation estimators.
Main Methods:
- A Monte Carlo simulation involving 900 conditions and 450,000 datasets.
- Evaluation of five factor retention methods: Minimum Average Partial (MAP), Parallel Analysis (PA), and three Exploratory Graph Analysis (EGA) variants (EGA-Walk, EGA-Leiden, EGA-TMFG).
- Comparison of six correlation matrix estimators: Pearson, polychoric, and four fuzzy-based variants.
Main Results:
- Pairwise LID led to overfactoring in GLASSO-based EGA methods and PA.
- Testlet LID resulted in high MAP accuracy due to error compensation, not structural identification.
- Correlation matrix choice had minimal impact; fuzzy variants were similar to Pearson.
- Polychoric estimator showed condition-dependent performance, with benefits in local independence but drawbacks under severe testlet-LID.
- EGA-TMFG demonstrated the highest resilience to LID.
Conclusions:
- LID structure and factor loading strength are key determinants of retention accuracy.
- Correlation matrix preprocessing offers no significant corrective benefit for LID.
- EGA-TMFG is recommended for dimensionality assessment when local dependence is suspected.
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