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Rotation Local Solutions in Multidimensional Item Response Theory Models
Hoang V Nguyen1, Niels G Waller1
1University of Minnesota, Twin Cities, Minneapolis, USA.
Educational and Psychological Measurement
|November 1, 2024
Summary
Geomin rotation often yields local solutions in multidimensional, two-parameter logistic (M2PL) models, but these solutions may differ in measurement precision. Fit indices may misidentify the best rotation when multiple solutions arise.
Area of Science:
- Psychometrics
- Statistical Modeling
- Educational Measurement
Background:
- Factor rotation is crucial for interpreting complex multidimensional item response models.
- Local solutions (LS) in factor rotation can arise, potentially affecting model interpretation.
- The multidimensional, two-parameter logistic (M2PL) model is widely used in educational and psychological assessments.
Purpose of the Study:
- To investigate the convergence rates of local solutions (LS) for oblimin and geomin rotation algorithms in M2PL models.
- To examine the influence of various factors (slope parameters, indicators per factor, cross-loadings, factor correlations, model error, sample size) on LS rates.
- To assess the impact of LS on latent trait estimation precision and the reliability of structural fit indices.
Main Methods:
- Extensive Monte Carlo simulation study involving over 19,200 datasets across 96 model conditions.
- Simulation of M2PL models with correlated major and uncorrelated minor factors to represent model error.
- Performance evaluation of oblimin and geomin rotation algorithms, including over 7.6 million rotations.
Main Results:
- Both oblimin and geomin algorithms converged to local solutions under specific conditions.
- Geomin rotation demonstrated higher local solution rates across a majority of the simulated models.
- Identical item response patterns yielding local solutions resulted in varying latent trait estimates and measurement precision.
- Quantitative structural fit indices often misidentified the most accurate rotation when multiple solutions were present.
Conclusions:
- The choice of rotation algorithm (geomin vs. oblimin) impacts the likelihood of obtaining local solutions in M2PL models.
- Local solutions can lead to discrepancies in latent trait estimation and measurement precision.
- Standard fit indices may not reliably identify the best rotation when multiple solutions emerge, necessitating careful interpretation.
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