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Rotation Local Solutions in Multidimensional Item Response Theory Models.

Hoang V Nguyen1, Niels G Waller1

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Educational and Psychological Measurement
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Summary
This summary is machine-generated.

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.

Keywords:
factor rotationsgeominlocal solutionsmultidimensional item response theoryoblimin

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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.