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Multidimensional Polytomous DIF Detection Methods - A Monte Carlo Simulation Study.

Ana Ćosić Pilepić1, Tamara Mohorić1, Vladimir Takšić1

  • 1Faculty of Humanities and Social Sciences, Department of Psychology, University of Rijeka, Rijeka, Croatia.

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This study evaluated four methods for detecting differential item functioning (DIF) in complex data. Ordinal logistic regression, especially using latent trait estimates, showed the most reliable performance for identifying DIF in multidimensional assessments.

Keywords:
IRT likelihood ratio testMIMIC modeldifferential item functioninggraded response modellogistic regressionmultidimensional item response theorysimulation study

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Statistical Modeling

Background:

  • Differential Item Functioning (DIF) is crucial for ensuring fairness in assessments.
  • Detecting DIF in polytomous multidimensional data presents unique challenges.
  • Existing methods require evaluation for robustness under various conditions.

Purpose of the Study:

  • To compare the effectiveness of four DIF detection methods: IRT-LR, two ordinal logistic regression (OLR) approaches, and multidimensional MIMIC-interaction.
  • To evaluate method performance under simulated conditions varying DIF type, magnitude, group size, latent trait correlation, and group impact.
  • To identify the most robust and powerful method for DIF detection in simple-structure multidimensional polytomous data.

Main Methods:

  • A simulation study generated data from a two-dimensional graded response model with 28 five-category items.
  • Four DIF detection methods were applied: item response theory likelihood ratio test (IRT-LR), OLR with raw scores, OLR with latent trait estimates, and multidimensional MIMIC-interaction.
  • Simulation conditions manipulated DIF type (uniform, nonuniform), magnitude (0, 0.3, 0.6), group size ratio (1:1, 3:1), latent trait correlation (ρ = 0, 0.5), and group impact.

Main Results:

  • IRT-LR, OLR (raw scores), and OLR (latent trait estimates) generally controlled Type I error rates effectively.
  • The MIMIC-interaction model exhibited inflated Type I error in the presence of group impact.
  • All methods showed high power for moderate uniform DIF, but detection decreased for low or nonuniform DIF.
  • OLR with latent trait estimates demonstrated the most stable performance, balancing Type I error control and power.
  • OLR with raw scores performed better for moderate nonuniform DIF, while IRT-LR showed lower power.

Conclusions:

  • Regression-based approaches, particularly OLR using latent trait estimates, offer robust DIF detection for multidimensional polytomous assessments with simple structures.
  • The choice of method depends on specific data characteristics, especially the presence of group impact and the type of DIF.
  • Further research may explore extensions of these methods to more complex data structures.