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Summary
This summary is machine-generated.

This study compares linking methods for three-parameter testlet models. The item response function (IRF) and mean/least squares (MLS) methods effectively estimate linking coefficients, outperforming the test response function (TRF) method.

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item response theoryscale linking methodstestlet model

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Statistical Modeling

Background:

  • Test equating is crucial for score comparability across different test forms.
  • Previous work established the test response function (TRF) linking method for two-parameter testlet models.
  • Extending linking methods to more complex models, like the three-parameter testlet model, is essential for accurate measurement.

Purpose of the Study:

  • To formulate the linking task for a three-parameter testlet model using a bi-factor modeling perspective.
  • To present and compare three linking methods: TRF, mean/least squares (MLS), and item response function (IRF).
  • To evaluate the performance of different algorithms (genetic vs. quasi-Newton) in conjunction with these methods.

Main Methods:

  • Formulation of the three-parameter testlet model linking problem within a bi-factor modeling framework.
  • Implementation and comparison of TRF, MLS, and IRF linking methods.
  • Simulation studies to assess the accuracy of linking coefficient estimation under various conditions.
  • Evaluation of genetic algorithms versus quasi-Newton algorithms for optimization.

Main Results:

  • The item response function (IRF) and mean/least squares (MLS) methods demonstrated strong performance in estimating linking coefficients for testlet effects.
  • The test response function (TRF) method showed poorer performance in estimating these coefficients.
  • Genetic algorithms provided minimal improvement over other optimization methods for the TRF approach.
  • The minimization function for the TRF method was found to be less robust than that for the IRF method.

Conclusions:

  • The IRF and MLS methods are recommended for linking three-parameter testlet models due to their superior performance.
  • The choice of linking method significantly impacts the accuracy of equating.
  • Further research into optimizing the TRF method's minimization function may be warranted, or alternative methods should be prioritized.