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Asymptotically Correct Person Fit z-Statistics For the Rasch Testlet Model.

Zhongtian Lin1, Tao Jiang2, Frank Rijmen2

  • 1Financial Industry Regulatory Authority.

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Summary
This summary is machine-generated.

New person fit statistics, lzt and lzt*, are introduced for the Rasch testlet model, offering improved detection of aberrant responses in item response theory (IRT) analysis.

Keywords:
IRTPerson fitRasch testlet modellz statistic

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Item Response Theory

Background:

  • Established person fit statistics like lz and lz* are limited to unidimensional or joint multidimensional IRT models.
  • Existing methods often require simultaneous estimation of all latent traits, posing computational challenges.

Purpose of the Study:

  • To propose new person fit statistics, lzt and lzt*, specifically for the Rasch testlet model.
  • To extend the applicability of person fit evaluation to a broader range of IRT models, including those with testlet structures.

Main Methods:

  • Development of lzt and lzt* statistics based on a marginalized maximum likelihood ability estimator.
  • Extension of the Lord-Wingersky algorithm for the computation of the lzt* statistic.
  • Simulation studies to evaluate Type I error rates and power for detecting aberrant responses.

Main Results:

  • The proposed lzt* statistic demonstrates close-to-nominal Type I error rates and satisfactory power in simulations.
  • lzt and lzt* statistics generalize to lz and lz* for unidimensional models, validating their broader applicability.
  • A real data application illustrates the utility of the new statistics for mixed-structure tests.

Conclusions:

  • The lzt and lzt* statistics provide a valuable tool for assessing person fit within the Rasch testlet model.
  • These statistics enhance the evaluation of response behavior across a wider spectrum of IRT models.
  • The proposed methods are effective for identifying aberrant responses in complex testing structures.