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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, Washington, USA. lzt713@gmail.com.

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Summary
This summary is machine-generated.

This study introduces new person fit statistics, and , for the Rasch testlet model, extending existing methods for item response theory. These statistics effectively detect aberrant responses in complex test structures.

Keywords:
IRTPerson fitRasch testlet model

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Statistical Modeling

Background:

  • Established person fit statistics like and are limited to unidimensional or joint multidimensional item response theory (IRT) models.
  • Existing methods often require joint estimation of all latent traits, posing computational challenges.

Purpose of the Study:

  • To propose novel person fit statistics, and , specifically for the Rasch testlet model.
  • To extend the applicability of person fit evaluation to mixed-effects IRT models.
  • To provide computational algorithms for the proposed statistics.

Main Methods:

  • Development of and statistics based on a marginalized maximum likelihood ability estimator.
  • Extension of the Lord-Wingersky algorithm for computational efficiency.
  • Simulation studies to evaluate Type I error rates and power.

Main Results:

  • The proposed statistic demonstrates Type I error rates close to nominal levels.
  • shows satisfactory power in detecting aberrant responses.
  • The statistics reduce to established and for unidimensional models.

Conclusions:

  • The new statistics offer a robust method for person fit evaluation in Rasch testlet models.
  • These methods enhance the assessment of response behavior in mixed-structure tests.
  • The proposed statistics broaden the range of IRT models for which person fit can be assessed.