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IRT test equating in complex linkage plans.

Michela Battauz1

  • 1Department of Economics and Statistics, University of Udine, Via Tomadini 30/A, 33100, Udine, Italy, michela.battauz@uniud.it.

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This study presents item response theory equating methods for complex linkage plans using the common-item nonequivalent group design. An efficient averaging method for equating coefficients is introduced, with derived standard errors for indirect and average equating.

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Statistical Modeling

Background:

  • Equating is essential for comparing scores from different test forms.
  • Complex linkage plans with multiple forms and paths increase equating challenges.
  • The common-item nonequivalent group design is frequently used in large-scale assessments.

Purpose of the Study:

  • To develop and evaluate item response theory (IRT) equating methods for complex linkage plans.
  • To propose an efficient method for averaging equating coefficients across different linking paths.
  • To derive asymptotic standard errors for indirect and average equating coefficients.

Main Methods:

  • Application of item response theory (IRT) equating.
  • Utilizing the common-item nonequivalent group design.
  • Developing an averaging technique for multiple equating coefficients.
  • Deriving asymptotic standard errors for statistical inference.

Main Results:

  • An efficient method for averaging equating coefficients was developed.
  • Asymptotic standard errors for indirect and average equating were derived.
  • The proposed methodology was validated through simulation studies and a real data example.

Conclusions:

  • The presented IRT equating methods effectively address complex linkage plans.
  • The averaging method provides a more stable and reliable equating coefficient.
  • The derived standard errors allow for accurate statistical inference in complex equating scenarios.