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Asymptotic standard errors for reliability coefficients in item response theory.

Youjin Sung1, Yang Liu1

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This study introduces a new method to calculate standard errors for reliability coefficients in item response theory (IRT) models, accounting for both item parameter and sampling variability.

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Educational Measurement

Background:

  • Reliability coefficients are crucial for assessing measurement consistency.
  • Existing methods for standard error (SE) calculation in item response theory (IRT) models may not fully capture all sources of sampling variability.
  • Distinguishing between classical test theory (CTT) reliability and proportional reduction in mean squared error (PRMSE) is important.

Purpose of the Study:

  • To develop a general strategy for deriving standard errors (SEs) of reliability coefficients under item response theory (IRT) models.
  • To incorporate both item parameter estimation variability and sampling variability from moment substitution.
  • To apply the general theory to derive SEs for CTT reliability and PRMSE under the graded response model.

Main Methods:

  • Proposed a general strategy to derive SEs for reliability estimators.
  • Incorporated variability from both item parameter estimation and sample moment substitution.
  • Applied the theory to derive SEs for CTT reliability and PRMSE under the graded response model.

Main Results:

  • The derived SEs accurately capture sampling variability for reliability coefficients in IRT models.
  • The method is effective across various test lengths in moderate to large samples.
  • Simulation results validated the accuracy of the proposed SE formulas.

Conclusions:

  • The proposed general strategy provides a robust method for estimating model-based reliability coefficients and their SEs in IRT.
  • The derived SEs are accurate and applicable to reliability estimation in psychometric modeling.
  • This work advances the understanding of reliability estimation within IRT frameworks.