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Linking Item Response Model Parameters.

Wim J van der Linden1, Michelle D Barrett2

  • 1CTB/McGraw-Hill Education, 20 Ryan Ranch Road, Monterey, CA, 93940 , USA. wjvdlinden@gmail.com.

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|July 10, 2015
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Summary
This summary is machine-generated.

Linking item response model parameters does not require test equating. Instead, parameter linking is necessary due to the inherent lack of identifiability in item response models, adjusting for calibration restrictions.

Keywords:
3PL response modelitem calibrationlinking designlinking functionparameter identifiability

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Statistical Modeling

Background:

  • Item response models are widely used in educational and psychological assessments.
  • Linking item response model parameters across different calibrations is crucial for score comparability.
  • Current approaches often frame this as test equating, which may not be appropriate.

Purpose of the Study:

  • To challenge the conceptualization of parameter linking as test equating.
  • To propose that parameter linking is necessitated by model identifiability issues.
  • To formally characterize and derive linking functions for item response models.

Main Methods:

  • Theoretical analysis of item response models.
  • Development of theorems for linking functions.
  • Derivation of specific linking functions for the 3-parameter logistic (3PL) model.
  • Investigation of linking designs using common items or persons.

Main Results:

  • Item response models do not require test equating; parameter linking is driven by identifiability.
  • Formal characterization of linking functions for monotone, continuous response models.
  • Specific linking functions derived for different 3PL model parameterizations.
  • Methods to identify linking functions using commonalities in calibration designs.

Conclusions:

  • Parameter linking in item response models is fundamentally about addressing identifiability, not test equating.
  • The derived linking functions provide a formal framework for accurate parameter estimation across calibrations.
  • This approach offers a more precise method for maintaining score comparability in longitudinal or multi-form assessments.