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Item response theory-based continuous test norming.

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A new method, 2PL-norm, models item responses for psychological testing norms, offering greater accuracy than raw score methods. It provides superior credible interval coverage but may be less precise at the extreme ends of the score distribution.

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Area of Science:

  • Psychometrics
  • Psychological Measurement
  • Statistical Modeling

Background:

  • Norm-referenced psychological testing relies on standardized scores relative to a reference population.
  • Current continuous norming methods use raw test scores, overlooking individual item response data.
  • Age-dependent norming requires accurate transformation of raw scores into standardized scores.

Purpose of the Study:

  • To introduce a novel Bayesian item response theory model, 2PL-norm, for continuous norming in psychological testing.
  • To compare the accuracy and coverage of 2PL-norm against established raw score-based norming methods (cNORM, GAMLSS).
  • To provide practical guidance on selecting appropriate norming methods based on model assumptions and analytical goals.

Main Methods:

  • Developed a Bayesian two-parameter logistic (2PL) item response theory model (2PL-norm) incorporating age-dependent latent trait distributions.
  • Modeled individual item scores rather than aggregate raw scores.
  • Derived norms from estimated latent trait scores and age-dependent distribution parameters.

Main Results:

  • 2PL-norm demonstrated superior accuracy and credible interval coverage compared to cNORM and GAMLSS in simulations.
  • Raw score-based methods, particularly GAMLSS, showed better performance at the extreme tails of the norms.
  • Empirical data analysis confirmed the practical application and comparison of 2PL-norm, cNORM, and GAMLSS.

Conclusions:

  • 2PL-norm offers a more accurate and reliable method for psychological test norming when its assumptions are met.
  • GAMLSS is a preferable alternative to cNORM and may be better suited for analyses focused on extreme score estimates.
  • The study provides code for implementing 2PL-norm, facilitating its adoption in empirical practice.