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Item Parameter Recovery: Sensitivity to Prior Distribution.

Christine E DeMars1, Paulius Satkus2

  • 1James Madison University, Harrisonburg, VA, USA.

Educational and Psychological Measurement
|July 26, 2024
PubMed
Summary

For item response theory models, applying Bayesian priors to marginal maximum likelihood estimation improves parameter estimates, especially with small sample sizes. Priors on c-parameters are beneficial for samples >= 500, while both a- and c-parameters need priors for samples of 100.

Keywords:
BMEIRTMMAPMMLprior distribution

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Area of Science:

  • Psychometrics
  • Statistical modeling
  • Educational measurement

Background:

  • Marginal maximum likelihood (MML) is a common estimation method for item response theory (IRT) models.
  • Bayesian priors are often incorporated into MML estimation for three-parameter logistic (3PL) models, particularly with small sample sizes, to address estimation challenges.
  • Guidance on selecting appropriate priors for MML estimation is limited.

Purpose of the Study:

  • To investigate the impact of prior distributions on parameter estimation in 3PL IRT models using MML.
  • To determine the effectiveness of priors on different parameters (a, b, c) across various sample sizes.
  • To evaluate the influence of prior mode and strength on parameter estimate bias and root mean squared error (RMSE).

Main Methods:

  • Simulation study with varying sample sizes (≤1000).
  • Estimation of 3PL IRT models using marginal maximum likelihood.
  • Application of Bayesian priors to item parameters (a, b, c).
  • Analysis of parameter bias and RMSE under different prior conditions.

Main Results:

  • Without priors, small sample sizes (≤1000) often resulted in extreme and implausible parameter estimates.
  • Priors on c-parameters improved estimation for samples of 500 or more.
  • Priors on both a- and c-parameters were necessary for samples of size 100.
  • Parameter bias was influenced by the prior mode, but not significantly by prior strength (unless extremely informative).
  • RMSE for a- and b-parameters showed minimal dependence on prior mode or strength.
  • RMSE for c-parameters was affected by the prior mode for c.

Conclusions:

  • Bayesian priors are crucial for stable MML estimation of 3PL IRT models, especially with limited data.
  • Strategic application of priors, particularly on c-parameters, can mitigate estimation issues.
  • The choice of prior mode is important for reducing bias in c-parameter estimates.