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Bayesian Estimation of the Logistic Positive Exponent IRT Model

Author

Listed:
  • Heleno Bolfarine

    (Universidade de Sao Paulo)

  • Jorge Luis Bazan

    (Pontificia Universidad Católica, Perú)

Abstract

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric ICC treats both correct and incorrect answers symmetrically, which results in a logical contradiction in ordering examinees on the ability scale. A data set corresponding to a mathematical test applied in Peruvian public schools is analyzed, where comparisons with other parametric IRT models also are conducted. Several model comparison criteria are discussed and implemented. The main conclusion is that the LPE and RLPE IRT models are easy to implement and seem to provide the best fit to the data set considered.

Suggested Citation

  • Heleno Bolfarine & Jorge Luis Bazan, 2010. "Bayesian Estimation of the Logistic Positive Exponent IRT Model," Journal of Educational and Behavioral Statistics, , vol. 35(6), pages 693-713, December.
    • Handle: RePEc:sae:jedbes:v:35:y:2010:i:6:p:693-713
    DOI: 10.3102/1076998610375834
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    References listed on IDEAS

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    Cited by:

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    2. Shaobo Jin & Fan Yang-Wallentin, 2017. "Asymptotic Robustness Study of the Polychoric Correlation Estimation," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 67-85, March.

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