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A Quasi-Parametric Method for Fitting Flexible Item Response Functions

Author

Listed:
  • Longjuan Liang

    (Educational Testing Service)

  • Michael W. Browne

    (Ohio State University)

Abstract

If standard two-parameter item response functions are employed in the analysis of a test with some newly constructed items, it can be expected that, for some items, the item response function (IRF) will not fit the data well. This lack of fit can also occur when standard IRFs are fitted to personality or psychopathology items. When investigating reasons for misfit, it is helpful to compare item response curves (IRCs) visually to detect outlier items. This is only feasible if the IRF employed is sufficiently flexible to display deviations in shape from the norm. A quasi-parametric IRF that can be made arbitrarily flexible by increasing the number of parameters is proposed for this purpose. To take capitalization on chance into account, the use of Akaike information criterion or Bayesian information criterion goodness of approximation measures is recommended for suggesting the number of parameters to be retained. These measures balance the effect on fit of random error of estimation against systematic error of approximation. Computational aspects are considered and efficacy of the methodology developed is demonstrated.

Suggested Citation

  • Longjuan Liang & Michael W. Browne, 2015. "A Quasi-Parametric Method for Fitting Flexible Item Response Functions," Journal of Educational and Behavioral Statistics, , vol. 40(1), pages 5-34, February.
    • Handle: RePEc:sae:jedbes:v:40:y:2015:i:1:p:5-34
    DOI: 10.3102/1076998614556816
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    References listed on IDEAS

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    1. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    2. J. Ramsay & S. Winsberg, 1991. "Maximum marginal likelihood estimation for semiparametric item analysis," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 365-379, September.
    3. Carol Woods & David Thissen, 2006. "Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 281-301, June.
    4. J. Ramsay, 1991. "Kernel smoothing approaches to nonparametric item characteristic curve estimation," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 611-630, December.
    5. Carol M. Woods & David Thissen, 2006. "Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 281-301, June.
    6. J. Ramsay, 1977. "Monotonic weighted power transformations to additivity," Psychometrika, Springer;The Psychometric Society, vol. 42(1), pages 83-109, March.
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    Cited by:

    1. Leah M. Feuerstahler, 2019. "Metric Transformations and the Filtered Monotonic Polynomial Item Response Model," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 105-123, March.

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