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Nonparametric Item Response Curve Estimation With Correction for Measurement Error

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  • Hongwen Guo
  • Sandip Sinharay

Abstract

Nonparametric or kernel regression estimation of item response curves (IRCs) is often used in item analysis in testing programs. These estimates are biased when the observed scores are used as the regressor because the observed scores are contaminated by measurement error. Accuracy of this estimation is a concern theoretically and operationally. This study investigates the deconvolution kernel estimation of IRCs, which corrects for the measurement error in the regressor variable. A comparison of the traditional kernel estimation and the deconvolution estimation of IRCs is carried out using both simulated and operational data. It is found that, in item analysis, the traditional kernel estimation is comparable to the deconvolution kernel estimation in capturing important features of the IRC.

Suggested Citation

  • Hongwen Guo & Sandip Sinharay, 2011. "Nonparametric Item Response Curve Estimation With Correction for Measurement Error," Journal of Educational and Behavioral Statistics, , vol. 36(6), pages 755-778, December.
    • Handle: RePEc:sae:jedbes:v:36:y:2011:i:6:p:755-778
    DOI: 10.3102/1076998610396891
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    References listed on IDEAS

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    1. Wang, Xiao-Feng & Wang, Bin, 2011. "Deconvolution Estimation in Measurement Error Models: The R Package decon," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i10).
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    3. Delaigle, Aurore & Fan, Jianqing & Carroll, Raymond J., 2009. "A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 348-359.
    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. Wand, M. P., 1998. "Finite sample performance of deconvolving density estimators," Statistics & Probability Letters, Elsevier, vol. 37(2), pages 131-139, February.
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    Keywords

    IRC; IRT; CTT; measurement error;
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