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The Impact of Variability of Item Parameter Estimators on Test Information Function

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  • Jinming Zhang

Abstract

The impact of uncertainty about item parameters on test information functions is investigated. The information function of a test is one of the most important tools in item response theory (IRT). Inaccuracy in the estimation of test information can have substantial consequences on data analyses based on IRT. In this article, the major part (called the adjusted term) of the deviation of an estimated test information function from the true test information function due to the uncertainty of item parameters was approximated asymptotically, and a simulation study shows that this approximation captures the difference between the estimated and the true information functions rather well. A real data example shows that the magnitude of an estimated adjusted term can be substantially large when a sample size is relatively small.

Suggested Citation

  • Jinming Zhang, 2012. "The Impact of Variability of Item Parameter Estimators on Test Information Function," Journal of Educational and Behavioral Statistics, , vol. 37(6), pages 737-757, December.
    • Handle: RePEc:sae:jedbes:v:37:y:2012:i:6:p:737-757
    DOI: 10.3102/1076998612458321
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    References listed on IDEAS

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    1. Robert Tsutakawa & Jane Johnson, 1990. "The effect of uncertainty of item parameter estimation on ability estimates," Psychometrika, Springer;The Psychometric Society, vol. 55(2), pages 371-390, June.
    2. David Thissen & Howard Wainer, 1982. "Some standard errors in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 397-412, December.
    3. Sebie Oosterloo, 1984. "Confidence Intervals For Test Information And Relative Efficiency," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 38(2), pages 91-107, June.
    4. Jinming Zhang & Minge Xie & Xiaolan Song & Ting Lu, 2011. "Investigating the Impact of Uncertainty About Item Parameters on Ability Estimation," Psychometrika, Springer;The Psychometric Society, vol. 76(1), pages 97-118, January.
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