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Bootstrap-Calibrated Interval Estimates for Latent Variable Scores in Item Response Theory

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  • Yang Liu

    (University of Maryland)

  • Ji Seung Yang

    (University of Maryland)

Abstract

In most item response theory applications, model parameters need to be first calibrated from sample data. Latent variable (LV) scores calculated using estimated parameters are thus subject to sampling error inherited from the calibration stage. In this article, we propose a resampling-based method, namely bootstrap calibration (BC), to reduce the impact of the carryover sampling error on the interval estimates of LV scores. BC modifies the quantile of the plug-in posterior, i.e., the posterior distribution of the LV evaluated at the estimated model parameters, to better match the corresponding quantile of the true posterior, i.e., the posterior distribution evaluated at the true model parameters, over repeated sampling of calibration data. Furthermore, to achieve better coverage of the fixed true LV score, we explore the use of BC in conjunction with Jeffreys’ prior. We investigate the finite-sample performance of BC via Monte Carlo simulations and apply it to two empirical data examples.

Suggested Citation

  • Yang Liu & Ji Seung Yang, 2018. "Bootstrap-Calibrated Interval Estimates for Latent Variable Scores in Item Response Theory," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 333-354, June.
    • Handle: RePEc:spr:psycho:v:83:y:2018:i:2:d:10.1007_s11336-017-9582-9
    DOI: 10.1007/s11336-017-9582-9
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    References listed on IDEAS

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    Cited by:

    1. Chun Wang & Gongjun Xu & Xue Zhang, 2019. "Correction for Item Response Theory Latent Trait Measurement Error in Linear Mixed Effects Models," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 673-700, September.
    2. Xiang Liu & James Yang & Hui Soo Chae & Gary Natriello, 2020. "Power Divergence Family of Statistics for Person Parameters in IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 502-525, June.
    3. Yang Liu & Ji Seung Yang & Alberto Maydeu-Olivares, 2019. "Restricted Recalibration of Item Response Theory Models," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 529-553, June.

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