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Bootstrap-Calibrated Interval Estimates for Latent Variable Scores in Item Response Theory.
1Department of Human Development and Quantitative Methodology, University of Maryland, 1230B Benjamin Building, College Park, MD, 20742 , USA. yliu87@umd.edu.
Psychometrika
|September 8, 2017
Summary
Bootstrap calibration (BC) reduces sampling error in latent variable (LV) scores by adjusting posterior quantiles. This method improves interval estimates for LV scores derived from calibrated item response theory models.
Area of Science:
- Psychometrics
- Statistical modeling
- Educational measurement
Background:
- Item response theory (IRT) models require parameter calibration from data.
- Latent variable (LV) scores are affected by sampling error from parameter calibration.
- Existing methods may not fully account for calibration-induced error in LV score estimation.
Purpose of the Study:
- To introduce a novel resampling-based method, bootstrap calibration (BC), to mitigate carryover sampling error in LV score interval estimates.
- To enhance the accuracy of interval estimates for LV scores in IRT applications.
- To improve the coverage properties of LV score estimates.
Main Methods:
- Proposed bootstrap calibration (BC) method modifies plug-in posterior quantiles.
- BC aims to align plug-in posterior quantiles with true posterior quantiles across repeated data sampling.
- Investigated the use of BC with Jeffreys' prior for improved coverage of true LV scores.
Main Results:
- Monte Carlo simulations evaluated the finite-sample performance of the BC method.
- The BC method demonstrated a reduction in the impact of sampling error on LV score interval estimates.
- Application to empirical data supported the effectiveness of BC in improving score estimation.
Conclusions:
- Bootstrap calibration (BC) offers a viable approach to reduce sampling error in latent variable score estimation within IRT.
- The BC method enhances the reliability and accuracy of interval estimates for LV scores.
- Combining BC with appropriate priors, like Jeffreys' prior, can further improve estimation performance.
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