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Power Divergence Family of Statistics for Person Parameters in IRT Models

Author

Listed:
  • Xiang Liu

    (Columbia University
    Educational Testing Service)

  • James Yang

    (Columbia University)

  • Hui Soo Chae

    (Columbia University)

  • Gary Natriello

    (Columbia University)

Abstract

We generalize the power divergence (PD) family of statistics to the two-parameter logistic IRT model for the purpose of constructing hypothesis tests and confidence intervals of the person parameter. The well-known score test statistic is a special case of the proposed PD family. We also prove the proposed PD statistics are asymptotically equivalent and converge in distribution to $$\chi _{1}^2$$ χ 1 2 . In addition, a moment matching method is introduced to compare statistics and choose the optimal one within the PD family. Simulation results suggest that the coverage rate of the associated confidence interval is well controlled even under small sample sizes for some PD statistics. Compared to some other approaches, the associated confidence intervals exhibit smaller lengths while maintaining adequate coverage rates. The utilities of the proposed method are demonstrated by analyzing a real data set.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:85:y:2020:i:2:d:10.1007_s11336-020-09712-7
    DOI: 10.1007/s11336-020-09712-7
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    References listed on IDEAS

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    1. Yang Liu & Jan Hannig & Abhishek Pal Majumder, 2019. "Second-Order Probability Matching Priors for the Person Parameter in Unidimensional IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 701-718, September.
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