Power Divergence Family of Statistics for Person Parameters in IRT Models

Xiang Liu (), James Yang, Hui Soo Chae and Gary Natriello
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Xiang Liu: Columbia University
James Yang: Columbia University
Hui Soo Chae: Columbia University
Gary Natriello: Columbia University

Psychometrika, 2020, vol. 85, issue 2, No 12, 502-525

Abstract: 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.

Keywords: power divergence family; IRT; sufficient statistics; asymptotic distribution; interval estimation (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11336-020-09712-7

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