Liu Xiang, Yang James, Chae Hui Soo, Natriello Gary
Teachers College, Columbia University, New York, USA.
Educational Testing Service, 03-T, 660 Rosedale Road, Princeton, NJ, 08541, USA.
Psychometrika. 2020 Jun;85(2):502-525. doi: 10.1007/s11336-020-09712-7. Epub 2020 Jun 16.
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 [Formula: see text]. 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.
为了构建关于人参数的假设检验和置信区间，我们将统计量的幂散度（PD）族推广到双参数逻辑斯蒂项目反应理论（IRT）模型。著名的得分检验统计量是所提出的PD族的一个特殊情况。我们还证明了所提出的PD统计量渐近等价且依分布收敛于[公式：见原文]。此外，引入了矩匹配方法来比较统计量并在PD族中选择最优统计量。模拟结果表明，对于某些PD统计量，即使在小样本量情况下，相关置信区间的覆盖率也能得到很好的控制。与其他一些方法相比，相关置信区间在保持足够覆盖率的同时长度更短。通过分析一个实际数据集证明了所提方法的实用性。
