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.

中文翻译：

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IRT 模型中人员参数的幂发散统计族

我们将功率散度 (PD) 统计族推广到双参数逻辑 IRT 模型，目的是构建人员参数的假设检验和置信区间。众所周知的分数测试统计量是提议的 PD 系列的一个特例。我们还证明了所提出的 PD 统计量是渐近等价的，并且在分布上收敛于 $$\chi _{1}^2$$ χ 1 2 。此外，还引入了一种矩匹配方法来比较统计数据并在 PD 家族中选择最优的一个。模拟结果表明，即使在某些 PD 统计数据的小样本量下，相关置信区间的覆盖率也得到了很好的控制。与其他一些方法相比，相关的置信区间显示出更小的长度，同时保持足够的覆盖率。