Department of Human Development and Quantitative Methodology, University of Maryland, College Park, USA.
Department of Statistics and Operations Research, The University of North Carolina at Chapel Hill, Chapel Hill, USA.
Psychometrika. 2019 Sep;84(3):701-718. doi: 10.1007/s11336-019-09675-4. Epub 2019 Jul 1.
In applications of item response theory (IRT), it is often of interest to compute confidence intervals (CIs) for person parameters with prescribed frequentist coverage. The ubiquitous use of short tests in social science research and practices calls for a refinement of standard interval estimation procedures based on asymptotic normality, such as the Wald and Bayesian CIs, which only maintain desirable coverage when the test is sufficiently long. In the current paper, we propose a simple construction of second-order probability matching priors for the person parameter in unidimensional IRT models, which in turn yields CIs with accurate coverage even when the test is composed of a few items. The probability matching property is established based on an expansion of the posterior distribution function and a shrinkage argument. CIs based on the proposed prior can be efficiently computed for a variety of unidimensional IRT models. A real data example with a mixed-format test and a simulation study are presented to compare the proposed method against several existing asymptotic CIs.
在项目反应理论（IRT）的应用中，通常有兴趣计算具有规定的频率覆盖的个人参数的置信区间（CIs）。短测试在社会科学研究和实践中的广泛应用要求对基于渐近正态性的标准区间估计程序进行改进，例如 Wald 和贝叶斯 CIs，当测试足够长时，这些程序仅保持理想的覆盖范围。在本文中，我们提出了一种用于一维 IRT 模型中个人参数的二阶概率匹配先验的简单构造，这反过来又产生了即使测试仅由几个项目组成时也具有准确覆盖范围的 CIs。基于后验分布函数的展开和收缩论证来建立概率匹配特性。可以针对各种一维 IRT 模型有效地计算基于所提出的先验的 CIs。通过一个混合格式测试的实际数据示例和一个模拟研究来比较所提出的方法与几种现有的渐近 CIs。
