Department of Human Development, Teachers College of Columbia University, 525 West 120th Street, New York, NY, 10027-6696, USA.
Psychometrika. 2018 Mar;83(1):182-202. doi: 10.1007/s11336-017-9580-y. Epub 2017 Aug 23.
In educational and psychological measurement when short test forms are used, the asymptotic normality of the maximum likelihood estimator of the person parameter of item response models does not hold. As a result, hypothesis tests or confidence intervals of the person parameter based on the normal distribution are likely to be problematic. Inferences based on the exact distribution, on the other hand, do not suffer from this limitation. However, the computation involved for the exact distribution approach is often prohibitively expensive. In this paper, we propose a general framework for constructing hypothesis tests and confidence intervals for IRT models within the exponential family based on exact distribution. In addition, an efficient branch and bound algorithm for calculating the exact p value is introduced. The type-I error rate and statistical power of the proposed exact test as well as the coverage rate and the lengths of the associated confidence interval are examined through a simulation. We also demonstrate its practical use by analyzing three real data sets.
在教育和心理测量中，当使用简短的测试形式时，项目反应模型的个体参数的最大似然估计的渐近正态性不成立。因此，基于正态分布的个体参数的假设检验或置信区间可能存在问题。另一方面，基于精确分布的推断则不会受到这种限制。然而，精确分布方法的计算通常过于昂贵。在本文中，我们提出了一种基于精确分布的构建指数族中 IRT 模型的假设检验和置信区间的一般框架。此外，还引入了一种用于计算精确 p 值的有效分支定界算法。通过模拟，研究了所提出的精确检验的Ⅰ型错误率和统计功效以及相关置信区间的覆盖率和长度。我们还通过分析三个真实数据集展示了其实际用途。
