Department of Decision Sciences, Bocconi University, via Roentgen 1, 20136, Milano, Italy.
Psychometrika. 2021 Mar;86(1):131-166. doi: 10.1007/s11336-021-09747-4. Epub 2021 Feb 3.
In this paper, we consider the Rasch model and suggest novel point estimators and confidence intervals for the ability parameter. They are based on a proposed confidence distribution (CD) whose construction has required to overcome some difficulties essentially due to the discrete nature of the model. When the number of items is large, the computations due to the combinatorics involved become heavy, and thus, we provide first- and second-order approximations of the CD. Simulation studies show the good behavior of our estimators and intervals when compared with those obtained through other standard frequentist and weakly informative Bayesian procedures. Finally, using the expansion of the expected length of the suggested interval, we are able to identify reasonable values of the sample size which lead to a desired length of the interval.
在本文中，我们考虑了 Rasch 模型，并为能力参数提出了新的点估计量和置信区间。它们基于一个提议的置信分布（CD），其构建需要克服一些由于模型的离散性质而产生的困难。当项目数量较大时，由于涉及到的组合学计算变得繁重，因此，我们提供了 CD 的一阶和二阶逼近。模拟研究表明，与其他标准的频率主义和弱信息贝叶斯方法相比，我们的估计量和区间具有良好的性能。最后，通过扩展建议区间的期望长度，我们能够确定合理的样本量值，从而得到所需的区间长度。
