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 模型并建议了能力参数的新点估计量和置信区间。它们基于建议的置信分布 (CD)，由于模型的离散性，其构造需要克服一些困难。当项目的数量很大时，由于所涉及的组合计算会变得很繁重，因此，我们提供了 CD 的一阶和二阶近似值。模拟研究表明，与通过其他标准常客和弱信息贝叶斯程序获得的估计量和区间相比，我们的估计量和区间表现良好。最后，使用建议间隔的预期长度的扩展，我们能够确定导致期望间隔长度的样本大小的合理值。