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Efficient Standard Errors in Item Response Theory Models for Short Tests

机译：在短期测试中有效的项目响应理论模型中的高效标准误差

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摘要

In dichotomous item response theory (IRT) framework, the asymptotic standard error (ASE) is the most common statistic to evaluate the precision of various ability estimators. Easy-to-use ASE formulas are readily available; however, the accuracy of some of these formulas was recently questioned and new ASE formulas were derived from a general asymptotic theory framework. Furthermore, exact standard errors were suggested to better evaluate the precision of ability estimators, especially with short tests for which the asymptotic framework is invalid. Unfortunately, the accuracy of exact standard errors was assessed so far only in a very limiting setting. The purpose of this article is to perform a global comparison of exact versus (classical and new formulations of) asymptotic standard errors, for a wide range of usual IRT ability estimators, IRT models, and with short tests. Results indicate that exact standard errors globally outperform the ASE versions in terms of reduced bias and root mean square error, while the new ASE formulas are also globally less biased than their classical counterparts. Further discussion about the usefulness and practical computation of exact standard errors are outlined.
机译：在二分项响应理论（IRT）框架中，渐近标准误差（ASE）是评估各种能力估计器的精度最常见的统计数据。易于使用的ASE公式很容易获得;然而，最近一些这些公式的准确性受到质疑，并且新的ASE公式源自一般的渐近理论框架。此外，建议更好地评估能力估算器的精度，特别是渐近框架无效的短测试。不幸的是，到目前为止仅在一个非常限制的设置中评估了确切标准错误的准确性。本文的目的是为各种通常的IRT能力估算器，IRT模型以及短暂的测试进行渐近标准错误的完全比较（经典和新配方）渐近标准误差。结果表明，在减少偏差和根均方误差方面，全局标准误差全球优于ASE版本，而新的ASE公式也比其经典同行更少偏置。概述了关于确切标准误差的有用性和实际计算的进一步讨论。

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