Two-level Mokken scale analysis is a generalization of Mokken scale analysis for multi-rater data. The bias of estimated scalability coefficients for two-level Mokken scale analysis, the bias of their estimated standard errors, and the coverage of the confidence intervals has been investigated, under various testing conditions. It was found that the estimated scalability coefficients were unbiased in all tested conditions. For estimating standard errors, the delta method and the cluster bootstrap were compared. The cluster bootstrap structurally underestimated the standard errors of the scalability coefficients, with low coverage values. Except for unequal numbers of raters across subjects and small sets of items, the delta method standard error estimates had negligible bias and good coverage. Post hoc simulations showed that the cluster bootstrap does not correctly reproduce the sampling distribution of the scalability coefficients, and an adapted procedure was suggested. In addition, the delta method standard errors can be slightly improved if the harmonic mean is used for unequal numbers of raters per subject rather than the arithmetic mean.

中文翻译：

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两级可伸缩系数的偏差及其标准误差。

两级Mokken规模分析是对多评估者数据的Mokken规模分析的概括。在各种测试条件下，已经研究了用于两级Mokken规模分析的估计可伸缩性系数的偏差，其估计的标准误差的偏差以及置信区间的覆盖范围。发现在所有测试条件下估计的可伸缩性系数均无偏倚。为了估计标准误差，比较了增量方法和群集引导程序。集群自举在结构上低估了可伸缩性系数的标准误差，覆盖范围值低。除了主题和少数项目集上的评分者数量不相等外，增量法标准误估计值的偏差和覆盖范围都可以忽略不计。事后模拟表明，群集引导程序无法正确地再现可伸缩性系数的采样分布，并建议了一种适应性程序。此外，如果将谐波平均值用于每个主题的评分者数量不相等，而不是将算术平均值用于谐波，则可以稍微改善增量法标准误差。