Person fit statistics are frequently used to detect aberrant behavior when assuming an item response model generated the data. A common statistic, \(l_z\), has been shown in previous studies to perform well under a myriad of conditions. However, it is well-known that \(l_z\) does not follow a standard normal distribution when using an estimated latent trait. As a result, corrections of \(l_z\), called \(l_z^*\), have been proposed in the literature for specific item response models. We propose a more general correction that is applicable to many types of data, namely survey or tests with multiple item types and underlying latent constructs, which subsumes previous work done by others. In addition, we provide corrections for multiple estimators of \(\theta \), the latent trait, including MLE, MAP and WLE. We provide analytical derivations that justifies our proposed correction, as well as simulation studies to examine the performance of the proposed correction with finite test lengths. An applied example is also provided to demonstrate proof of concept. We conclude with recommendations for practitioners when the asymptotic correction works well under different conditions and also future directions.

当假设项目响应模型生成数据时，人员匹配统计经常用于检测异常行为。一个常见的统计数据\(l_z\)在之前的研究中已被证明在无数条件下表现良好。然而，众所周知，\(l_z\)在使用估计的潜在特征时不遵循标准正态分布。因此，\(l_z\) 的更正，称为\(l_z^*\)，已在文献中提出用于特定项目响应模型。我们提出了一种更普遍的修正，适用于多种类型的数据，即具有多种项目类型和潜在结构的调查或测试，其中包含其他人以前所做的工作。此外，我们为\(\theta \) 的多个估计量提供了修正，即潜在特征，包括 MLE、MAP 和 WLE。我们提供分析推导来证明我们提出的修正是合理的，以及模拟研究以检查在有限测试长度下提出的修正的性能。还提供了一个应用示例来演示概念验证。当渐近校正在不同条件和未来方向下运行良好时，我们为从业者提出建议。