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Modeling Omitted and Not-Reached Items in IRT Models

机译：IRT模型中省略和未达到的项目

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摘要

Item nonresponse is a common problem in educational and psychological assessments. The probability of unplanned missing responses due to omitted and not-reached items may stochastically depend on unobserved variables such as missing responses or latent variables. In such cases, missingness cannot be ignored and needs to be considered in the model. Specifically, multidimensional IRT models, latent regression models, and multiple-group IRT models have been suggested for handling nonignorable missing responses in latent trait models. However, the suitability of the particular models with respect to omitted and not-reached items has rarely been addressed. Missingness is formalized by response indicators that are modeled jointly with the researcher's target model. We will demonstrate that response indicators have different statistical properties depending on whether the items were omitted or not reached. The implications of these differences are used to derive a joint model for nonignorable missing responses with ability to appropriately account for both omitted and not-reached items. The performance of the model is demonstrated by means of a small simulation study.
机译：项目无反应是教育和心理评估中的一个常见问题。由于遗漏和未到达项目而导致计划外缺失响应的概率可能随机取决于未观察到的变量，如缺失响应或潜在变量。在这种情况下，不能忽略缺失，需要在模型中加以考虑。具体而言，多维IRT模型、潜在回归模型和多组IRT模型被建议用于处理潜在特质模型中不可忽略的缺失反应。然而，关于遗漏和未达到项目的特定模型的适用性很少得到解决。缺失通过与研究者的目标模型联合建模的响应指标形式化。我们将证明响应指标具有不同的统计特性，这取决于项目是否被忽略。这些差异的含义被用来推导一个不可忽略的缺失反应的联合模型，该模型能够适当地解释遗漏和未达到的项目。通过一个小型仿真研究，证明了该模型的性能。

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