In large-scale educational assessment data consistent with a simple-structure multidimensional item response theory (MIRT) model, where every item measures only one latent variable, separate unidimensional item response theory (UIRT) models for each latent variable are often calibrated for practical reasons. While this approach can be valid for data from a linear test, unacceptable item parameter estimates are obtained when data arise from a multistage test (MST). We explore this situation from a missing data perspective and show mathematically that MST data will be problematic for calibrating multiple UIRT models but not MIRT models. This occurs because some items that were used in the routing decision are excluded from the separate UIRT models, due to measuring a different latent variable. Both simulated and real data from the National Assessment of Educational Progress are used to further confirm and explore the unacceptable item parameter estimates. The theoretical and empirical results confirm that only MIRT models are valid for item calibration of multidimensional MST data.

中文翻译：

---

用于多维多阶段测试的项目参数估计的IRT和MIRT模型

在符合简单结构多维项目反应理论（MIRT）模型的大型教育评估数据中，每个项目仅测量一个潜在变量，出于实际原因，通常会针对每个潜在变量对单独的一维项目反应理论（UIRT）模型进行校准。尽管此方法对于线性测试的数据可能有效，但是当数据来自多阶段测试（MST）时，会获得不可接受的项目参数估计值。我们从数据丢失的角度探讨了这种情况，并从数学上证明了MST数据对于校准多个UIRT模型而不是MIRT模型会产生问题。发生这种情况的原因是，由于测量了不同的潜在变量，因此从单独的UIRT模型中排除了在路由决策中使用的某些项目。来自国家教育进展评估的模拟数据和真实数据都用于进一步确认和探索不可接受的项目参数估计。理论和经验结果证实，只有MIRT模型对多维MST数据的项目校准有效。