The higher-order structure and attribute hierarchical structure are two popular approaches to defining the latent attribute space in cognitive diagnosis models. However, to our knowledge, it is still impossible to integrate them to accommodate the higher-order latent trait and hierarchical attributes simultaneously. To address this issue, this article proposed a sequential higher-order latent structural model (LSM) by incorporating various hierarchical structures into a higher-order latent structure. The feasibility of the proposed higher-order LSM was examined using simulated data. Results indicated that, in conjunction with the deterministic-inputs, noisy “and” gate model, the sequential higher-order LSM produced considerable improvement in person classification accuracy compared with the conventional higher-order LSM, when a certain attribute hierarchy existed. An empirical example was presented as well to illustrate the application of the proposed LSM.

中文翻译：

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认知诊断评估中分层属性的顺序高阶潜在结构模型

高阶结构和属性层次结构是在认知诊断模型中定义潜在属性空间的两种流行方法。然而，据我们所知，仍然不可能将它们集成在一起以同时容纳高阶潜在特征和层次属性。为了解决这个问题，本文通过将各种层次结构合并到高阶潜在结构中，提出了一个顺序的高阶潜在结构模型（LSM）。使用模拟数据检查了提出的高阶LSM的可行性。结果表明，与传统的高阶LSM相比，结合确定性输入，嘈杂的“和”门模型，相继的高阶LSM在人员分类准确性方面产生了可观的改善，当某个属性层次结构存在时。还提供了一个经验示例来说明所提出的LSM的应用。