The latent attribute space in cognitive diagnosis models (CDMs) is often assumed to be unstructured or saturated. In recent years, the number of latent attributes in real tests has often been found to be large, and polytomous latent attributes have been advocated. Therefore, it is preferable to adopt substantive theories to connect seemingly unrelated latent attributes, to replace the unstructured or saturated latent structural models (LSMs) with structured or parsimonious ones, with simplified parameter estimation. In the present study, we developed a partial mastery, higher-order LSM for polytomous attributes, which was built upon the framework of adjacent-category logit models to account for a higher-order latent structure of multiple polytomous attributes. The proposed model can be incorporated into many existing CDMs. We conducted simulations to evaluate the psychometric properties of the proposed model and obtained good parameter recovery. We then provided an empirical example to demonstrate the applications and the advantages of the proposed model.

中文翻译：

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认知诊断评估中多分属性的部分掌握、高阶潜在结构模型

认知诊断模型 (CDM) 中的潜在属性空间通常被假定为非结构化或饱和的。近年来，经常发现实际测试中的潜在属性数量较多，提倡多分潜在属性。因此，最好采用实质性理论来连接看似无关的潜在属性，用结构化或简约的模型代替非结构化或饱和的潜在结构模型（LSM），并简化参数估计。在本研究中，我们为多分属性开发了一种部分掌握的高阶 LSM，它建立在相邻类别 logit 模型的框架上，以解释多个多分属性的高阶潜在结构。提议的模型可以并入许多现有的 CDM。我们进行了模拟以评估所提出模型的心理测量特性，并获得了良好的参数恢复。然后，我们提供了一个实证示例来演示所提出模型的应用和优势。