Learning Latent and Hierarchical Structures in Cognitive Diagnosis Models
Learning Latent and Hierarchical Structures in Cognitive Diagnosis Models
复制标题
DOI：
10.1007/s11336-022-09867-5
复制
发表时间：
2021-04
期刊：
影响因子：
3
通讯作者：
Chenchen Ma;Ouyang Jing;Gongjun Xu
中科院分区：
文献类型：
--
作者：
Chenchen Ma;Ouyang Jing;Gongjun Xu
认知诊断模型是一类特殊的离散隐变量模型，广泛应用于教育和心理测量领域。CDMs的一个关键组成部分是Q矩阵，它表征了项目与潜在属性之间的依赖结构。此外，在许多应用中，研究人员还假设潜在属性之间存在一定的层次结构来表征它们的依赖性。在大多数CDM应用中，属性-属性层次结构，项目-属性Q矩阵，项目级诊断模型，以及潜在属性的数量，需要完全或部分预先指定，然而，这可能是主观的和错误的，最近的许多研究指出。本文认为，共同学习这些潜在的和层次结构的CDM从观测数据与最小的模型假设的问题。具体而言，惩罚似然方法提出了选择的属性数量和估计的潜在和层次结构的同时。为了提高计算效率，提出了一种期望最大化（EM）算法，并在较弱的条件下建立了统计一致性理论。仿真研究和教育评估中真实的数据应用表明，该方法具有良好的性能。
Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models that are widely used in educational and psychological measurement. A key component of CDMs is the Q-matrix characterizing the dependence structure between the items and the latent attributes. Additionally, researchers also assume in many applications certain hierarchical structures among the latent attributes to characterize their dependence. In most CDM applications, the attribute–attribute hierarchical structures, the item-attribute Q-matrix, the item-level diagnostic models, as well as the number of latent attributes, need to be fully or partially pre-specified, which however may be subjective and misspecified as noted by many recent studies. This paper considers the problem of jointly learning these latent and hierarchical structures in CDMs from observed data with minimal model assumptions. Specifically, a penalized likelihood approach is proposed to select the number of attributes and estimate the latent and hierarchical structures simultaneously. An expectation-maximization (EM) algorithm is developed for efficient computation, and statistical consistency theory is also established under mild conditions. The good performance of the proposed method is illustrated by simulation studies and real data applications in educational assessment.