面向多域有序评估的内生性感知认知诊断模型
Endogeneity-Aware Cognitive Diagnostic Model for Multidomain Ordinal Assessments
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中文总结 AI 辅助
针对传统认知诊断模型无法表征多域潜在属性定向依赖的问题，提出内生性感知认知诊断模型EACDM，通过联合估计实现更准确的属性关系分析，在模拟与帕金森病数据中验证了其有效性。
中文摘要 AI 辅助
多域评估量表会产生有序项目反应，这类反应通常通过潜在属性概貌进行汇总。传统认知诊断模型（CDMs）可为这类概貌提供可解释的测量模型，但一般无法表示不同域间潜在属性的定向依赖关系。我们提出一种面向多变量有序评估的内生性感知认知诊断模型（EACDM），该模型结合了块结构诊断测量组件与逻辑结构组件：前者通过块对角Q矩阵将项目组与域特定二元属性关联，后者将一个属性块对另一个属性块及被试层面协变量进行回归，同时考虑潜在分类不确定性。该公式形成了一个简约框架，用于研究诊断属性间的内生关系，且不会破坏域特定测量结构。我们确立了Q矩阵、有效载荷、潜在概貌概率及结构系数的可识别性条件，并开发了马尔可夫链蒙特卡洛算法以联合估计测量与结构组件。模拟研究表明，所提EACDM能准确恢复项目参数、潜在结构及结构系数，而当存在内生性时，传统CDMs无法恢复真实值。我们将该方法应用于帕金森病数据，以探究非运动潜在特质如何与运动损伤概貌相关联。
英文摘要
Multidomain assessment batteries generate ordinal item responses that are often summarized through latent attribute profiles. Conventional cognitive diagnostic models (CDMs) provide interpretable measurement models for such profiles, but they typically do not represent directed dependence among latent attributes from distinct domains. We propose an endogeneity-aware cognitive diagnostic model (EACDM) for multivariate ordinal assessments. The model combines a block-structured diagnostic measurement component, in which item groups are linked to domain-specific binary attributes through a block-diagonal Q-matrix, with a logistic structural component, in which one attribute block is regressed on another block and subject-level covariates while accounting for latent classification uncertainty. This formulation yields a parsimonious framework for studying endogenous relationships among diagnostic attributes without collapsing domain-specific measurement structure. We establish identifiability conditions for the Q-matrix, effective loadings, latent-profile probabilities, and structural coefficients, and develop a Markov chain Monte Carlo algorithm for joint estimation of the measurement and structural components. Simulation studies demonstrate accurate recovery of item parameters, latent structures, and structural coefficients for the proposed EACDM, whereas conventional CDMs can fail to recover the ground truth when endogeneity is present. We apply the proposed method to Parkinson's disease data to examine how non-motor latent traits relate to motor impairment profiles.
