Hybrid cognitive diagnostic model

Hybrid cognitive diagnostic model
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混合认知诊断模型

DOI:
10.1007/s41237-020-00111-x
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发表时间:
2020
期刊:
影响因子:
--
通讯作者:
K.
K.
中科院分区:
--
文献类型:
--
作者:
Yamaguchi;K.;& Okada;K.

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认知诊断模型可以根据属性之间的相互作用类型分为两类:析取和合取。前者的代表性示例是“确定性输入噪声或门”(DINO)模型,而后者的代表性示例是“确定性输入噪声与门”(DINA)模型。然而,将交互形式固定为析取或合取可能基于强假设。因此,我们开发了一个新的混合认知诊断模型,其中的项目反应函数表示为一个加权的析取和合取项目反应函数的混合。这使得有可能估计每个项目的每种相互作用类型的定量程度,同时将参数保持在合理的范围内。该模型被形式化为贝叶斯模型,并使用汉密尔顿蒙特卡罗算法进行估计。蒙特卡洛模拟证实了所提出的方法的足够的参数恢复。在对实际数学测试数据的实证应用中,该模型取得了比DINA和DINO模型更好的预测性能。所获得的混合权重的后验被认为是异质项目之间,表明所提出的方法的关键优势。
Cognitive diagnostic models can be classified into two categories based on the type of interaction between attributes: disjunctive and conjunctive. A representative example of the former is the “Deterministic Input Noisy-Or gate” (DINO) model, and of the latter is the “Deterministic Input Noisy-And gate” (DINA) model. However, fixing the interaction form to be either disjunctive or conjunctive may be based on a strong assumption. Therefore, we developed a new hybrid cognitive diagnostic model in which the item response function is represented as a weighted mixture of disjunctive and conjunctive item response functions. This made it possible to estimate the quantitative degree of each interaction type for each item, while keeping the parameters within reasonable limits. The proposed model was formalized as a Bayesian model and estimated using the Hamiltonian Monte Carlo algorithm. A Monte Carlo simulation confirmed adequate parameter recovery of the proposed method. In an empirical application to actual mathematics test data, the proposed model achieved better predictive performance than the DINA and DINO models. The obtained posteriors of the mixture weights were found to be heterogeneous among items, indicating key advantages of the proposed approach.
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