Abstract
In cognitive diagnostic assessment (CDA), clustering analysis is an efficient approach to classify examinees into attribute-homogeneous groups. Many researchers have proposed different methods, such as the nonparametric method with Hamming distance, K-means method, and hierarchical agglomerative cluster analysis, to achieve the classification goal. In this paper, according to their responses, we introduce a spectral clustering algorithm (SCA) to cluster examinees. Simulation studies are used to compare the classification accuracy of the SCA, K-means algorithm, G-DINA model and its related reduced cognitive diagnostic models. A real data analysis is also conducted to evaluate the feasibility of the SCA. Some research directions are discussed in the final section.
Highlights
In the past decades, there has been a significant increasing interest in cognitive diagnostic assessment (CDA) that allows for the purpose of identifying the presence or absence of specific fine-grained attributes required for solving problems on a test in educational and psychological assessment
The previous study had shown that K-means has favorable performance in clustering examinees who possess the same attribute profiles (Chiu et al, 2009)
We introduced the SCA for grouping examinees’ attribute profiles into specific clusters in CDA
Summary
There has been a significant increasing interest in cognitive diagnostic assessment (CDA) that allows for the purpose of identifying the presence or absence of specific fine-grained attributes required for solving problems on a test in educational and psychological assessment. One of them usually uses cognitive diagnosis models (CDMs) to estimate the attribute profile for each examinee, which can be called parametric technique. The differences between these CDMs are assumptions about how cognitive attributes affect examinees’ responses in CDAs. The deterministic input; noisy “and” gate (DINA; Junker and Sijtsma, 2001), and noisy input; deterministic “and” gate model (NIDA; Junker and Sijtsma, 2001) are the typical conjunctive models, which require examinees must master all required attributes, even lacking one required attribute will lead to a totally wrong response. Interpretable CDMs include the linear logistic model (LLM; Maris, 1999) the additive CDM (A-CDM; de la Torre, 2011) and the reduced reparameterized
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