Assessing the Dimensionality of the Latent Attribute Space in Cognitive Diagnosis Through Testing for Conditional Independence

The higher-order structure and attribute hierarchical structure are two popular approaches to defining the latent attribute space in cognitive diagnosis models. However, to our knowledge, it is still impossible to integrate them to accommodate the higher-order latent trait and hierarchical attributes simultaneously. To address this issue, this article proposed a sequential higher-order latent structural model (LSM) by incorporating various hierarchical structures into a higher-order latent structure. The feasibility of the proposed higher-order LSM was examined using simulated data. Results indicated that, in conjunction with the deterministic-inputs, noisy “and” gate model, the sequential higher-order LSM produced considerable improvement in person classification accuracy compared with the conventional higher-order LSM, when a certain attribute hierarchy existed. An empirical example was presented as well to illustrate the application of the proposed LSM.

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Latent Attribute Space Tree Classifiers

Journal of Software ◽

10.3724/sp.j.1001.2009.03319 ◽

2010 ◽

Vol 20 (7) ◽

pp. 1735-1745

Author(s):

Ping HE ◽

Xiao-Hua XU ◽

Ling CHEN

Keyword(s):

Latent Attribute ◽

Attribute Space

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On Permissible Attribute Classes in Noncompensatory Cognitive Diagnosis Models

Methodology ◽

10.1027/1614-2241/a000079 ◽

2014 ◽

Vol 10 (3) ◽

pp. 100-107 ◽

Cited By ~ 6

Author(s):

Jürgen Groß ◽

Ann Cathrice George

Keyword(s):

Diagnostic Information ◽

Cognitive Diagnosis ◽

Latent Classes ◽

Psychometric Test ◽

Cognitive Diagnosis Models ◽

Dina Model

When a psychometric test has been completed by a number of examinees, an afterward analysis of required skills or attributes may improve the extraction of diagnostic information. Relying upon the retrospectively specified item-by-attribute matrix, such an investigation may be carried out by classifying examinees into latent classes, consisting of subsets of required attributes. Specifically, various cognitive diagnosis models may be applied to serve this purpose. In this article it is shown that the permission of all possible attribute combinations as latent classes can have an undesired effect in the classification process, and it is demonstrated how an appropriate elimination of specific classes may improve the classification results. As an easy example, the popular deterministic input, noisy “and” gate (DINA) model is applied to Tatsuoka’s famous fraction subtraction data, and results are compared to current discussions in the literature.

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