On Permissible Attribute Classes in Noncompensatory Cognitive Diagnosis Models

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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