The Hierarchy Consistency Index: Evaluating Person Fit for Cognitive Diagnostic Assessment

Abstract

In this article, we introduce a person‐fit statistic called the hierarchy consistency index (HCI) to help detect misfitting item response vectors for tests developed and analyzed based on a cognitive model. The HCI ranges from −1.0 to 1.0, with values close to −1.0 indicating that students respond unexpectedly or differently from the responses expected under a given cognitive model. A simulation study was conducted to evaluate the power of the HCI in detecting different types of misfitting item response vectors. Simulation results revealed that the detection rate of the HCI was a function of type of misfit, item discriminating power, and test length. The best detection rates were achieved when the HCI was applied to tests that consisted of a large number of highly discriminating items. In addition, whether a misfitting item response vector can be correctly identified depends, to a large degree, on the number of misfits of the item response vector relative to the cognitive model. When misfitting response behavior only affects a small number of item responses, the resulting item response vector will not be substantially different from the expectations under the cognitive model and consequently may not be statistically identified as misfitting. As an item response vector deviates further from the model expectations, misfits are more easily identified and consequently higher detection rates of the HCI are expected.

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