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Identifiability and Cognitive Diagnosis Models

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Handbook of Diagnostic Classification Models

Part of the book series: Methodology of Educational Measurement and Assessment ((MEMA))

Abstract

Cognitive Diagnosis Models (CDMs) are popular statistical tools in cognitive diagnosis assessment. CDMs can be viewed as restricted latent class models with constraints introduced by the Q-matrix and assumptions of how skill variables that are assigned to items via the Q-Matrix interact in the item function. As many other latent variable models do, the CDMs often suffer from nonidentifiability. This chapter focuses on the identifiability issue of the CDMs and present conditions to ensure identifiability, which can be directly applied to most of the CDMs.

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Notes

  1. 1.

    For readers who are more interested in how to use the identifiability results in practice, this section can be skipped, as well as the discussion of Eqs. (16.12) and (16.13) and Remark 5, which are based on this section.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Michigan, Ann Arbor, MI, USA

    Gongjun Xu

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  1. Gongjun Xu
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Correspondence to Gongjun Xu .

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Editors and Affiliations

  1. National Board of Medical Examiners (NBME), Philadelphia, PA, USA

    Matthias von Davier

  2. Teachers College, Columbia University, New York, NY, USA

    Young-Sun Lee

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Xu, G. (2019). Identifiability and Cognitive Diagnosis Models. In: von Davier, M., Lee, YS. (eds) Handbook of Diagnostic Classification Models. Methodology of Educational Measurement and Assessment. Springer, Cham. https://doi.org/10.1007/978-3-030-05584-4_16

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  • DOI: https://doi.org/10.1007/978-3-030-05584-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-05583-7

  • Online ISBN: 978-3-030-05584-4

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