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Bridging Parametric and Nonparametric Methods in Cognitive Diagnosis

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Abstract

A number of parametric and nonparametric methods for estimating cognitive diagnosis models (CDMs) have been developed and applied in a wide range of contexts. However, in the literature, a wide chasm exists between these two families of methods, and their relationship to each other is not well understood. In this paper, we propose a unified estimation framework to bridge the divide between parametric and nonparametric methods in cognitive diagnosis to better understand their relationship. We also develop iterative joint estimation algorithms and establish consistency properties within the proposed framework. Lastly, we present comprehensive simulation results to compare different methods and provide practical recommendations on the appropriate use of the proposed framework in various CDM contexts.

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Authors and Affiliations

  1. Department of Statistics, University of Michigan, 1085 South University, Ann Arbor, 48108, USA

    Chenchen Ma & Gongjun Xu

  2. University of Hong Kong, Pok Fu Lam, Hong Kong

    Jimmy de la Torre

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  1. Chenchen Ma
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  2. Jimmy de la Torre
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  3. Gongjun Xu
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Correspondence to Gongjun Xu.

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This research is partially supported by NSF CAREER SES-1846747, DMS-1712717, SES-1659328.

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Ma, C., de la Torre, J. & Xu, G. Bridging Parametric and Nonparametric Methods in Cognitive Diagnosis. Psychometrika 88, 51–75 (2023). https://doi.org/10.1007/s11336-022-09878-2

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