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Bi-factor and Second-Order Copula Models for Item Response Data

Author

Listed:
  • Sayed H. Kadhem

    (University of East Anglia)

  • Aristidis K. Nikoloulopoulos

    (University of East Anglia)

Abstract

Bi-factor and second-order models based on copulas are proposed for item response data, where the items are sampled from identified subdomains of some larger domain such that there is a homogeneous dependence within each domain. Our general models include the Gaussian bi-factor and second-order models as special cases and can lead to more probability in the joint upper or lower tail compared with the Gaussian bi-factor and second-order models. Details on maximum likelihood estimation of parameters for the bi-factor and second-order copula models are given, as well as model selection and goodness-of-fit techniques. Our general methodology is demonstrated with an extensive simulation study and illustrated for the Toronto Alexithymia Scale. Our studies suggest that there can be a substantial improvement over the Gaussian bi-factor and second-order models both conceptually, as the items can have interpretations of discretized maxima/minima or mixtures of discretized means in comparison with discretized means, and in fit to data.

Suggested Citation

  • Sayed H. Kadhem & Aristidis K. Nikoloulopoulos, 2023. "Bi-factor and Second-Order Copula Models for Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 132-157, March.
    • Handle: RePEc:spr:psycho:v:88:y:2023:i:1:d:10.1007_s11336-022-09894-2
    DOI: 10.1007/s11336-022-09894-2
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    References listed on IDEAS

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    Cited by:

    1. Sayed H. Kadhem & Aristidis K. Nikoloulopoulos, 2023. "Factor Tree Copula Models for Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 776-802, September.

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