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

Sayed H. Kadhem and Aristidis K. Nikoloulopoulos ()
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Sayed H. Kadhem: University of East Anglia
Aristidis K. Nikoloulopoulos: University of East Anglia

Psychometrika, 2023, vol. 88, issue 1, No 7, 132-157

Abstract: 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.

Keywords: Bi-factor model; conditional independence; limited information; second-order model; tail dependence/asymmetry; truncated vines (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11336-022-09894-2

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