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.
Original language | English |
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Pages (from-to) | 132-157 |
Number of pages | 26 |
Journal | Psychometrika |
Volume | 88 |
Early online date | 21 Nov 2022 |
DOIs | |
Publication status | Published - Mar 2023 |
Keywords
- Bi-factor model
- conditional independence
- limited information
- second-order model
- tail dependence/asymmetry
- truncated vines