biostudies-literatureUnknown88(1)Kadhem SHBi-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.Psychometrika132-157https://www.ebi.ac.uk/biostudies/studies/S-EPMC9977904biostudies-literatureBi-factor and Second-Order Copula Models for Item Response Data.PMC9977904Kadhem SHNikoloulopoulos AKfalseBi-factor and Second-Order Copula Models for Item Response Data.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.2023-01-01T00:00:00Z2023 Mar2025-04-22T21:47:51.659Z2025-04-06T03:43:10.293ZS-EPMC99779043641482510.1007/s11336-022-09894-2