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Name: Sayed H. Kadhem 

Talk Title: Bi-factor and second-order copula models for item response data

Abstract: In the context of item response data, latent maxima, minima and means can arise depending on how a respondent considers specific items. An item might make the respondent think about past events. The case of a  latent maxima/minima can occur if the participant's response is based on a best or worst case. For different dependent items based on latent maxima or minima, multivariate extreme value and copula theory can be used to select suitable distributions for the latent variables. Copulas that arise from extreme value theory have more probability in one joint tail (upper or lower) than expected with a multivariate normal (MVN) distribution. Even, in the case where  the item responses are based on discretizations of latent variables that are means, then it is possible that there can be more probability in both the joint upper and joint lower tail, compared with MVN distributed latent variables.  This happens if the respondents consist of a "mixture” population (e.g., different locations or genders). From the theory of elliptical distributions and copulas, it is known that the multivariate Student-t distribution as a scale mixture of MVN has more dependence in the tails.  We propose copula extensions for bi-factor and second-order models. The construction of the models exploits the use of  bivariate copulas that link the observed variables to the common and group-specific factors. Our general models include the Gaussian bi-factor and second-order models as special cases, have interpretations of latent maxima/minima (in comparison with latent means) 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. Joint work with Aristidis K. Nikoloulopoulos. Related preprint: https://arxiv.org/abs/2102.10660. 

This talk is a contributed talk at EVA 2021. View the programme here.