Factor tree copula models for item response data

Kadhem, Sayed H. and Nikoloulopoulos, Aristidis K. ORCID: https://orcid.org/0000-0003-0853-0084 (2023) Factor tree copula models for item response data. Psychometrika, 88 (3). pp. 776-802. ISSN 0033-3123

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Factor copula models for item response data are more interpretable and fit better than (truncated) vine copula models when dependence can be explained through latent variables, but are not robust to violations of conditional independence. To circumvent these issues, truncated vines and factor copula models for item response data are joined to define a combined model, the so-called factor tree copula model, with individual benefits from each of the two approaches. Rather than adding factors and causing computational problems and difficulties in interpretation and identification, a truncated vine structure is assumed on the residuals conditional on one or two latent variables. This structure can be better explained as a conditional dependence given a few interpretable latent variables. On the one hand, the parsimonious feature of factor models remains intact and any residual dependencies are being taken into account on the other. We discuss estimation along with model selection. In particular, we propose model selection algorithms to choose a plausible factor tree copula model to capture the (residual) dependencies among the item responses. Our general methodology is demonstrated with an extensive simulation study and illustrated by analyzing Post-Traumatic Stress Disorder.

Item Type: Article
Uncontrolled Keywords: conditional dependence,factor copula models,latent variable models,truncated vine copula models,psychology(all),applied mathematics,4* ,/dk/atira/pure/subjectarea/asjc/3200
Faculty \ School: Faculty of Science > School of Computing Sciences
UEA Research Groups: Faculty of Science > Research Groups > Data Science and Statistics
Faculty of Science > Research Groups > Statistics
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Depositing User: LivePure Connector
Date Deposited: 24 May 2023 11:32
Last Modified: 05 Dec 2023 02:28
URI: https://ueaeprints.uea.ac.uk/id/eprint/92159
DOI: 10.1007/s11336-023-09917-6

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