Factor copula models for mixed data

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Abstract

We develop factor copula models to analyse the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric and nonlinear dependence. They can be explained as conditional independence models with latent variables that do not necessarily have an additive latent structure. We focus on important issues of interest to the social data analyst, such as model selection and goodness of fit. Our general methodology is demonstrated with an extensive simulation study and illustrated by reanalysing three mixed response data sets. Our studies suggest that there can be a substantial improvement over the standard factor model for mixed data and make the argument for moving to factor copula models.

Original languageEnglish
Pages (from-to)365-403
Number of pages39
JournalBritish Journal of Mathematical and Statistical Psychology
Volume74
Issue number3
Early online date16 Mar 2021
DOIs
Publication statusPublished - Nov 2021

Keywords

  • canonical vines
  • conditional independence
  • goodness of fit
  • latent variable models
  • model selection
  • tail dependence/asymmetry

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