Factor copula models for item response data

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Abstract

Factor or conditional independence models based on copulas are proposed for multivariate discrete data such as item responses. The factor copula models 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 factor models based on the discretized multivariate normal distribution (or multidimensional normal ogive model). Details on maximum likelihood estimation of parameters for the factor copula model are given, as well as analysis of the behavior of the log-likelihood. Our general methodology is illustrated with several item response data sets, and it is shown that there is a substantial improvement on existing models both conceptually and in fit to data.
Original languageEnglish
Pages (from-to)126-150
JournalPsychometrika
Volume80
Issue number1
Early online date1 Dec 2013
DOIs
Publication statusPublished - Mar 2015

Keywords

  • conditional independence
  • factor model dependence structure
  • latent variable model
  • limited information
  • partial correlation

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