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Factor Copula Models for Item Response Data

Published online by Cambridge University Press:  01 January 2025

Aristidis K. Nikoloulopoulos  and
Harry Joe
Aristidis K. Nikoloulopoulos*
Affiliation:
University of East Anglia
Harry Joe
Affiliation:
University of British Columbia
*
Requests for reprints should be sent to Aristidis K. Nikoloulopoulos, School of Computing Sciences, University of East Anglia, Norwich NR4 7TJ, UK. E-mail: A.Nikoloulopoulos@uea.ac.uk
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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.

Keywords

conditional independencefactor model dependence structurelatent variable modellimited informationpartial correlation
Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 1 , March 2015 , pp. 126 - 150
Copyright
Copyright © 2013 The Psychometric Society

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