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Factor Copula Models for Item Response Data

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  • Aristidis Nikoloulopoulos
  • Harry Joe

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. Copyright The Psychometric Society 2015

Suggested Citation

  • Aristidis Nikoloulopoulos & Harry Joe, 2015. "Factor Copula Models for Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 126-150, March.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:1:p:126-150
    DOI: 10.1007/s11336-013-9387-4
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    References listed on IDEAS

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    7. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    8. Joe, Harry, 2005. "Asymptotic efficiency of the two-stage estimation method for copula-based models," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 401-419, June.
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    11. Krupskii, Pavel & Joe, Harry, 2013. "Factor copula models for multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 85-101.
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    Cited by:

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    2. Zhang, Xi & Li, Jian, 2018. "Credit and market risks measurement in carbon financing for Chinese banks," Energy Economics, Elsevier, vol. 76(C), pages 549-557.
    3. Nguyen, Hoang & Ausín, M. Concepción & Galeano, Pedro, 2020. "Variational inference for high dimensional structured factor copulas," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    4. Ban Kheng Tan & Anastasios Panagiotelis & George Athanasopoulos, 2017. "Bayesian Inference for a 1-Factor Copula Model," Monash Econometrics and Business Statistics Working Papers 6/17, Monash University, Department of Econometrics and Business Statistics.
    5. Michael Stanley Smith, 2021. "Implicit Copulas: An Overview," Papers 2109.04718, arXiv.org.
    6. Jonas Moss & Steffen Grønneberg, 2023. "Partial Identification of Latent Correlations with Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 241-252, March.
    7. Sayed H. Kadhem & Aristidis K. Nikoloulopoulos, 2023. "Bi-factor and Second-Order Copula Models for Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 132-157, March.
    8. Sayed H. Kadhem & Aristidis K. Nikoloulopoulos, 2023. "Factor Tree Copula Models for Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 776-802, September.
    9. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    10. Aristidis K. Nikoloulopoulos, 2022. "An one‐factor copula mixed model for joint meta‐analysis of multiple diagnostic tests," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1398-1423, July.
    11. Panagiotelis, Anastasios & Czado, Claudia & Joe, Harry & Stöber, Jakob, 2017. "Model selection for discrete regular vine copulas," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 138-152.
    12. Oh, Rosy & Jeong, Himchan & Ahn, Jae Youn & Valdez, Emiliano A., 2021. "A multi-year microlevel collective risk model," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 309-328.
    13. Krupskii, Pavel & Joe, Harry, 2015. "Structured factor copula models: Theory, inference and computation," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 53-73.
    14. Aristidis K. Nikoloulopoulos & Peter G. Moffatt, 2019. "Coupling Couples With Copulas: Analysis Of Assortative Matching On Risk Attitude," Economic Inquiry, Western Economic Association International, vol. 57(1), pages 654-666, January.

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