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A D‐vine copula‐based model for repeated measurements extending linear mixed models with homogeneous correlation structure

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  • Matthias Killiches
  • Claudia Czado

Abstract

We propose a model for unbalanced longitudinal data, where the univariate margins can be selected arbitrarily and the dependence structure is described with the help of a D‐vine copula. We show that our approach is an extremely flexible extension of the widely used linear mixed model if the correlation is homogeneous over the considered individuals. As an alternative to joint maximum–likelihood a sequential estimation approach for the D‐vine copula is provided and validated in a simulation study. The model can handle missing values without being forced to discard data. Since conditional distributions are known analytically, we easily make predictions for future events. For model selection, we adjust the Bayesian information criterion to our situation. In an application to heart surgery data our model performs clearly better than competing linear mixed models.

Suggested Citation

  • Matthias Killiches & Claudia Czado, 2018. "A D‐vine copula‐based model for repeated measurements extending linear mixed models with homogeneous correlation structure," Biometrics, The International Biometric Society, vol. 74(3), pages 997-1005, September.
    • Handle: RePEc:bla:biomet:v:74:y:2018:i:3:p:997-1005
    DOI: 10.1111/biom.12867
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    References listed on IDEAS

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    1. 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.
    2. Sun, Jiafeng & Frees, Edward W. & Rosenberg, Marjorie A., 2008. "Heavy-tailed longitudinal data modeling using copulas," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 817-830, April.
    3. Smith, Michael Stanley, 2015. "Copula modelling of dependence in multivariate time series," International Journal of Forecasting, Elsevier, vol. 31(3), pages 815-833.
    4. Kraus, Daniel & Czado, Claudia, 2017. "D-vine copula based quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 1-18.
    5. Smith, Michael & Min, Aleksey & Almeida, Carlos & Czado, Claudia, 2010. "Modeling Longitudinal Data Using a Pair-Copula Decomposition of Serial Dependence," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1467-1479.
    6. Nagler, Thomas & Czado, Claudia, 2016. "Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 69-89.
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    Cited by:

    1. Genest Christian & Scherer Matthias, 2019. "The world of vines: An interview with Claudia Czado," Dependence Modeling, De Gruyter, vol. 7(1), pages 169-180, January.
    2. Chu, Amanda M.Y. & Ip, Chun Yin & Lam, Benson S.Y. & So, Mike K.P., 2022. "Vine copula statistical disclosure control for mixed-type data," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).

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