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Modelling covariance structure in bivariate marginal models for longitudinal data

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  • Jing Xu
  • Gilbert Mackenzie

Abstract

It can be more challenging to efficiently model the covariance matrices for multivariate longitudinal data than for the univariate case, due to the correlations arising between multiple responses. The positive-definiteness constraint and the high dimensionality are further obstacles in covariance modelling. In this paper, we develop a data-based method by which the parameters in the covariance matrices are replaced by unconstrained and interpretable parameters with reduced dimensions. The maximum likelihood estimators for the mean and covariance parameters are shown to be consistent and asymptotically normally distributed. Simulations and real data analysis show that the new approach performs very well even when modelling bivariate nonstationary dependence structures. Copyright 2012, Oxford University Press.

Suggested Citation

  • Jing Xu & Gilbert Mackenzie, 2012. "Modelling covariance structure in bivariate marginal models for longitudinal data," Biometrika, Biometrika Trust, vol. 99(3), pages 649-662.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:3:p:649-662
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    File URL: http://hdl.handle.net/10.1093/biomet/ass031
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    Cited by:

    1. Mike K. P. So & Wing Ki Liu & Amanda M. Y. Chu, 2018. "Bayesian Shrinkage Estimation Of Time-Varying Covariance Matrices In Financial Time Series," Advances in Decision Sciences, Asia University, Taiwan, vol. 22(1), pages 369-404, December.
    2. Kohli, Priya & Garcia, Tanya P. & Pourahmadi, Mohsen, 2016. "Modeling the Cholesky factors of covariance matrices of multivariate longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 87-100.
    3. Rhee, Anbin & Kwak, Min-Sun & Lee, Keunbaik, 2022. "Robust modeling of multivariate longitudinal data using modified Cholesky and hypersphere decompositions," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    4. Lee, Keunbaik & Lee, Chang-Hoon & Kwak, Min-Sun & Jang, Eun Jin, 2021. "Analysis of multivariate longitudinal data using ARMA Cholesky and hypersphere decompositions," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    5. Feng, Sanying & Lian, Heng & Xue, Liugen, 2016. "A new nested Cholesky decomposition and estimation for the covariance matrix of bivariate longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 98-109.
    6. Fang, Qian & Yu, Chen & Weiping, Zhang, 2020. "Regularized estimation of precision matrix for high-dimensional multivariate longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    7. So Yeon Chun & Michael W. Browne & Alexander Shapiro, 2018. "Modified Distribution-Free Goodness-of-Fit Test Statistic," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 48-66, March.

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