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A joint modelling approach for longitudinal studies

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  • Weiping Zhang
  • Chenlei Leng
  • Cheng Yong Tang

Abstract

type="main" xml:id="rssb12065-abs-0001"> In longitudinal studies, it is of fundamental importance to understand the dynamics in the mean function, variance function and correlations of the repeated or clustered measurements. For modelling the covariance structure, Cholesky-type decomposition-based approaches have been demonstrated to be effective. However, parsimonious approaches for directly revealing the correlation structure between longitudinal measurements remain less well explored, and existing joint modelling approaches may encounter difficulty in interpreting the covariation structure. We propose a novel joint mean–variance correlation modelling approach for longitudinal studies. By applying hyperspherical co-ordinates, we obtain an unconstrained parameterization for the correlation matrix that automatically guarantees its positive definiteness, and we develop a regression approach to model the correlation matrix of the longitudinal measurements by exploiting the parameterization. The modelling framework proposed is parsimonious, interpretable and flexible for analysing longitudinal data. Extensive data examples and simulations support the effectiveness of the approach proposed.

Suggested Citation

  • Weiping Zhang & Chenlei Leng & Cheng Yong Tang, 2015. "A joint modelling approach for longitudinal studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 219-238, January.
    • Handle: RePEc:bla:jorssb:v:77:y:2015:i:1:p:219-238
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    File URL: http://hdl.handle.net/10.1111/rssb.2014.77.issue-1
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    1. Xu, Lin & Xiang, Sijia & Yao, Weixin, 2019. "Robust maximum Lq-likelihood estimation of joint mean–covariance models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 397-411.
    2. Guanyu Hu & Ming-Hui Chen & Nalini Ravishanker, 2023. "Bayesian analysis of spherically parameterized dynamic multivariate stochastic volatility models," Computational Statistics, Springer, vol. 38(2), pages 845-869, June.
    3. Guney, Yesim & Arslan, Olcay & Yavuz, Fulya Gokalp, 2022. "Robust estimation in multivariate heteroscedastic regression models with autoregressive covariance structures using EM algorithm," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    4. Qingze Li & Jianxin Pan, 2022. "Permutation Variation and Alternative Hyper-Sphere Decomposition," Mathematics, MDPI, vol. 10(4), pages 1-19, February.
    5. Pourahmadi, Mohsen & Wang, Xiao, 2015. "Distribution of random correlation matrices: Hyperspherical parameterization of the Cholesky factor," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 5-12.
    6. Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Zhang, Jiajia, 2022. "Empirical likelihood inference for longitudinal data with covariate measurement errors: An application to the LEAN study," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    7. Zhang, Lin & Chen, Xiaohui & Khatab, Abdelhakim & An, Youjun & Feng, XiaoNing, 2024. "Joint optimization of selective maintenance and repairpersons assignment problem for mission-oriented systems operating under s-dependent competing risks," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    8. Yujing Shao & Lei Wang, 2022. "Generalized partial linear models with nonignorable dropouts," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 223-252, February.
    9. 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).
    10. Luo, Renwen & Pan, Jianxin, 2022. "Conditional generalized estimating equations of mean-variance-correlation for clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    11. Zhao, Yan-Yong & Lin, Jin-Guan & Zhao, Jian-Qiang & Miao, Zhang-Xiao, 2022. "Estimation of semi-varying coefficient models for longitudinal data with irregular error structure," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    12. Ruey S. Tsay & Mohsen Pourahmadi, 2017. "Modelling structured correlation matrices," Biometrika, Biometrika Trust, vol. 104(1), pages 237-242.
    13. 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).
    14. Lei Wang & Wei Ma, 2021. "Improved empirical likelihood inference and variable selection for generalized linear models with longitudinal nonignorable dropouts," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 623-647, June.
    15. Jia Chen & Degui Li & Yingcun Xia, 2015. "New Semiparametric Estimation Procedure for Functional Coefficient Longitudinal Data Models," Discussion Papers 15/17, Department of Economics, University of York.
    16. Weiping Zhang & Feiyue Xie & Jiaxin Tan, 2020. "A robust joint modeling approach for longitudinal data with informative dropouts," Computational Statistics, Springer, vol. 35(4), pages 1759-1783, December.
    17. Chen, Jia & Li, Degui & Xia, Yingcun, 2019. "Estimation of a rank-reduced functional-coefficient panel data model with serial correlation," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 456-479.
    18. Wagner Hugo Bonat & Bent Jørgensen, 2016. "Multivariate covariance generalized linear models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(5), pages 649-675, November.
    19. Lu, Fei & Xue, Liugen & Cai, Xiong, 2020. "GEE analysis in joint mean-covariance model for longitudinal data," Statistics & Probability Letters, Elsevier, vol. 160(C).
    20. Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Xu, Wanghong, 2019. "A novel robust approach for analysis of longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 83-95.
    21. Yixin Chen & Weixin Yao, 2017. "Unified Inference for Sparse and Dense Longitudinal Data in Time-varying Coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 268-284, March.
    22. Lee, Keunbaik & Baek, Changryong & Daniels, Michael J., 2017. "ARMA Cholesky factor models for the covariance matrix of linear models," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 267-280.

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