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Analysis of multivariate longitudinal data using ARMA Cholesky and hypersphere decompositions

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  • Lee, Keunbaik
  • Lee, Chang-Hoon
  • Kwak, Min-Sun
  • Jang, Eun Jin

Abstract

In longitudinal data with many replications, the high-order autoregressive (AR) structure of covariance matrix is required to capture the serial correlations between repeated outcomes. Thus, the high-order AR structure requires many parameters underlying the dynamic data dependence. In this paper, we proposed an autoregressive moving-average (ARMA) structure of covariance matrix involving multivariate linear models instead of the high-order AR structure of covariance matrix. We decomposed the covariance matrix using autoregressive moving-average Cholesky decomposition (ARMACD) to explain the correlations between responses at each time point, the correlation within separate responses over time, and the cross-correlation between different responses at different times. The ARMACD facilitates nonstationarity and heteroscedasticity of the covariance matrix, and the estimated covariance matrix is guaranteed to be positive definite. We illustrated the proposed methods using data derived from a study of nonalcoholic fatty liver disease.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:csdana:v:156:y:2021:i:c:s0167947320302358
    DOI: 10.1016/j.csda.2020.107144
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    References listed on IDEAS

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    1. 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.
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    4. 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.
    5. 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.
    6. Kim, Chulmin & Zimmerman, Dale L., 2012. "Unconstrained models for the covariance structure of multivariate longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 104-118.
    7. 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.
    8. Keunbaik Lee & Hyunsoon Cho & Min‐Sun Kwak & Eun Jin Jang, 2020. "Estimation of covariance matrix of multivariate longitudinal data using modified Choleksky and hypersphere decompositions," Biometrics, The International Biometric Society, vol. 76(1), pages 75-86, March.
    9. Keunbaik Lee & Hoimin Jung & Jae Keun Yoo, 2019. "Modeling of the ARMA random effects covariance matrix in logistic random effects models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 281-299, June.
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    Cited by:

    1. 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).

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