IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v156y2021ics0167947320302358.html
   My bibliography  Save this article

Analysis of multivariate longitudinal data using ARMA Cholesky and hypersphere decompositions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947320302358
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2020.107144?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Jianxin Pan, 2003. "On modelling mean-covariance structures in longitudinal studies," Biometrika, Biometrika Trust, vol. 90(1), pages 239-244, March.
    7. 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.
    8. Dayanand Naik & Shantha Rao, 2001. "Analysis of multivariate repeated measures data with a Kronecker product structured covariance matrix," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(1), pages 91-105.
    9. 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.
    10. Jing Xu & Gilbert Mackenzie, 2012. "Modelling covariance structure in bivariate marginal models for longitudinal data," Biometrika, Biometrika Trust, vol. 99(3), pages 649-662.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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).
    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. 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.
    4. 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.
    5. Rabe Anasu & Shangodoyin D. K. & Thaga K., 2019. "Linear Cholesky Decomposition Of Covariance Matrices In Mixed Models With Correlated Random Effects," Statistics in Transition New Series, Polish Statistical Association, vol. 20(4), pages 59-70, December.
    6. Anasu Rabe & D. K. Shangodoyin & K. Thaga, 2019. "Linear Cholesky Decomposition Of Covariance Matrices In Mixed Models With Correlated Random Effects," Statistics in Transition New Series, Polish Statistical Association, vol. 20(4), pages 59-70, December.
    7. 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).
    8. Yicong Lin & Hanno Reuvers, 2019. "Efficient Estimation by Fully Modified GLS with an Application to the Environmental Kuznets Curve," Papers 1908.02552, arXiv.org, revised Aug 2020.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Luo, Renwen & Pan, Jianxin, 2022. "Conditional generalized estimating equations of mean-variance-correlation for clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    14. Xueying Zheng & Wing Fung & Zhongyi Zhu, 2013. "Robust estimation in joint mean–covariance regression model for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 617-638, August.
    15. Dengke Xu & Zhongzhan Zhang & Liucang Wu, 2014. "Bayesian analysis of joint mean and covariance models for longitudinal data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2504-2514, November.
    16. Wojciech Łukaszonek, 2017. "A Multidimensional And Dynamised Classification Of Polish Provinces Based On Selected Features Of Higher Education In 2002–2013," Statistics in Transition New Series, Polish Statistical Association, vol. 18(2), pages 271-290, June.
    17. Filipiak, Katarzyna & Klein, Daniel & Roy, Anuradha, 2016. "Score test for a separable covariance structure with the first component as compound symmetric correlation matrix," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 105-124.
    18. Wenqi Zhang & William Kleiber & Bri‐Mathias Hodge & Barry Mather, 2022. "A nonstationary and non‐Gaussian moving average model for solar irradiance," Environmetrics, John Wiley & Sons, Ltd., vol. 33(3), May.
    19. Li, Erning & Pourahmadi, Mohsen, 2013. "An alternative REML estimation of covariance matrices in linear mixed models," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1071-1077.
    20. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:156:y:2021:i:c:s0167947320302358. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.