IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v115y2017icp267-280.html
   My bibliography  Save this article

ARMA Cholesky factor models for the covariance matrix of linear models

Author

Listed:
  • Lee, Keunbaik
  • Baek, Changryong
  • Daniels, Michael J.

Abstract

In longitudinal studies, serial dependence of repeated outcomes must be taken into account to make correct inferences on covariate effects. As such, care must be taken in modeling the covariance matrix. However, estimation of the covariance matrix is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcome these limitations, two Cholesky decomposition approaches have been proposed: modified Cholesky decomposition for autoregressive (AR) structure and moving average Cholesky decomposition for moving average (MA) structure, respectively. However, the correlations of repeated outcomes are often not captured parsimoniously using either approach separately. In this paper, we propose a class of flexible, nonstationary, heteroscedastic models that exploits the structure allowed by combining the AR and MA modeling of the covariance matrix that we denote as ARMACD. We analyze a recent lung cancer study to illustrate the power of our proposed methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:115:y:2017:i:c:p:267-280
    DOI: 10.1016/j.csda.2017.05.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947317300956
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2017.05.001?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. Jianxin Pan, 2003. "On modelling mean-covariance structures in longitudinal studies," Biometrika, Biometrika Trust, vol. 90(1), pages 239-244, March.
    2. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    3. Lee, Keunbaik & Yoo, Jae Keun, 2014. "Bayesian Cholesky factor models in random effects covariance matrix for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 111-116.
    4. Weiping Zhang & Chenlei Leng, 2012. "A moving average Cholesky factor model in covariance modelling for longitudinal data," Biometrika, Biometrika Trust, vol. 99(1), pages 141-150.
    5. Lee, Keunbaik & Lee, JungBok & Hagan, Joseph & Yoo, Jae Keun, 2012. "Modeling the random effects covariance matrix for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1545-1551.
    6. 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.
    7. Michael J. Daniels, 2002. "Bayesian analysis of covariance matrices and dynamic models for longitudinal data," Biometrika, Biometrika Trust, vol. 89(3), pages 553-566, August.
    8. Mohsen Pourahmadi, 2007. "Cholesky Decompositions and Estimation of A Covariance Matrix: Orthogonality of Variance--Correlation Parameters," Biometrika, Biometrika Trust, vol. 94(4), pages 1006-1013.
    9. Patrick J. Heagerty, 1999. "Marginally Specified Logistic-Normal Models for Longitudinal Binary Data," Biometrics, The International Biometric Society, vol. 55(3), pages 688-698, September.
    10. Daniels, M.J. & Pourahmadi, M., 2009. "Modeling covariance matrices via partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2352-2363, November.
    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. 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.
    2. 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).
    3. 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).
    4. 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.
    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. 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.

    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. 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).
    2. 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.
    3. 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.
    4. 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.
    5. Lee, Keunbaik & Yoo, Jae Keun, 2014. "Bayesian Cholesky factor models in random effects covariance matrix for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 111-116.
    6. 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.
    7. Lee, Keunbaik & Lee, JungBok & Hagan, Joseph & Yoo, Jae Keun, 2012. "Modeling the random effects covariance matrix for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1545-1551.
    8. Daniels, M.J. & Pourahmadi, M., 2009. "Modeling covariance matrices via partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2352-2363, November.
    9. Luo, Renwen & Pan, Jianxin, 2022. "Conditional generalized estimating equations of mean-variance-correlation for clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    10. Lu, Fei & Xue, Liugen & Cai, Xiong, 2020. "GEE analysis in joint mean-covariance model for longitudinal data," Statistics & Probability Letters, Elsevier, vol. 160(C).
    11. 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.
    12. Luigi Spezia, 2019. "Modelling covariance matrices by the trigonometric separation strategy with application to hidden Markov models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 399-422, June.
    13. 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.
    14. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
    15. 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.
    16. Gul Inan & Ozlem Ilk, 2019. "A marginalized multilevel model for bivariate longitudinal binary data," Statistical Papers, Springer, vol. 60(3), pages 601-628, June.
    17. Tsukuma, Hisayuki, 2016. "Minimax estimation of a normal covariance matrix with the partial Iwasawa decomposition," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 190-207.
    18. 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).
    19. Wang, Y. & Daniels, M.J., 2013. "Bayesian modeling of the dependence in longitudinal data via partial autocorrelations and marginal variances," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 130-140.
    20. Yu, Jing & Nummi, Tapio & Pan, Jianxin, 2022. "Mixture regression for longitudinal data based on joint mean–covariance model," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

    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:115:y:2017:i:c:p:267-280. 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.