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ARMA Cholesky factor models for the covariance matrix of linear models

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  • 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
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    References listed on IDEAS

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    2. 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.
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    6. 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.
    7. 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.
    8. 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.
    9. Daniels, M.J. & Pourahmadi, M., 2009. "Modeling covariance matrices via partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2352-2363, November.
    10. 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.
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    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, Statistics Poland, 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.

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