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CN 34-1054/N

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Open AccessOpen Access JUSTC Original Paper

A robust joint modeling approach for longitudinal data

  • Department of Statistics and Finance University of Science and Technology of China

Funds:  Supported by National Key Research & Development Plan(2016YFC0800104), National Natural Science Foundation of China(11671374, 71771203,71631006).
Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.03.009
More Information
  • Author Bio:

    TAN Jiaxin, female, born in 1993,Research field: Longitudinal data analysis. E-mail: tjxggsd@163.com

  • Corresponding author: ZHANG Weiping
  • Received Date: 02 May 2019
  • Accepted Date: 14 June 2019
  • Rev Recd Date: 14 June 2019
  • Publish Date: 31 March 2020
    Abstract

  • Abstract

    A robust method is proposed for analyzing longitudinal continuous responses

    Abstract

    A robust method is proposed for analyzing longitudinal continuous responses
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    • References(27)
  • [1]
    DIGGLE P J. The analysis of longitudinal data[J]. Journal of the American Statistical Association, 2002, 90: 1231-1232.
    [2]
    POURAHMADI M. Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterisation[J]. Biometrika, 1999, 86:677-690.
    [3]
    POURAHMADI M. Maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix[J]. Biometrika, 2000, 87: 425-435.
    [4]
    POURAHMADI M. Cholesky decompositions and estimation of a covariance matrix: Orthogonality of variance-correlation parameters[J]. Biometrika, 2007, 94: 1006-1013.
    [5]
    PAN J, MACKENZIE G. Model selection for joint mean-covariance structures in longitudinal studies[J]. Biometrika, 2003, 90: 239-244.
    [6]
    YE H, PAN J. Modeling covariance structures in generalized estimating equations for longitudinal data[J]. Biometrika, 2006, 93: 927-941.
    [7]
    LENG C, ZHANG W, PAN J. Semiparametric mean-covariance regression analysis for longitudinal data[J]. Journal of the American Statistical Association, 2010, 105: 181-193.
    [8]
    ZHANG W, LENG C. A moving average Cholesky factor model in covariance modeling for longitudinal data[J]. Biometrika, 2012, 99: 141-150.
    [9]
    ZHANG W, LENG C, TANG C Y. A joint modelling approach for longitudinal studies[J]. Journal of the Royal Statistical Society, 2015, 77: 219-238.
    [10]
    CROUX C, GIJBELS I, PROSDOCOMO I. Robust estimation of mean and dispersion functions in extended generalized additive models[J]. Biometrics, 2012, 68: 31-44.
    [11]
    ZHENG X, FUNG W K, ZHU Z. Robust estimation in joint mean-covariance regression model for longitudinal data[J]. Annals of the Institute of Statistical Mathematics, 2013, 65: 617-638.
    [12]
    LV J, GUO C, LI T, et al. Adaptive robust estimation in joint mean-covariance regression model for bivariate longitudinal data[J]. Statistics, 2018, 52(1):64-83.
    [13]
    LIANG K Y, ZEGER S L. Longitudinal data analysis using generalized linear models[J]. Biometrika, 1986, 73: 13-22.
    [14]
    LANGE K L. Robust statistical modeling using the t distribution[J]. Publications of the American Statistical Association, 1989, 84: 881-896.
    [15]
    LIN T I, WANG Y J. A robust approach to joint modeling of mean and scale covariance for longitudinal data[J]. Journal of Statistical Planning & Inference, 2009, 139(9): 3013-3026.
    [16]
    MAADOOLIAT M, POURAHMADI M, HUANG J Z. Robust estimation of the correlation matrix of longitudinal data[J]. Statistics and Computing, 2013, 23(1): 17-28.
    [17]
    LIN T I, WANG W L. Bayesian inference in joint modeling of location and scale parameters of the t distribution for longitudinal data[J]. Journal of Statistical Planning & Inference, 2011, 141: 1543-1553.
    [18]
    LIU C, RUBIN D B. ML estimation of the t distribution using EM and its extensions, ECM and ECME[J]. Statistic Sinica, 1995, 5(1): 19-39.
    [19]
    LIN P. Some characterizations of the multivariate t distribution[J]. Journal of Multivariate Analysis, 1972, 2: 339-344.
    [20]
    KOTZ S, NADARAJAH S. Multivariate t Distributions and Their Applications[M]. Cambridge, UK: Cambridge University Press, 2004.
    [21]
    CHIU T Y M, LEONARD T, TSUI K W. The matrix-logarithm covariance model[J]. Journal of American Statistical Association, 1996, 91: 198-210.
    [22]
    WHITE H. Maximum likelihood estimation of misspecied models[J]. Econometrica, 1982, 50: 1-25.
    [23]
    FERNANDEZ C, STEEL M F J. Multivariate student-t regression models: pitfalls and inference[J]. Biometrika, 1999, 86: 153-167.
    [24]
    LOUIS T A. Finding the observed information matrix when using the EM algorithm[J]. Journal of the Royal Statistical Society B, 1982, 44: 226-233.
    [25]
    MENG X L, RUBIN D B. Maximum likelihood estimation via the ECM algorithm: A general framework[J]. Biometrika, 1993, 80: 267-278.
    [26]
    TUKEY J W. One degree of freedom for non-Additivity[J]. Biometrics, 1949, 5: 232-242.
    [27]
    ZEGER S L， DIGGLE P J. Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters[J]. Biometrics, 1994, 50: 689-699.
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    [1]
    DIGGLE P J. The analysis of longitudinal data[J]. Journal of the American Statistical Association, 2002, 90: 1231-1232.
    [2]
    POURAHMADI M. Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterisation[J]. Biometrika, 1999, 86:677-690.
    [3]
    POURAHMADI M. Maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix[J]. Biometrika, 2000, 87: 425-435.
    [4]
    POURAHMADI M. Cholesky decompositions and estimation of a covariance matrix: Orthogonality of variance-correlation parameters[J]. Biometrika, 2007, 94: 1006-1013.
    [5]
    PAN J, MACKENZIE G. Model selection for joint mean-covariance structures in longitudinal studies[J]. Biometrika, 2003, 90: 239-244.
    [6]
    YE H, PAN J. Modeling covariance structures in generalized estimating equations for longitudinal data[J]. Biometrika, 2006, 93: 927-941.
    [7]
    LENG C, ZHANG W, PAN J. Semiparametric mean-covariance regression analysis for longitudinal data[J]. Journal of the American Statistical Association, 2010, 105: 181-193.
    [8]
    ZHANG W, LENG C. A moving average Cholesky factor model in covariance modeling for longitudinal data[J]. Biometrika, 2012, 99: 141-150.
    [9]
    ZHANG W, LENG C, TANG C Y. A joint modelling approach for longitudinal studies[J]. Journal of the Royal Statistical Society, 2015, 77: 219-238.
    [10]
    CROUX C, GIJBELS I, PROSDOCOMO I. Robust estimation of mean and dispersion functions in extended generalized additive models[J]. Biometrics, 2012, 68: 31-44.
    [11]
    ZHENG X, FUNG W K, ZHU Z. Robust estimation in joint mean-covariance regression model for longitudinal data[J]. Annals of the Institute of Statistical Mathematics, 2013, 65: 617-638.
    [12]
    LV J, GUO C, LI T, et al. Adaptive robust estimation in joint mean-covariance regression model for bivariate longitudinal data[J]. Statistics, 2018, 52(1):64-83.
    [13]
    LIANG K Y, ZEGER S L. Longitudinal data analysis using generalized linear models[J]. Biometrika, 1986, 73: 13-22.
    [14]
    LANGE K L. Robust statistical modeling using the t distribution[J]. Publications of the American Statistical Association, 1989, 84: 881-896.
    [15]
    LIN T I, WANG Y J. A robust approach to joint modeling of mean and scale covariance for longitudinal data[J]. Journal of Statistical Planning & Inference, 2009, 139(9): 3013-3026.
    [16]
    MAADOOLIAT M, POURAHMADI M, HUANG J Z. Robust estimation of the correlation matrix of longitudinal data[J]. Statistics and Computing, 2013, 23(1): 17-28.
    [17]
    LIN T I, WANG W L. Bayesian inference in joint modeling of location and scale parameters of the t distribution for longitudinal data[J]. Journal of Statistical Planning & Inference, 2011, 141: 1543-1553.
    [18]
    LIU C, RUBIN D B. ML estimation of the t distribution using EM and its extensions, ECM and ECME[J]. Statistic Sinica, 1995, 5(1): 19-39.
    [19]
    LIN P. Some characterizations of the multivariate t distribution[J]. Journal of Multivariate Analysis, 1972, 2: 339-344.
    [20]
    KOTZ S, NADARAJAH S. Multivariate t Distributions and Their Applications[M]. Cambridge, UK: Cambridge University Press, 2004.
    [21]
    CHIU T Y M, LEONARD T, TSUI K W. The matrix-logarithm covariance model[J]. Journal of American Statistical Association, 1996, 91: 198-210.
    [22]
    WHITE H. Maximum likelihood estimation of misspecied models[J]. Econometrica, 1982, 50: 1-25.
    [23]
    FERNANDEZ C, STEEL M F J. Multivariate student-t regression models: pitfalls and inference[J]. Biometrika, 1999, 86: 153-167.
    [24]
    LOUIS T A. Finding the observed information matrix when using the EM algorithm[J]. Journal of the Royal Statistical Society B, 1982, 44: 226-233.
    [25]
    MENG X L, RUBIN D B. Maximum likelihood estimation via the ECM algorithm: A general framework[J]. Biometrika, 1993, 80: 267-278.
    [26]
    TUKEY J W. One degree of freedom for non-Additivity[J]. Biometrics, 1949, 5: 232-242.
    [27]
    ZEGER S L， DIGGLE P J. Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters[J]. Biometrics, 1994, 50: 689-699.
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