IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v189y2022ics0047259x21002049.html
   My bibliography  Save this article

Latent Gaussian copula models for longitudinal binary data

Author

Listed:
  • Peng, Cheng
  • Yang, Yihe
  • Zhou, Jie
  • Pan, Jianxin

Abstract

Longitudinal binary data arise commonly in a variety of fields including public health, biomedicine, finance, agriculture and social science, among many others. In longitudinal binary studies, the aims are to assess the association of longitudinal binary response with certain covariates of interest, and to quantify the within-subject correlations for longitudinal binary responses. In the literature, various methods were developed to model longitudinal binary data but little work was done to account for the fact that the correlation coefficients of correlated binary responses have the so-called Fréchet–Hoeffding bounds. Ignoring this fact can lead to incorrect statistical inferences for longitudinal binary data. In this paper, based on latent Gaussian copula a new statistical modeling method is proposed to model the mean and within-subject correlation structures, simultaneously, for longitudinal binary data. Specifically, the mean structure is modeled by a semiparametric regression model, and the within-subject correlation coefficients are modeled through introducing a latent Gaussian copula model with certain latent correlation structures characterized by some parameters. Generalized estimating equations are then proposed to estimate the parameters in the mean and latent correlation structures, and consistency and asymptotic normality of the resulting parameter estimators are established. The proposed model and method ensure that the estimated correlation coefficients must satisfy the Fréchet–Hoeffding bounds for longitudinal binary data. Simulation studies show that the proposed method has a stable numerical performance. A practical data set is analyzed using the proposed method for illustration.

Suggested Citation

  • Peng, Cheng & Yang, Yihe & Zhou, Jie & Pan, Jianxin, 2022. "Latent Gaussian copula models for longitudinal binary data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jmvana:v:189:y:2022:i:c:s0047259x21002049
    DOI: 10.1016/j.jmva.2021.104940
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X21002049
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2021.104940?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. You-Gan Wang, 2003. "Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance," Biometrika, Biometrika Trust, vol. 90(1), pages 29-41, March.
    2. He, Xuming & Fung, Wing K. & Zhu, Zhongyi, 2005. "Robust Estimation in Generalized Partial Linear Models for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1176-1184, December.
    3. S. le Cessie & J. C. van Houwelingen, 1994. "Logistic Regression for Correlated Binary Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 95-108, March.
    4. You-Gan Wang & Vincent J. Carey, 2004. "Unbiased Estimating Equations From Working Correlation Models for Irregularly Timed Repeated Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 845-853, January.
    5. Leng, Chenlei & Zhang, Weiping & Pan, Jianxin, 2010. "Semiparametric Mean–Covariance Regression Analysis for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 181-193.
    6. Huang, Chao & Farewell, Daniel & Pan, Jianxin, 2017. "A calibration method for non-positive definite covariance matrix in multivariate data analysis," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 45-52.
    7. Fan, Jianqing & Huang, Tao & Li, Runze, 2007. "Analysis of Longitudinal Data With Semiparametric Estimation of Covariance Function," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 632-641, June.
    8. Huajun Ye & Jianxin Pan, 2006. "Modelling of covariance structures in generalised estimating equations for longitudinal data," Biometrika, Biometrika Trust, vol. 93(4), pages 927-941, December.
    9. Wei Pan, 2001. "Akaike's Information Criterion in Generalized Estimating Equations," Biometrics, The International Biometric Society, vol. 57(1), pages 120-125, March.
    10. Huang, Youjun & Pan, Jianxin, 2021. "Joint generalized estimating equations for longitudinal binary data," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    11. N. Rao Chaganty & Harry Joe, 2004. "Efficiency of generalized estimating equations for binary responses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 851-860, November.
    12. Hin, Lin-Yee & Carey, Vincent J. & Wang, You-Gan, 2007. "Criteria for WorkingCorrelationStructure Selection in GEE: Assessment via Simulation," The American Statistician, American Statistical Association, vol. 61, pages 360-364, November.
    Full references (including those not matched with items on IDEAS)

    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. Luo, Renwen & Pan, Jianxin, 2022. "Conditional generalized estimating equations of mean-variance-correlation for clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    2. Liya Fu & Yangyang Hao & You-Gan Wang, 2018. "Working correlation structure selection in generalized estimating equations," Computational Statistics, Springer, vol. 33(2), pages 983-996, June.
    3. Xu, Jianwen & Wang, You-Gan, 2014. "Intra-cluster correlation structure in longitudinal data analysis: Selection criteria and misspecification tests," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 70-77.
    4. 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.
    5. Chen, Ziqi & Shi, Ning-Zhong & Gao, Wei & Tang, Man-Lai, 2011. "Efficient semiparametric estimation via Cholesky decomposition for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3344-3354, December.
    6. Merlo, Luca & Petrella, Lea & Salvati, Nicola & Tzavidis, Nikos, 2022. "Marginal M-quantile regression for multivariate dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    7. Fu, Liya & Wang, You-Gan, 2016. "Efficient parameter estimation via Gaussian copulas for quantile regression with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 492-502.
    8. Wang, You-Gan & Hin, Lin-Yee, 2010. "Modeling strategies in longitudinal data analysis: Covariate, variance function and correlation structure selection," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3359-3370, December.
    9. Huang, Youjun & Pan, Jianxin, 2021. "Joint generalized estimating equations for longitudinal binary data," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    10. Kwon, Yongchan & Choi, Young-Geun & Park, Taesung & Ziegler, Andreas & Paik, Myunghee Cho, 2017. "Generalized estimating equations with stabilized working correlation structure," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 1-11.
    11. María Carmen Pardo & Rosa Alonso, 2019. "Working correlation structure selection in GEE analysis," Statistical Papers, Springer, vol. 60(5), pages 1447-1467, October.
    12. Rui Li & Chenlei Leng & Jinhong You, 2017. "A Semiparametric Regression Model for Longitudinal Data with Non-stationary Errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 932-950, December.
    13. Hines, R.J. O'Hara & Hines, W.G.S., 2010. "Indices for covariance mis-specification in longitudinal data analysis with no missing responses and with MAR drop-outs," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 806-815, April.
    14. Samuel D. Oman & Victoria Landsman & Yohay Carmel & Ronen Kadmon, 2007. "Analyzing Spatially Distributed Binary Data Using Independent-Block Estimating Equations," Biometrics, The International Biometric Society, vol. 63(3), pages 892-900, September.
    15. Vens, Maren & Ziegler, Andreas, 2012. "Generalized estimating equations and regression diagnostics for longitudinal controlled clinical trials: A case study," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1232-1242.
    16. 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.
    17. Ziqi Chen & Man†Lai Tang & Wei Gao, 2018. "A profile likelihood approach for longitudinal data analysis," Biometrics, The International Biometric Society, vol. 74(1), pages 220-228, March.
    18. You-Gan Wang & Xu Lin, 2005. "Effects of Variance-Function Misspecification in Analysis of Longitudinal Data," Biometrics, The International Biometric Society, vol. 61(2), pages 413-421, June.
    19. Lv, Jing & Guo, Chaohui & Yang, Hu & Li, Yalian, 2017. "A moving average Cholesky factor model in covariance modeling for composite quantile regression with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 129-144.
    20. Chaohui Guo & Hu Yang & Jing Lv, 2018. "Two step estimations for a single-index varying-coefficient model with longitudinal data," Statistical Papers, Springer, vol. 59(3), pages 957-983, September.

    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:jmvana:v:189:y:2022:i:c:s0047259x21002049. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.