IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v116y2013icp130-140.html
   My bibliography  Save this article

Bayesian modeling of the dependence in longitudinal data via partial autocorrelations and marginal variances

Author

Listed:
  • Wang, Y.
  • Daniels, M.J.

Abstract

Many parameters and positive-definiteness are two major obstacles in estimating and modeling a correlation matrix for longitudinal data. In addition, when longitudinal data is incomplete, incorrectly modeling the correlation matrix often results in bias in estimating mean regression parameters. In this paper, we introduce a flexible and parsimonious class of regression models for a covariance matrix parameterized using marginal variances and partial autocorrelations. The partial autocorrelations can freely vary in the interval (−1,1) while maintaining positive definiteness of the correlation matrix so the regression parameters in these models will have no constraints. We propose a class of priors for the regression coefficients and examine the importance of correctly modeling the correlation structure on estimation of longitudinal (mean) trajectories and the performance of the DIC in choosing the correct correlation model via simulations. The regression approach is illustrated on data from a longitudinal clinical trial.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:116:y:2013:i:c:p:130-140
    DOI: 10.1016/j.jmva.2012.11.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X12002692
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2012.11.010?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. Merlise Clyde & Edward I. George, 2000. "Flexible empirical Bayes estimation for wavelets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 681-698.
    2. Michael J. Daniels & Robert E. Kass, 2001. "Shrinkage Estimators for Covariance Matrices," Biometrics, The International Biometric Society, vol. 57(4), pages 1173-1184, December.
    3. Chenguang Wang & Michael J. Daniels, 2011. "A Note on MAR, Identifying Restrictions, Model Comparison, and Sensitivity Analysis in Pattern Mixture Models with and without Covariates for Incomplete Data," Biometrics, The International Biometric Society, vol. 67(3), pages 810-818, September.
    4. Joe, Harry, 2006. "Generating random correlation matrices based on partial correlations," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2177-2189, November.
    5. Daniels, Michael J., 2006. "Bayesian modeling of several covariance matrices and some results on propriety of the posterior for linear regression with correlated and/or heterogeneous errors," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1185-1207, May.
    6. Frederick Wong, 2003. "Efficient estimation of covariance selection models," Biometrika, Biometrika Trust, vol. 90(4), pages 809-830, December.
    7. John C. Liechty, 2004. "Bayesian correlation estimation," Biometrika, Biometrika Trust, vol. 91(1), pages 1-14, March.
    8. 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.
    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. M. Pourahmadi & M. J. Daniels, 2002. "Dynamic Conditionally Linear Mixed Models for Longitudinal Data," Biometrics, The International Biometric Society, vol. 58(1), pages 225-231, March.
    11. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    12. Alan Agresti & David B. Hitchcock, 2005. "Bayesian inference for categorical data analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(3), pages 297-330, December.
    13. Smith M. & Kohn R., 2002. "Parsimonious Covariance Matrix Estimation for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1141-1153, December.
    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. Hui Yao & Sungduk Kim & Ming-Hui Chen & Joseph G. Ibrahim & Arvind K. Shah & Jianxin Lin, 2015. "Bayesian Inference for Multivariate Meta-Regression With a Partially Observed Within-Study Sample Covariance Matrix," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 528-544, June.

    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. Daniels, M.J. & Pourahmadi, M., 2009. "Modeling covariance matrices via partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2352-2363, November.
    2. 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.
    3. Carter, Christopher K. & Wong, Frederick & Kohn, Robert, 2011. "Constructing priors based on model size for nondecomposable Gaussian graphical models: A simulation based approach," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 871-883, May.
    4. Daniels, Michael J., 2006. "Bayesian modeling of several covariance matrices and some results on propriety of the posterior for linear regression with correlated and/or heterogeneous errors," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1185-1207, May.
    5. Smith, Michael Stanley, 2015. "Copula modelling of dependence in multivariate time series," International Journal of Forecasting, Elsevier, vol. 31(3), pages 815-833.
    6. Bo Cai & David B. Dunson, 2006. "Bayesian Covariance Selection in Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 62(2), pages 446-457, June.
    7. Hui Yao & Sungduk Kim & Ming-Hui Chen & Joseph G. Ibrahim & Arvind K. Shah & Jianxin Lin, 2015. "Bayesian Inference for Multivariate Meta-Regression With a Partially Observed Within-Study Sample Covariance Matrix," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 528-544, June.
    8. Paolo Giordani & Xiuyan Mun & Robert Kohn, 2012. "Efficient Estimation of Covariance Matrices using Posterior Mode Multiple Shrinkage," Journal of Financial Econometrics, Oxford University Press, vol. 11(1), pages 154-192, December.
    9. Michael S. Smith & Shaun P. Vahey, 2016. "Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 416-434, July.
    10. Helen Armstrong & Christopher K. Carter & Kevin K. F. Wong & Robert Kohn, 2007. "Bayesian Covariance Matrix Estimation using a Mixture of Decomposable Graphical Models," Discussion Papers 2007-13, School of Economics, The University of New South Wales.
    11. Wang, Hao, 2010. "Sparse seemingly unrelated regression modelling: Applications in finance and econometrics," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2866-2877, November.
    12. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    13. Koop, Gary & Korobilis, Dimitris, 2016. "Model uncertainty in Panel Vector Autoregressive models," European Economic Review, Elsevier, vol. 81(C), pages 115-131.
    14. Dimitris Korobilis, 2013. "Var Forecasting Using Bayesian Variable Selection," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 204-230, March.
    15. Peter J. Danaher & Michael S. Smith, 2011. "Rejoinder--Estimation Issues for Copulas Applied to Marketing Data," Marketing Science, INFORMS, vol. 30(1), pages 25-28, 01-02.
    16. Andrew Gelman, 2003. "A Bayesian Formulation of Exploratory Data Analysis and Goodness‐of‐fit Testing," International Statistical Review, International Statistical Institute, vol. 71(2), pages 369-382, August.
    17. Jean-Paul Fox & Joris Mulder & Sandip Sinharay, 2017. "Bayes Factor Covariance Testing in Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 979-1006, December.
    18. Davide Delle Monache & Ivan Petrella & Fabrizio Venditti, 2021. "Price Dividend Ratio and Long-Run Stock Returns: A Score-Driven State Space Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 1054-1065, October.
    19. Dimitris Korobilis & Kenichi Shimizu, 2022. "Bayesian Approaches to Shrinkage and Sparse Estimation," Foundations and Trends(R) in Econometrics, now publishers, vol. 11(4), pages 230-354, June.
    20. Andrea Gabrio & Michael J. Daniels & Gianluca Baio, 2020. "A Bayesian parametric approach to handle missing longitudinal outcome data in trial‐based health economic evaluations," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 607-629, February.

    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:116:y:2013:i:c:p:130-140. 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.