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

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  • 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
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    References listed on IDEAS

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    7. 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.
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    10. Michael J. Daniels & Robert E. Kass, 2001. "Shrinkage Estimators for Covariance Matrices," Biometrics, The International Biometric Society, vol. 57(4), pages 1173-1184, December.
    11. 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.
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