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

Authors:
Y. Wang;M. J. Daniels
Affiliations:
Department of Biostatistics, University of Florida, Dauer Hall, Gainesville, FL 32611, United States;Section of Integrative Biology, Division of Statistics & Scientific Computation, University of Texas at Austin, 141MC Patterson Hall, Austin, TX 78712, United States
Venue:
Journal of Multivariate Analysis
Year:
2013

Citing 3
Cited 0

Bayesian modeling of several covariance matrices and some results on propriety of the posterior for linear regression with correlated and/or heterogeneous errors

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Generating random correlation matrices based on partial correlations

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Modeling covariance matrices via partial autocorrelations

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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.