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Bayesian modeling of the dependence in longitudinal data via partial autocorrelations and marginal variances. (English) Zbl 1277.62088
Summary: Many parameters and positive-definiteness are two major obstacles in estimating and modeling a correlation matrix for longitudinal data. In addition, when longitudinal data are incomplete, incorrectly modeling the correlation matrix often results in bias in estimating the mean regression parameters. 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 deviance information criterion (DIC) in choosing the correct correlation model via simulations. The regression approach is illustrated on data from a longitudinal clinical trial.

62F15 Bayesian inference
62J12 Generalized linear models (logistic models)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H20 Measures of association (correlation, canonical correlation, etc.)
62P10 Applications of statistics to biology and medical sciences; meta analysis
65C60 Computational problems in statistics (MSC2010)
Full Text: DOI
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