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A SEMIPARAMETRIC BAYESIAN APPROACH TO MULTIVARIATE LONGITUDINAL DATA
Author(s) -
Ghosh Pulak,
Hanson Timothy
Publication year - 2010
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2010.00581.x
Subject(s) - multivariate statistics , mathematics , multivariate normal distribution , skewness , statistics , random effects model , bayesian probability , parametric statistics , semiparametric model , econometrics , medicine , meta analysis
Summary We extend the standard multivariate mixed model by incorporating a smooth time effect and relaxing distributional assumptions. We propose a semiparametric Bayesian approach to multivariate longitudinal data using a mixture of Polya trees prior distribution. Usually, the distribution of random effects in a longitudinal data model is assumed to be Gaussian. However, the normality assumption may be suspect, particularly if the estimated longitudinal trajectory parameters exhibit multi‐modality and skewness. In this paper we propose a mixture of Polya trees prior density to address the limitations of the parametric random effects distribution. We illustrate the methodology by analysing data from a recent HIV‐AIDS study.