Modelling the random effects covariance matrix in longitudinal data.
A common class of models for longitudinal data are random effects (mixed) models. In these models, the random effects covariance matrix is typically assumed constant across subject. However, in many situations this matrix may differ by measured covariates. In this paper, we propose an approach to model the random effects covariance matrix by using a special Cholesky decomposition of the matrix. In particular, we will allow the parameters that result from this decomposition to depend on subject-specific covariates and also explore ways to parsimoniously model these parameters. An advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix. In addition, the parameters resulting from this decomposition have a sensible interpretation. We propose fully Bayesian modelling for which a simple Gibbs sampler can be implemented to sample from the posterior distribution of the parameters. We illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects.
Department of Statistics, University of Florida, Gainesville, FL 32611, USA. mdaniels@stat.ufl.edu
Michael J
MJ
Daniels
Yan D
YD
Zhao
D000928:Antidepressive Agents / Q000627:therapeutic use; D003863:Depression / Q000628:therapy; D006801:Humans; D008137:Longitudinal Studies; D015233:Models, Statistical; D011613:Psychotherapy
D000928:Antidepressive Agents