PLACE:  319 Snedecor

SPEAKER:
Mike Daniels
Iowa State University

TITLE:
Dynamic Models and Bayesian Analysis of Covariance Matrices in Longitudinal Data

ABSTRACT:

 Modeling the within-subject covariance structure is of great importance in
 longitudinal and epidemiological studies.  Using the (square-root free)
 Cholesky decomposition, we show that any such dependence structure (covariance
 matrix) can be realized through special dynamic models with two design
 matrices, the first, corresponding to the mean, is fixed and the second,
 depending on the lagged responses and the mean parameters, is random.  This
 class of dynamic models includes, for example, all general linear models,
 stationary time series models, variable-order antedependence models, and
 time-varying parameter autoregressive models. The close connection with mixed
 and state space models allows the use of the current conceptual, computational
 and software developments from these areas.  We provide a convenient and
 intuitive framework for developing partially conjugate prior distributions for
 covariance matrices and show their connections with the (generalized) inverse
 Wishart priors.  Our priors offer many advantages in regard to elicitation,
 positive definiteness, computations using Gibbs sampling, and modeling
 covariances using covariates. Iteratively reweighted least squares and Bayesian
 estimation methods are developed. Specific attention is given to how these
 models can be fit in standard software packages.
 
 

COFFEE: 3:45 p.m., 104 Snedecor