Statistics and Data Science Seminar
Mohsen Pourahmadi
Division of Statistics, Northern Illinois University
Generalized Linear Models For the Covariance Matrix of Longitudinal Data
Abstract: We survey the progress made in modelling covariance matrices from the
perspective of generalized linear models (GLM) and show how one can move beyond
the use of the identity and logarithmic link functions, and prespecified
structures. Observing that most time-domain models (ARMA, state-space,....) in
time series analysis are means to diagonalize a Toeplitz covariance matrix via a
unit lower triangular matrix (Cholesky decomposition), we discuss the
distinguished role of the Cholesky decomposition in providing a systematic and
data-based procedure for formulating and fitting parsimonious models for general
covariance matrices guaranteeing the positive-definiteness of the estimates.
Pulling together some techniques from regression and time series analyses
provide the necessary tools for the procedure which reduces the unintuitive task
of modelling covariance matrices to that of a sequence of regression models. The
procedure is illustrated using a real longitudinal dataset.Once a bona fide
GLM framework for modelling covariances is found, its bayesian, nonparametric,
generalized additive and other extensions can be developed in direct analogy
with the respective extensions of the traditional GLM.
Tea will be provided at 3:15pm.
Wednesday November 2, 2005 at 3:30 PM in SEO 512