Statistics Seminar: Pourahmadi -- Generalized Linear Models for the Covariance Matrix of Longitudinal Data

Mohsen Pourahmadi Department of Statistics Texas A&M University 

Location: Carslaw 829 

Time: 11-12am Tuesday, July 14, 2009 (*** note the unusual time and location ***) 

Title: Generalized Linear Models for the Covariance Matrix of Longitudinal Data 

Abstract: Finding an unconstrained and statistically interpretable reparameterization of
a general covariance matrix is still an open problem in statistics.  Its solution is
crucial for parsimonious and sparse modeling, and guaranteeing the positive-definiteness
of an estimated covariance matrix in all areas of statistics dealing with correlated
data, including the longitudinal (panel, functional, spectroscopic, repeated measure,
...)  data.  It is known that some estimated covariance matrices are not necessarily
positive-definite, and recently due to popularity of generalized estimating equations
(GEE) and SAS PROC Mixed, there has been a growing tendency to pick a covariance matrix
for a data set from a long and expanding menu of covariance matrices, a task which is
difficult even for the experts.  In this presentation, pooling together ideas from
regression and time series analysis, I will discuss a data-based, general-purpose method
extending the framework of generalized linear models (GLMs) to covariance matrices,
where a link function is introduced through the Cholesky decomposition.  It reduces the
difficult and unintuitive task of modeling a covariance matrix to that of modeling a
sequence of (auto) regressions.  Therefore, all existing regression machineries and
approaches such as parametric, semiparametric, nonparametric, Bayesian, shrinkage
(Ridge, Lasso, ...), etc.  can be brought to the service of modeling covariances.