In this presentation, regression models of covariance matrices will be introduced. Two types
of models will be discussed: (1) regressing covariance matrices on scalar covariates of interest,
named as Covariate Assisted Principal (CAP) regression, and (2) regressing covariance matrices
on covariance matrices, i.e., the Covariance-on-Covariance Regression (
CoCR). For (1), the goal
is to use covariates to explain variation in covariance matrices across units. An optimization-
based method for identifying components associated with the covariates using a generalized linear model is introduced. Two approaches for high-dimensional covariance matrix outcomes
will be discussed. This type of models is motivated by resting-state functional magnetic reso-
nance imaging (fMRI) studies, in which brain functional connectivity is an important and widely
used measure of individual and group differences. Our work introduces modeling approaches
that regress whole-brain functional connectivity on covariates and enable identification of brain
subnetworks. The
CoCR model assumes that there exists (at least) a pair of linear projections
on outcome covariance matrices and predictor covariance matrices such that a log-linear model
links the variances in the projection spaces, as well as additional covariates of interest. An ordi-
nary least square type of estimator, which relaxes the distributional assumption, is proposed to
simultaneously identify the projections and estimate model coefficients. Under regularity con-
ditions, the proposed estimator is asymptotically consistent. This type of model is motivated
by utilizing functional connectivity within the resting-state network to predict brain connec-
tivity within a corresponding task-state network. Applying to data collected in the Human
Connectome Project Aging study, three networks, corresponding to a global signal network, a
task-related network, and a task-unrelated network, are identified.
Virtual: Zoom Link to Follow
4 October 2023
1:30pm