Generalized Linear Mixed Model with Matrix Response of Brain Imaging Data

Oregon Convention Center 

In recent years, there has been a rapid emergence of multiple-subject network longitudinal data, characterized by individual connectivity matrices for each subject, mapped across a consistent set of nodes, and accompanied by information on subject-specific covariates. We introduce a novel generalized linear mixed model, designed to treat these networks as matrix-valued responses and leverage subject covariates as predictors. Our model captures the population-level connectivity patterns via a low-rank intercept matrix and articulates the impact of subject covariates using a sparse slope tensor. We have developed an efficient MCEM algorithm embedding alternating gradient descent method for parameter estimation and edge selection. The effectiveness of our approach is validated through simulations through various data settings and applied in two brain connectivity studies, showcasing its practical utility in contemporary network analysis. Extensive simulation studies demonstrate that our proposed model overperforms the element-wise penalized generalized linear mixed models with LASSO or SCAD penalty.

Generalized Linear Mixed Model

Monte Carlo EM Algorithm

Longitudinal data

Matrix Response

Low Rank Structure

Tensor Slope 

Section on Statistics in Imaging