Multilevel Matrix-Variate Analysis and Its Application to Accelerometry-Measured Physical Activity in Clinical Populations

Document Type


Publication Date


Journal / Book Title

Journal of the American Statistical Association


The number of studies where the primary measurement is a matrix is exploding. In response to this, we propose a statistical framework for modeling populations of repeatedly observed matrix-variate measurements. The 2D structure is handled via a matrix-variate distribution with decomposable row/column-specific covariance matrices and a linear mixed effect framework is used to model the multilevel design. The proposed framework flexibly expands to accommodate many common crossed and nested designs and introduces two important concepts: the between-subject distance and intraclass correlation coefficient, both defined for matrix-variate data. The computational feasibility and performance of the approach is shown in extensive simulation studies. The method is motivated by and applied to a study that monitored physical activity of individuals diagnosed with congestive heart failure (CHF) over a 4- to 9-month period. The long-term patterns of physical activity are studied and compared in two CHF subgroups: with and without adverse clinical events. Supplementary materials for this article, that include de-identified accelerometry and clinical data, are available online.



Published Citation

Huang, L., Bai, J., Ivanescu, A., Harris, T., Maurer, M., Green, P., & Zipunnikov, V. (2018). Multilevel matrix-variate analysis and its application to accelerometry-measured physical activity in clinical populations. Journal of the American Statistical Association.