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

Lei Huang, Jiawei Bai, Andrada Ivanescu, Tamara Harris, Mathew Maurer, Philip Green and Vadim Zipunnikov

Journal of the American Statistical Association, 2019, vol. 114, issue 526, 553-564

Abstract: 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.

Date: 2019
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DOI: 10.1080/01621459.2018.1482750

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