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, Vadim Zipunnikov

Research output: Contribution to journalArticle


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.

Original languageEnglish
Pages (from-to)553-564
Number of pages12
JournalJournal of the American Statistical Association
Issue number526
Publication statusPublished - 3 Apr 2019



  • Actigraphy
  • Principal component analysis
  • Separable covariance

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