Separability tests for high-dimensional,low-sample size multivariate repeated measures data |
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Authors: | Sean L Simpson Lloyd J Edwards Martin A Styner Keith E Muller |
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Institution: | 1. Department of Biostatistical Sciences, Wake Forest University School of Medicine, Winston-Salem, NC 27157-1063, USA;2. Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7420, USA;3. Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7420, USA;4. Departments of Psychiatry and Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7160, USA;5. Department of Health Outcomes and Policy, University of Florida, Gainesville, FL 32610-0177, USA |
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Abstract: | Longitudinal imaging studies have moved to the forefront of medical research due to their ability to characterize spatio-temporal features of biological structures across the lifespan. Valid inference in longitudinal imaging requires enough flexibility of the covariance model to allow reasonable fidelity to the true pattern. On the other hand, the existence of computable estimates demands a parsimonious parameterization of the covariance structure. Separable (Kronecker product) covariance models provide one such parameterization in which the spatial and temporal covariances are modeled separately. However, evaluating the validity of this parameterization in high dimensions remains a challenge. Here we provide a scientifically informed approach to assessing the adequacy of separable (Kronecker product) covariance models when the number of observations is large relative to the number of independent sampling units (sample size). We address both the general case, in which unstructured matrices are considered for each covariance model, and the structured case, which assumes a particular structure for each model. For the structured case, we focus on the situation where the within-subject correlation is believed to decrease exponentially in time and space as is common in longitudinal imaging studies. However, the provided framework equally applies to all covariance patterns used within the more general multivariate repeated measures context. Our approach provides useful guidance for high dimension, low-sample size data that preclude using standard likelihood-based tests. Longitudinal medical imaging data of caudate morphology in schizophrenia illustrate the approaches appeal. |
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Keywords: | Kronecker product separable covariance multivariate repeated measures likelihood ratio test spatio-temporal data linear exponent autoregressive model |
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