title: Kronecker product linear exponent AR(1) correlation structures for multivariate repeated measures.
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. Credible models of the correlations in longitudinal imaging require two or more pattern components. Valid inference requires enough flexibility of the correlation model to allow reasonable fidelity to the true pattern. On the other hand, the existence of computable estimates demands a parsimonious parameterization of the correlation structure. For many one-dimensional spatial or temporal arrays, the linear exponent autoregressive (LEAR) correlation structure meets these two opposing goals in one model. The LEAR structure is a flexible two-parameter correlation model that applies to situations in which the within-subject correlation decreases exponentially in time or space. It allows for an attenuation or acceleration of the exponential decay rate imposed by the commonly used continuous-time AR(1) structure. We propose the Kronecker product LEAR correlation structure for multivariate repeated measures data in which the correlation between measurements for a given subject is induced by two factors (e.g., spatial and temporal dependence). Excellent analytic and numerical properties make the Kronecker product LEAR model a valuable addition to the suite of parsimonious correlation structures for multivariate repeated measures data. Longitudinal medical imaging data of caudate morphology in schizophrenia illustrates the appeal of the Kronecker product LEAR correlation structure.
authors.affiliation: Department of Biostatistical Sciences, Wake Forest School of Medicine, Winston-Salem, North Carolina, United States of America ; Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America.
authors.forename: Sean L
authors.initials: SL
authors.lastname: Simpson
authors.affiliation: Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America.
authors.forename: Lloyd J
authors.initials: LJ
authors.lastname: Edwards
authors.affiliation: Departments of Psychiatry and Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, United States of America.
authors.forename: Martin A
authors.initials: MA
authors.lastname: Styner
authors.affiliation: Department of Health Outcomes and Policy, University of Florida, Gainesville, Florida, United States of America.
authors.forename: Keith E
authors.initials: KE
authors.lastname: Muller
mesh_terms: D002421:Caudate Nucleus / Q000473:pathology*; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008962:Models, Theoretical; D015999:Multivariate Analysis; D012559:Schizophrenia / Q000473:pathology*; D059008:Time-Lapse Imaging / Q000379:methods*