Longitudinal imaging studies are moving increasingly to the forefront of medical research due to their ability to characterize spatio-temporal features of biological structures
across the lifespan. Modeling the correlation pattern of these types of data can be immensely important for proper analyses. Accurate inference requires proper choice of the correlation model. Optimal efficiency of the estimation procedure demands a parsimonious parameterization of the correlation structure, with sufficient sensitivity to detect the range of correlation patterns that may occur. The linear exponent autoregressive (LEAR) correlation structure is a flexible two-parameter correlation model that can be applied in situations in which the within subject correlation is believed to decrease 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. 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 concerning schizophrenia and caudate morphology exemplifies the benefits of the Kronecker product LEAR correlation structure.
KEY WORDS: Multivariate repeated measures; Kronecker product; Generalized autoregressive model; Doubly multivariate data; Spatio-temporal data; Separable covariance.