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.
Highlights
Multivariate repeated measures studies are characterized by data that have more than one set of correlated outcomes or repeated factors
We model the caudate data with the general linear model for multivariate repeated measures data defined in the previous section
We first assume a separable covariance and model the temporal and spatial factor-specific correlations of the model errors with continuous-time AR(1), damped exponential (DE), and linear exponent autoregressive (LEAR) structures in order to assess the best model via the AIC 1⁄2AIC~{2l(yi; b,Si)z2ðqzwÞ, where q is the number of fixed effect parameters and w is the number of unique covariance parameters
Summary
Multivariate repeated measures studies are characterized by data that have more than one set of correlated outcomes or repeated factors. Spatio-temporal data fall into this more general category, since the outcome variables repeat in both space and time. Valid analysis requires accurately modeling the correlation pattern. Muller et al and Gurka et al showed that underspecifying the correlation structure can severely inflate test size of tests of fixed effects in the general linear mixed model [1,2]. Modeling the correlation pattern separately for each repeated factor with multivariate repeated measures data has substantial advantages. The approach allows for the choosing and tuning of each model separately, which improves accuracy and makes model fitting easier. The approach uses fewer parameters than an unstructured model. The Kronecker product combines the factor-specific correlation structures into an overall correlation model
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
