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General Multi-Level Linear Modelling for Group Analysis in FMRI

FMRIB Technical Report TR01CB1
(A related paper has been accepted for publication in NeuroImage)

Christian F. Beckmann*, Mark Jenkinson* and Stephen M. Smith

Oxford Centre for Functional Magnetic Resonance Imaging of the Brain (FMRIB),
Department of Clinical Neurology, University of Oxford, John Radcliffe Hospital,
Headley Way, Headington, Oxford, UK
Corresponding author:
* These authors contributed equally to the work.


This paper discusses general modelling of multi-subject and/or multi-session FMRI data. In particular, we show that a two-level mixed-effects model (where parameters of interest at the group level are estimated from parameter and variance estimates from the single-session level) can be made equivalent to a single complete mixed-effects model (where parameters of interest at the group level are estimated directly from all of the original single-sessions' time-series data) if the (co-)variance at the second level is set equal to the sum of the (co-)variances in the single-level form, using the BLUE with known covariances. This result has significant implications for group studies in FMRI, since it shows that the group analysis only requires values of the parameter estimates and their (co-)variance from the first level, generalising the well established 'summary statistics' approach in FMRI. The simple and generalised framework allows for different pre-whitening and different first-level regressors to be used for each subject. The framework incorporates multiple levels and cases such as repeated measures, paired or unpaired $ t$-tests and $ F$-tests at the group level; explicit examples of such models are given in the paper. Using numerical simulations based on typical first level covariance structures from real FMRI data we demonstrate that by taking into account lower-level covariances and heterogeneity a substantial increase in higher-level $ Z$-score is possible.  

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Next: Introduction
Christian Beckmann 2003-07-16