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
-tests and 
-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 
-score is possible.