In this section we discuss the limitations of the model framework presented above. The first and most obvious limitation is that the framework is purely linear, as it is an instance of the GLM. Linear modelling, however, is a very common and flexible model for FMRI data. Secondly, in order for the model to be decomposed into two levels, and hence allow for efficient two-level computation, it is necessary that the stacked first-level covariance matrix, , does not contain any non-zero off-diagonal blocks. This is equivalent to assuming that the first-level residuals are not correlated between sessions or subjects.

Efficient computation at the second-level requires full access to the
first-level parameter estimates and associated covariances. This
involves both the variances of the parameter estimates and the
covariances *between* different parameters. It is not sufficient
to only use the first-level statistical parametric maps
(i.e. -scores, -scores or -scores). Finally, the estimation
of covariance parameters at the second-level often imposes
restrictions in the types of model which are practically estimable.
This is often more problematic at the second level because there is
usually only a small number of subjects/sessions that are being
modelled. For instance, while it is possible to formulate a model
where the variance about the group mean is different for each
session/subject, such a model is not estimable because there is only a
single measurement per session/subject.