Dear Mark,

>I am trying to run a 2nd level ANOVA of a number of F-contrasts using
>SPM2. From previous posts at the SPM-list, I can see that one has to use
>the beta-images from the 1st level analysis and then define the F-contrast
>after having performed the 2nd level analysis. I have 6 different (groups)
>effects from 1st level t....
>
>.. Today, at the SPM-list, a reply was posted by S. F. W. Neggers, who one
>year ago encountered the same problem, i.e. for some combinations of number
>of groups and replications it failed. He had come to the same conclusion
>that it seemed to be a bug in SPM, and he has stopped using 2nd level ANOVAs
>for F-contrasts.

I just wanted to comment on your difficulties to supplement Will's
excellent advice.  I am sorry you have had problems with the non-sphericity
estimation.   The reason it crashed was that one, or more covariance
components
could not be estimated.

The problem here is more about specification of the non-sphericity (than a
mathematical
issue).  Specifying covariance components Q{i} is a bit like specifying
response
components X(:,i) in the design matrix.  Usually, because of our
assumptions (e.g.
i.i.d) about the errors, this part of model specification is implicit.
However,
SPM now allows arbitrary covariance structures (whether or not is the
covariance
components can be estimated).  To avoid asking people to specify
potentially very
complicated covariances we have tried to simplify the specification by
using the experimental design and prompting for a few answers about
independence
and identity.  These questions represent a balance between simplicity and
latitude
of model specification.  I wanted to apologise because we are still trying
to find
the right balance:

The updated version of the SPM questions Will referred to, reflect the fact
we have not
finalised the best way of specifying the components.  I suspect you have
used an
earlier version that automatically assumes correlations among the errors
and created
too many covariance components (you could see this by looking at
SPM.xVi.V{:}).
The new specification may be more parsimonious (although we have also made
spm_reml
more robust).

As an example of this problem, consider your own design.  Ideally you would
like to model
different error variance components for the linear and quadratic contrasts,
from the first-level
(i.e. two components).  However, the second-level SPM model does not know
that the six conditions
comprise 3 linear and 3 quadratic observations.  It therefore creates at
least 6 components
(and more if the errors are not independent).  It is perfectly possible to
delete
unwanted components from SPM.xVi.V{:} before estimation - but this entails
some expertise
and confidence in model specification.  It may be some time before we find
a foolproof and
easy way to specify these components. In the interim, try to keep things as
simple as possible
and only use non-spherical models when they are clearly motivated.  In your
case there is a clear
motivation (i.e. an inference about the coefficients of a polynomial
expansion).

I hope this explains the problems you and some of our colleagues have been
experiencing - Karl