Dear Tom and Karl:
So then to sum up if one has two random effects groups in which at least
some members of each group are identical then one cannot do a conjunction
across groups?
Is there a way to get around this? If not is there some way to estimate how
anticonservative a positive correlation is?
Finally, the reason I asked this in the first place was that I wanted to
show where the results of two random effects analyses showed an overlap in
their activations. Judging by this discussion there is really no
statistical way to do this if the groups have common members. Is that correct?
Darren
At 02:45 PM 6/28/2002 +0100, Karl Friston wrote:
>Dear Tom,
>
>I was assuming that the non-sphericity estimated using ReML
>enters into the orthogonalization of contrasts enforced by
>conjunction analyses.
>
>I have just looked and it does not - so you are absolutely
>right! In short the orthogonalization use for conmjunctions
>assumes the errors are uncorrelated (before filtering).
>
>love Karl
>
>
>At 08:10 28/06/2002 -0400, Thomas E Nichols wrote:
> >
> >Hi Karl,
> >
> >> >I agree for SPM99, and this was my precise concern when I asked the
> >> >question, though not with so many symbols. However, is it true that the
>use
> >> >of the non-sphericity correction in SPM2 will deal with this?
> >>
> >> Yes. In fact this was one of the principle motivations for introducing
> >> the non-sphericity option. Tom refers to a fairly subtle form of
> >> non-sphericity induced by correlations among contrasts from each
> >> subject. In other situations, the variance of the contrasts may differ
> >> (e.g. contrasts testing for the hrf and its derivative) which produces
> >> another, simpler, form of non-sphericity (heteroscedasticity).
> >>
> >> In short, allowing for non-sphericity enables mulitple contrasts from
> >> a single subject to be taken up to the second level without assuming
> >> sphericity. This, in turn, enables conjuctions of contrasts at the
> >> second-level.
> >
> >But the non-sphericity correction simply gets the variance estimate
> >right, no? It won't produce independent contrasts (suitable for min{}
> >inference), right?
> >
> >Or am I missing something...
> >
> >-Tom
> >
> >
> >
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Darren R. Gitelman, M.D.
Cognitive Neurology and Alzheimer¹s Disease Center
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