Dear Elinor,

>My name is E Elinor Chen, a postdoc at the Brain Research Imaging Center at
>the University of Chicago. I am working with Ana Solodkin and Steve Small
>using SEM for the analysis of fMRI data. Steve suggested that I email you
>about a question on a recent paper.
>
>In one of your interesting papers (published in NeuroImage, 2002. Attention
>to Action: specific modulation corticocortical interactions in Humans.) , a
>one-sample t-test was performed on each path connection for all subjects in
>order to test a null hypothesis (single path coefficient equals zero) at a
>group level. To be honest with you, I don't quite understand the statistical
>principle behind it, since I thought that the path coefficient depends on
>other path coefficients in the network. I am well aware of the difficulty
>drawing conclusions at a group level using SEM, since the variability among
>subjects is very large as you have mentioned in your other papers.

I understand your reservations.  However, conditional dependency among path
coefficient estimates in SEM would only be an issue if you wanted to compare
all the connections at the same time.  When comparing single connections with
a T-test this is not a problem.  A Bonferroni correction for the number of
T-tests will ensure valid inference, even in the context of correlated
estimators.

>And if it is statistically valid, does this mean we really do not need to
>compare networks, using for instance the stacked method? I understand that
>the different types of analysis (t-test and stacked model) would lead to
>different interpretations. On the other hand, I would like to have a better
>understanding of the validity and overall value of this approach.

Yes.  In fact, the idea of performing group comparisons using a stacked
model approach is quite a novel one and involves constructing multi-subject
networks.  See the paper below.  However, it may be simpler to use classical
tests (e.g. the T-test) to compare the path coefficients estimated using  more
conventional single-subject SEMs.  Note that inference about group
differences with a T-Test uses the coefficients from the SEM but does
not call on SEM for inference.

I hope this helps - Karl


Neuroimage. 2002 Nov;17(3):1459-69. Effective connectivity and intersubject
variability: using a multisubject network to test differences and
commonalities.

Mechelli A, Penny WD, Price CJ, Gitelman DR, Friston KJ.
Wellcome Department of Imaging Neuroscience, Institute of Neurology, 12
Queen Square, London, WCIN 3BG, United Kingdom. [log in to unmask]

This article is about intersubject variability in the functional
integration of activity in different brain regions. Previous studies of
functional and effective connectivity have dealt with intersubject
variability by analyzing data from different subjects separately or
pretending the data came from the same subject. These approaches do not
allow one to test for differences among subjects. The aim of this work was
to illustrate how differences in connectivity among subjects can be
addressed explicitly using structural equation modeling. This is enabled by
constructing a multisubject network that comprises m regions of interest
for each of the n subjects studied, resulting in a total of m x n nodes.
Constructing a network of regions from different subjects may seem
counterintuitive but embodies two key advantages. First, it allows one to
test directly for differences among subjects by comparing models that do
and do not allow a particular connectivity parameter to vary over subjects.
Second, a multisubject network provides additional degrees of freedom to
estimate the model's free parameters. Any neurobiological hypothesis
normally addressed by single-subject or group analyses can still be tested,
but with greater sensitivity. The common influence of experimental
variables is modeled by connecting a virtual node, whose time course
reflects stimulus onsets, to the sensory or "input" region in all subjects.
Further experimental changes in task or cognitive set enter through
modulation of the connections. This approach allows one to model both
endogenous (or intrinsic) variance and exogenous effects induced by
experimental design. We present a functional magnetic resonance imaging
study that uses a multisubject network to investigate intersubject
variability in functional integration in the context of single word and
pseudoword reading. We tested whether the effect of word type on the
reading-related coupling differed significantly among subjects. Our results
showed that a number of forward and backward connections were stronger for
reading pseudowords than words, and, in one case, connectivity showed
significant intersubject variability. The discussion focuses on the
implications of our findings and on further applications of the
multisubject network analysis.