Group analyses

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Group analyses
Will Penny

• Wellcome Dept. of Imaging Neuroscience
• University College London

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Data
fMRI, single subject
EEG/MEG, single subject
Time
fMRI, multi-subject
ERP/ERF, multi-subject
Hierarchical model for all imaging data!
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Reminder voxel by voxel
model specification
parameter estimation
Time
hypothesis
statistic
Time
Intensity
single voxel time series
SPM
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General Linear Model


Error Covariance

• Model is specified by
• Design matrix X
• Assumptions about e

N number of scans p number of regressors
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Estimation
1. ReML-algorithm
2. Weighted Least Squares
Friston et al. 2002, Neuroimage
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Hierarchical model
Multiple variance components at each level
Hierarchical model
At each level, distribution of parameters is
given by level above.
What we dont know distribution of parameters
and variance parameters.
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Example Two level model




Second level
First level
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Estimation
Hierarchical model
Single-level model
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Group analysis in practice
Many 2-level models are just too big to compute.
And even if, it takes a long time!
Is there a fast approximation?
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Summary Statistics approach
Second level
First level
Data Design Matrix Contrast Images
SPM(t)
One-sample t-test _at_ 2nd level
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Validity of approach
The summary stats approach is exact if for each
session/subject
Within-session covariance the same
First-level design the same
All other cases Summary stats approach seems to
be robust against typical violations.
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Auditory Data
Summary statistics
Hierarchical Model
Friston et al. (2004) Mixed effects and fMRI
studies, Neuroimage
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Multiple contrasts per subject
Stimuli
Auditory Presentation (SOA 4 secs) of words
Motion Sound Visual Action
jump click pink turn
Subjects
(i) 12 control subjects
fMRI, 250 scans per subject, block design
Scanning
What regions are affected by the semantic content
of the words?
Question
U. Noppeney et al.
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ANOVA
1st level
3.Visual
4.Action
1.Motion
2.Sound
?
?
?
2nd level
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ANOVA
1st level
Visual
Action
Motion
Sound
?
?
?
2nd level
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Summary
Linear hierarchical models are general enough
for typical multi-subject imaging data (PET,
fMRI, EEG/MEG).
Summary statistics are robust approximation for
group analysis.
Also accomodates multiple contrasts per subject.