1. Wellcome Dept. of Imaging Neuroscience University College London
Group analyses
Will Penny
Wellcome Dept. of Imaging Neuroscience
University College London

2. Data Time fMRI, single subject EEG/MEG, single subject
fMRI, multi-subject
ERP/ERF, multi-subject
Hierarchical model for all imaging data!

3. Reminder: voxel by voxel
model
specification
parameter
estimation
Time
hypothesis
statistic
Time
Intensity
single voxel
time series
SPM

4. General Linear Model = +
Error Covariance
Model is specified by
Design matrix X
Assumptions about e
N: number of scans
p: number of regressors

5. 2. Weighted Least Squares
Estimation
1. ReML-algorithm L l g
2. Weighted Least Squares
Friston et al. 2002, Neuroimage

6. Hierarchical model Multiple variance components at each level
At each level, distribution of parameters is given by level above.
What we don’t know: distribution of parameters and variance parameters.

7. Example: Two level model= + = +
Second level
First level

8. Estimation
Hierarchical
model
Single-level
model

9. 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?

10. Summary Statistics approach
First level
Second level
Data Design Matrix Contrast Images
SPM(t)
One-sample
2nd level

11. 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.

12. Auditory Data Summary statistics Hierarchical Model
Friston et al. (2004) Mixed effects and fMRI studies, Neuroimage

13. 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.

14. ANOVA = = = ? ? ? 1st level: 2nd level: 1.Motion 2.Sound 3.Visual
4.Action ? = ? = ? =
2nd level:

15. ANOVA
1st level:
Motion
Sound
Visual
Action ? = ? = ? =
2nd level:

16. 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.