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

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

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

4. General Linear Model = + Model is specified by 1.Design matrix X 2.Assumptions about  Model is specified by 1.Design matrix X 2.Assumptions about  N: number of scans p: number of regressors N: number of scans p: number of regressors Error Covariance

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

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 Hierarchical model Single-level 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. Data Design Matrix Contrast Images SPM(t) Summary Statistics approach Second level First level One-sample t-test @ 2 nd level One-sample t-test @ 2 nd level

11. Validity of approach The summary stats approach is exact if for each session/subject: All other cases: Summary stats approach seems to be robust against typical violations. Within-session covariance the same First-level design the same

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

13. Multiple contrasts per subject Stimuli: Auditory Presentation (SOA = 4 secs) of words Subjects: fMRI, 250 scans per subject, block design fMRI, 250 scans per subject, block design Scanning: U. Noppeney et al. (i) 12 control subjects MotionSoundVisualAction “jump”“click”“pink”“turn” Question: What regions are affected by the semantic content of the words? What regions are affected by the semantic content of the words?

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

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

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.