1. A very dumb dummy thinks about modelling, contrasts, and basis functions.?

2. What is the best way to model my experiment?
Model baseline?
Specific questions?
Prior Assumptions?
Number of parameters?

3. Example Finger tapping experiment
4 different forces used (parametric design)
interleaved with rest periods

4. What is the best way to model my experiment?
Model baseline?
more contrasts
It will be convolved
Issue of what a baseline is
Specific questions?
Prior Assumptions?
Number of parameters?

5. What is the best way to model my experiment?
Model baseline?
Specific questions?
Parametric increase
Mean effect
Difference between specific levels of factor (force)
Prior Assumptions?
Number of parameters?

6. What is the best way to model my experiment?
Model baseline?
Specific questions?
Prior Assumptions?
Linear / log increase?
Number of parameters?

7. What is the best way to model my experiment?
Model baseline?
Specific questions?
Prior Assumptions?
Number of parameters?
Too many to model individually? (DOF at 1st level)
Issues at the 2nd level

8. Possibilities for this example
Nonparametric
Main effects / contrast
Linear parametric
Mean correction of linear parametric
Quadratic parametric

9. Non Parametric design Time (scans) Regressors 1 2 3 4 5
Model differences between levels / pairs of levels, model overall mean effect of press
Regressors

10. Non Parametric design Time (scans) Possible Contrasts
main effect of pressing
linear increase
log increase
Model differences between levels / pairs of levels, model overall mean effect of press
Regressors

11. What if you have too many conditions?
Imagine one hundred force levels instead of 4.
Remember a degree of freedom is lost for every condition modelled …
There may also be limits on the number of contrasts which can be taken to the second level

12. Linear Parametric design
Regressors: 1: 2: 3:
LINEAR
PARAMETRIC
ALL
PRESS
MEAN
Parametric due to prior model
All press to relax assumption about difference between press and rest
SPM mean corrects to 0

13. Mean Corrected Linear Parametric design
Regressors NEW REGRESSORS 1: 2: 3:
MEAN CORRECTED

14. But I expect a log parametric response not linear!

15. Quadratic Parametric design
Linear
Log
All press
mean
Regressors
Quadratic is values from linear squared.

16. Summary: What is the best way to model my experiment?
Model baseline?
more contrasts
It will be convolved
Issue of what a baseline is
Specific questions?
Parametric increase
Mean effect
Difference between specific levels of factor (force)
Prior Assumptions?
Linear / log increase?
Number of parameters?
Too many to model individually? (lose DOF)
Issues at the 2nd level

17. Which statistical test should I use?
T-test – tests specific one-way hypothesis
F-test – test more generally for related activity

18. contrast of estimated parameters
T test - one dimensional contrasts - SPM{t }
Tests one very specific hypothesis.
User must specify whether looking for an increase or a decrease.
T =
contrast of estimated parameters
variance estimate
s2c’(X’X)+c
c’b

19. T test - one dimensional contrasts - SPM{t }
Linear
Log
Press
Mean
Regressors
Contrasts T1 T2 T3 T4 T5 T6 T7 T8
8 T-tests required to test for all possible
activities in this design matrix!!

20. F-test (SPM{F })
Tests multiple linear hypotheses: checks whether the tested effects explain
significant variance within the data.
F =
error variance estimate
additional variance accounted for by tested effects

21. F test - one dimensional contrasts - SPM{f }
Linear
Log
Press
Mean
Regressors
Contrasts T1 T2 T3 T4 T5 T6 T7 T8
A single F-test will tell you if any of these
Contrasts would contain significant activity.

22. Switching gears… basis functions
Once we have the design, how do we relate it to our data?

23. Switching gears… basis functions
Once we have the design, how do we relate it to our data?
Time series of haemodynamic responses

24. Switching gears… basis functions
Once we have the design, how do we relate it to our data?
Time series of haemodynamic responses
Fit these using some shape…

25. A bad model ...

26. A « better » model ...

27. Basis functions
Can be used in combination to describe any point on a plane.
For instance, the (x, y) axes of a graph are basis functions which combine to describe points on the graph
The basis functions used in SPM are curves used to ‘describe’ or fit the haemodynamic response.

32. Summary
The same question can be modelled in multiple ways, but these are not always equally good, and there are many trade-offs.
T tests examine specific one-way questions
F tests can look significance within any of several questions (like an ANOVA)
Basis functions combine to describe the haemodynamic response