Contrast and Inferences

1. Contrast and Inferences Joy Geng Beatriz Calvo

2. Remember, what do we use fMRI for: • Functionalspecialisation: • Identification of regionally specific effects that can be attributed to changing stimuli or task conditions • Functional integration: • Identification of interactions among specialised cortical areas and how these interactions depend upon context Choose design according our aim!

3. Before starting the experiment we need to have clear… • Hypothesis/ Question when making inferences about activations, we can have an… • Anatomically closed hypothesis: (hypothesis driven) we can report uncorrected p value • Anatomically open hypothesis: (we have to use correction methods)

4. Before starting the experiment we need to have clear… • Hypothesis / Question • Design that help me to answer my question • How I am going to build my SPM model • How I am going to analyse my data • I am going to use, Inference / contrast / Statistic • What contrasts and inferences are made is dependent on choice of experimental design theoretical review how SPM does it

5. What I can use... (some examples) • Can be used with event related or block designs. • Cognitive subtraction (subtractions designs) • Cognitive conjunction • Interactions, main /simple effects (factorial designs)

6. Cognitive subtraction • Conceptual framework very used in psychology • Definition: the difference between two task can be formulate as a separable cognitive or sensorimotor component • Then, regionally specific differences in haemodynamic response, evoked by the two task, identify the corresponding functionally specialised area • Many subtraction designs relay on the assumption of pure insertion

7. the pure insertion problem • Pure insertion: A new cognitive (A) component is added to a task, the implementation of the pre-existing components (e.g., B) remains unaffected. • Pure insertion requires that an extra cognitive component can be introduced without affecting the expression of existing components • If this were not the case the difference between tasks that did, and did not, include component B would depend on the presence of component A. • Pure insertion discounts both functional and psychological interactions and therefore represent a very restricted precondition for cognitive subtraction

8. Assumptions of cognitive subtraction • The experimental task and baseline/ control task must be identical in every way except for the process of interest B A Region(s) involved in the cognitive/ sensorimotor process of interest Baseline/controltask identical to A except for process of interest Activation task involving process of interest

9. An example… Question: areas for biological motion? Task A Task B Regions involved in biological motion? Activation task Point light display movie Baseline / controltask Point light display static image MT / V5 STS Frontal eye fields Cerebellum Parietal cortex Violates assumption 1: task A and B identical but the process of interest Many processes in addition to presence of biological motion in A including visual motion and eye movements

10. An example… Question: areas for biological motion? Task A Task B Regions involved in biological motion? Activation task Point light display moves Baseline / controltask Random dots moves MT / V5 STS Frontal eye fields Cerebellum Parietal cortex A better baseline to answer this question….

11. Assumptions of cognitive subtraction 2. There must be no implicit processing of the component of interest in the baseline/control task B A Region(s) involved in the cognitive/ sensorimotor process of interest Baseline/controltask identical to A except for process of interest Activation task involving process of interest

12. An example… Question: is inferotemporal cortex involve in the semantic processing? Task A Task B Regions involved in semantic processing? Activation task read words aloud Baseline / controltask look at words • Violates assumption 2: • Not implicit processing of the component of interest in the baseline task • difficult not to read (silently) a visually presented word, and if this is the case there will be semantic processing due to implicit reading of words in B

13. So, when using substraction design, remember! • The experimental task and baseline/ control task must be identical in every way except for the process of interest 2. There must be no implicit processing of the component of interest in the baseline task

14. Conjunctions • Cognitive conjunctions can be an extension of the subtraction technique • Cognitive conjunctions combine a series of subtractions with the aim of isolating a process that is common to two (or more) task pairs • The assumption of pure insertion can be avoided by extracting the presence of a main effect in the absence of an interaction • Conjunctions have the advantage of testing the effect independently of the task context, thereby controlling for influences of the effect on the context.

15. An example… B1 Baseline task Name colour A1 Activation task Name objects - = A2 Activation task Looking At objects B2 Baseline task Looking at colours - =

16. Using Conjunctions, remenber... • Baseline tasks can be high level or low level • The only restriction is that differences between the task pairs both contain the component of interest • The analysis results in any commonality in activation differences between the task pairs • The resulting region should be uniquely associated with the process of interest, not any interactions specific to each subtraction

17. Factorial Design • In factorial designs there are two or more factors • The main effects of each factoridentify brain areas that respond to that particular factor of interest • The interaction between factorsidentifies brain areas where the effect of one factor varies depending on the presence or absence of the other factor • This allows to measure the effect of one factor on the expression of the other factor

18. Factor A A1 A2 B1 1 2 Factor B B2 3 4 Factorial design 2x2 SPM representation 1 2 3 4

19. Factor A A1 A2 B1 1 2 Factor B B2 3 4 Main effects Main effect of factor A1 (1+3)-(2+4) [1 -1 1 -1] Factor A1 BOLD signal in voxel Y Factor A2 B1 B2

20. Factor A A1 A2 B1 1 2 Factor B B2 3 4 Main effects Main effect of factor B1 (1+2)-(3+4) [1 1 - 1 -1] Factor A1 BOLD signal in voxel Y Factor A2 B1 B2

21. A1 A2 B1 1 2 B2 3 4 Interaction effect (A x B) A A 1 2 3 4 factor B(1) factor B(2) Interactions between factors

22. Factor A A1 A2 B1 1 2 Factor B B2 3 4 Interactions … Interaction between the factors (1-2)-(3-4) 1 -1 -1 1 Factor A1 BOLD signal in voxel Y Factor A2 B1 B2

23. Factor A A1 A2 B1 1 2 Factor B B2 3 4 Crossover interaction Interaction between the factors A1 B1 y A2 B2: (1-2)-(3-4) 1 -1 -1 1 Factor A2 BOLD signal in voxel Y Factor A1 B1 B2

24. So, • Now we have clear what comparisons we want to make… to answer our question • How do I do it in SPM? • I have my nice design matrix… Y= X. β+ ε Observed data Design matrix Parameters Error

25. First level (single subject): design matrix A regressor, X,= timeseries of expected activation based on, e.g stimulus onsets for one condition of interest session 1 Mean or constant term, X Data, Y (e.g. swufMAO*.img filenames) Y = X + e

26. Time series of expected activation for a regressor, X Blocked Event related

27. Fitting X to Y gives you one  (parameter estimate) for each column of X, a μand e. Betas provide information about fit of regressor X to data, Y, in each voxel 0 100 -10 +10 -0.01 +0.01 0 1 2 = * 5 * 50 + + … + Y = X1 * 1+… + Xn * μ + e

28. Now we that we have our betas for every regressor for every voxel for every subject, what next? Contrast Vectors A1 A2 • Each value in the contrast vector represents a weight for each beta in regression model • e.g. 2x2 exp with factor A (a1,a2) x B (b1, b2) • model has four regressors of interest: a1, a2, b1, b2 • Main effect of A: [1 1 -1 -1] • Simple effect of B in A: [1 -1 0 0] • Interaction of A and B: [1 -1 -1 1] • Contrast image (con*.img): contains information about betas * contrast weights (CT) B1 1 2 B2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Y = X1 * 1+… + Xn * μ + e * [1] [.. -1..0 ..0]

29. T statistic (spmT*.img): is activation correlated with condition A greater than that with condition B in voxel x? Contrast vector = [1 1 -1 -1] or [-1 -1 1 1] Ho: A = B H1: A > B, B > A One-tailed Comparison of betas to variance in usual way, T(df) = (CT / SD((CT)) Now we that we have our betas for every regressor for every voxel for every subject, what next? T statistic

30. Now we that we have our betas for every regressor for every voxel for every subject, what next? F statistic • What overall differences exist for conditions A than B? Do the treatment effects explain the data better than the subject (/grand mean) effects and residual errors? • Contrast vector: [ 1 1 0 0; • 0 0 1 1] • compares with baseline • Ho: A = baseline = B • H1: A ≠ baseline or baseline ≠ B • Contrast vector: [ 1 1 -1 -1] • gives differences in both directions (pos/neg), equivalent to two-tailed T statistic • Ho: A = B (same as B = A) • H1: A ≠ B

31. How to interpret nondirectional tests? Parameter estimates • Find coordinates of voxel of interest • Plot contrast estimates, and ‘y’ to see values per subject

32. Now we that we have our contrast images for comparisons of interest for every subject, what next? Contrasts at second level • Second level • T and F contrasts • Take contrasts images from first level relevant for analysis … start again with basic model… • Nonsphericity correction? • Replications (random/ fixed effects) • Grand mean scaling • Global normalization

34. Betas from model without baseline regressors Betas from model with baseline regressors Modelling the baseline or no? Same but mean-centred ->makes a difference for “1 0” contrasts, but not “1 – 1” contrasts