Dear Eric,
> I am trying to understand exactly how the GLM works. I have a design where I show people statements that are either neutral (N), threats (T) and responses to threats (R). For illustrative purposes, assume I do 10 trials of each, each for 10 seconds. So, N for 10, T for 10, R for 10, then repeat. This gives me three column timing files that look like:
> N =
> 0 10 1
> 30 10 1
> 60 10 1
> 90 10 1
> …
> 270 10 1
>
> T =
> 10 10 1
> 40 10 1
> 70 10 1
> 100 10 1
> …
> 280 10 1
>
> R =
> 20 10 1
> 50 10 1
> 80 10 1
> 110 10 1
> …
> 290 10 1
>
> QUESTION #1: Should I set these up as 3 EV’s or 2 EV’s and have one as a dummy?
This would make no practical difference. Use whatever design that makes setting up the contrast weight vectors most intuitive to you.
>
> Ignoring convolution for a movement, if I set them up as three EV’s then I have a regression of the form: Y=bX, where Y is the level of activation, b is a 3 by 1 vector of parameters and X is the following matrix (assume a TR of 5000 ms so that in each 10 second period there are two observations in a particular voxel):
>
> 1 0 0
> 1 0 0
> 0 1 0
> 0 1 0
> 0 0 1
> 0 0 1
> 1 0 0
> 1 0 0
> 0 1 0
> 0 1 0
> 0 0 1
> 0 0 1
> …repeat 8 more times.
>
> In this case X is full rank, but if FSL includes a column of 1’s as an intercept term in the regression, then X is not. That is where question 1 comes from. Most software automatically includes a column of 1’s. Can someone clarify this point?
It doesn't matter if X is of full rank or not. Even for a rank deficient design there will still be valid contrasts. As an example, say you have two tasks A and B and that your design is ABAB... It is then valid to look for differences between A and B through a [-1 1] contrast, but you canNOT look for A (over and above some unobserved baseline) through [1 0].
FSL convention is to not add a constant for 1st level designs and instead subtract the mean from each time-series. Other packages have chosen different conventions.
>
> Now, further assume that half of the trials are of one type and half of another. For my particular experiment half of the questions we directed to “you” and half to “us”, but let’s just call them type 1 and type 2, and assume that the first half were type 1 and the second half were type 2. (I randomized, but that makes the question I am asking more difficult).
>
> Now I set up six EVs: N1, N2, T1, T2, R1, R2
>
> N1 has timing
> 0 10 1
> 30 10 1
> 60 10 1
> 90 10 1
> 120 10 1
> N2 has timing
> 150 10 1
> 180 10 1
> 210 10 1
> 240 10 1
> 270 10 1
>
> I won’t list the others, but you get the point.
>
> I am interested in the question is N1 different than N2, and I set up the contrast:
> 1 -1 0 0 0 0
>
> I am also interested in the whether N is different than T, which means is the N text (both N1 and N2) different than the T text (both T1 and T2). So I set up the contrast:
> 1 -1 -1 0 0
>
> This is (N1 + N2) > (T1 + T2)
>
> When I had only 3 EVs I set up the contrast
> 1 -1 0
>
> Theoretically, these should give the same result.
>
> QUESTION 2: Why do these not give the same result? Why does the contrast 1 1 -1 -1 0 0 give different results than the contrast 1 -1 0 when I divide the three EVs up into six EVs? It’s not just slightly different, because we would expect some loss of degrees of freedom. It gives different numbers of clusters in different areas.
>
This is, as you imply, puzzling. If N1 and N2 were massively different (and the same for T1 and T2) I could imagine that 6 EVs would do a better job of modelling the variance and give you higher sensitivity. But I would assume you don't design the tasks in that way.
One general advice is to never look at clustered and thresholded maps when comparing analyses. Look instead at the raw z-images. The thresholding can cause surprisingly large differences in z-maps that are quite similar to start with.
Good luck Jesper
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