Dear Anderson & FSL list,

Following recent posts on the design matrix for e.g. randomise, I started doubting about my own glm approach. I am originally trained with the SPM gui, where one can build contrasts on the go (e.g. define post-hoc t-contrasts only after seeing an interaction effect in F-contrast). For the FSL/glm approach, all contrasts need to be built beforehand (also post-hoc t-contrasts) to run at once in randomise, so an extra amount of forward-planning is needed.
I read about several approaches that I had not applied so far. I hope someone could help figure out what the best GLM design would be for my analyses.

I have a sample of 50 participants, split in two even groups (group1, group2). First I want to compare the groups on FA values, as obtained by TBSS, and second I want to regress the FA values (whole sample & group interaction) with two behavioral measurements (behav1, behav2). These two behavioral measurements negatively correlate with each other, and both also correlate with age (one shows a positive, the other shows a negative correlation). Therefore I want to add age as a nuisance variable, to make sure I don't look at age effects.

For my study I have the following 5 research questions:
- group difference on FA, irrespective of behavioral measurements
- (whole sample) association with behav1
- group * behav1 interaction (and post-hoc t-test, if the interaction is significant)
- (whole sample) association with behav2
- group * behav2 interaction (and post-hoc t-test, if the interaction is significant)

eventually I want to apply this same approach on tractography data, so it would be good to have things straight on a correct design at this point.

Until now I have created 5 separate design.mat files for the 5 questions above (mainly due to the order in which I explored my dataset and tried out designs in the beginning), but I can imagine this is not optimal due to multiple comparisons, and degrees of freedom?


Therefore my first question: can I create an optimal glm design that combines (several of) these questions?

For instance 3 designs:
1. main group comparison, irrespective of behavioral measurement
2. behav1, with EVs and contrasts exploring both a main effect of behav1, and a group interaction
3. behav2, with EVs and contrasts exploring both a main effect of behav1, and a group interaction

However, in a recent post I read that the main group difference (irrespective of behavioral measurement) and the behavioral regression could be entered in one design, together with the nuisance variable (although now behavior * group interaction was studied in this post, as far as I could see)
 (https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind1502&L=FSL&F=&S=&X=0911D30C4E89A0952E&Y=sjoerds.zs%40gmail.com&P=234382). 
So then for me this would look like:
(EV1 = intercept? 50 ones??)
EV2 = group1 (25 ones, 25 zeros)
EV3 = group2 (25 zeros, 25 ones)
EV4 = nuisance (50 demeaned values based on whole sample mean)
EV5 = group1 behav (25 demeaned values - based on whole sample mean? 25 zeros for group2)
EV6 = group2 behav (25 demeaned values - based on whole sample mean? 25 zeros for group1)

In that case it was suggested to simply make the F-contrast 0 1 -1 0 0 0 for group differences, and two t-contrasts for possible post-hoc tests:
0 1 -1 0 0 0
0 -1 1 0 0 0

And then I assume, the whole-sample regression with behav would be contrasted as:

t-contrast 0 0 0 0 1 1 (for a positive association)
and 
t-contrast 0 0 0 0 -1 -1 (for a positive association)

and group-interaction on behav would be:
f-contrast 0 0 0 0 1 -1 (plus respective t-contrasts if f-contrast shows significance)

However, not taking the two behav EVs (of interest) into account in the first contrast (0 1 -1 0 0 0), I assume that these behav EVs are also considered nuisance variables, and therefore they influence the explained variance between the groups? This is the reason why I earlier built separate GLMs for the non-behavior related group differences, versus regression with behavior. But do I understand correctly now that it is also fine to combine these EVs in one design? How does randomise see the difference between nuisance variables and variables of interest then?
I do assume that the regressions with the two different behavioral measurements should however be defined in two separate designs, especially because of their colinearity. But if I combine pure (non-behavior related) group difference EVs with behavioral EVs, I have the same first contrast (0 1 -1 0 0 0) in both designs (for behav1 and behav2).. hence my confusion.


One other important question: I have manually demeaned both my behav and nuisance (age) parameters. Therefore I don't add the -D in the command in randomise, but did add an intercept as first EV (filed with ones, and all following EVs move a number). But now I read that it was adviced against it?
So, in my case: do I need to add an intercept, and how do I handle demeaning??

Thanks in advance!
Best,
Zsuzsi

-- 
Z. Sjoerds, PhD
Postdoctoral researcher

Max Planck Institute for Human Cognitive and Brain Sciences
Fellow-Group Cognitive and Affective Control of Behavioral Adaptation
Group Schlagenhauf, Room C211
Stephanstraβe 1A
04103 Leipzig
Germany

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