[VoxBo] Question about multiple contrasts in a glm

[Daniel Y Kimberg]

David January wrote:
> Hello everyone,
>
> I'm trying to find a linear trend among conditions in my data.  The
> glm I have designed can be abstracted to be of the following kind,
> with the conditions as column headings and the contrast covariates I
> have included in the glm as the numbers below the column headings:
>
> Rest CondA CondB CondC
> 0          1           1          1
> 0          -1           0         1
> 0          .5          -1        .5
>
> This combination of covariates should allow me to detect any relation
> among the conditions that I care about.
>
> My question is this: if I want to which regions are showing the
> pattern C > B > A, what do I enter in voxelsurfer (or vbview) to find
> this?  I want B > rest, so I don't think I should just generate a
> parametric map for covariate 2 alone; I should do both 1 and 2, right?
>  But is just giving each of them a weight of 1 (and giving the 3rd a 0
> weight) the correct thing to do?  Is there a problem with having the
> weights I enter not even out to 0 (the way I would if I were directly
> comparing A and B, for example)?  Also, when I do a random effects
> analysis, should I set the contrast to include both covs 1 and 2?
> would that cause any problems?

If I understand correctly, it sounds like you need the voxel/region to
support C>B and B>A and B>rest.  I don't think there's a way to test
all three hypotheses with a single statistical contrast.  For example,
while your second covariate, in the context of the first, will be
sensitive to an increasing ABC function, it will also do well any time
the overall slope from A to C is positive, even if the true slope from
A to B is negative.  However, if by "linear trend" you just mean that
you want a positive slope for the trend line plotting condition
against activation, then you should be fine.

Restricting your contrast to where B>rest (or maybe ABC>rest?) is a
separate issue.  Generally speaking you can't test conjuntions of
hypotheses in a single t-test just by weighting more covariates.  If
you need multiple things to be true, you probably need to carry out
all the relevant contrasts and either look at the intersection or
(perhaps more powerful) look at your contrasts of greatest interest in
regions defined by the more trivial contrasts.  E.g., you might define
an ROI using your first covariate, and then within that ROI look for
B-A and C-B, and plot the overlap.

I hope this helps a bit, I'm not sure I really understood what you're
trying to test here.

> Sorry to be asking such a question, but my understanding of the
> semantics of the commands is limited.

Little if any of this is specific to VoxBo, or to image analysis in
general.  I find it helpful when I'm trying to sort out how to model
something to use a stats package to see what different potential
models are sensitive to.  I have a few small statistical
demonstrations up on the VoxBo wiki, and I've actually started to work
on one describing how to test for a parametric effect, but it's not
really ready to be posted yet.

dan