Thanks, Donald -- that does help quite a bit. I realized, though, that
I left an important element out of my question -- while it's true that
the the A-B beta weights are different than the B-A beta weights, what
is really perplexing us is what you're hinting at:
> One solution might be to look at the significance of the gPPI effects, rather than the amplitudes. This might provide a better relationship of the upper and lower triangles.
This is actually where we first noticed the asymmetry between the
upper and lower triangles. For our ~40 subjects, we extracted the
betas for the seed-->target (or target-->seed) model, then filled
the cells of our 20x20 matrix with the result of a 1-sample t-test
over those values. Plotting the group t-stats for A-B against the
t-stats for B-A also reveals no relationship between the upper and
lower triangles of that matrix.
It's possible that some of our seed regions time courses are more
correlated with the modeled task, which would change the amount of
unexplained variance that the respective models have to work with, but
I'm still surprised that there's no relationship between the A-B and
B-A pairs...
Thanks, again,
Todd
On Mon, Apr 14, 2014 at 1:00 PM, MCLAREN, Donald
<[log in to unmask]> wrote:
> Todd,
>
> I think this is a reasonable finding.
>
> In correlations (e.g. resting state), when you switch X and Y, you get the
> same correlation, but the slope is inverted (e.g. slope of 3 becomes 1/3).
> Now if you did this for two tasks (slopes of 3 and 4 and 1/3 and 1/4,
> respectively). A->B effect would be 1 and B-->A effect would be -1/12. Thus,
> gPPI would not be expected to have a clear relationship for A-->B and B-->A.
>
> If you work through the gPPI model:
> If the target region is perfectly predicted by the task regressors, seed
> regressor, and PPI regressors; then you invert the design with the predicted
> target region signal as the seed, you don't get the inverse relationship
> (e.g. if contrast 1 for A->B is 0.5, then contrast 1 for B->A won't be 0.5
> nor will it be -0.5.
>
> The contrast difference between A-->B and B-->A is dependent on both the
> gPPI beta terms and the seed beta term. If you add the gPPI and seed terms,
> then divide 1 by the slope, you'll get close to the reverse slopes and see
> approximately the new contrast value. It's not 100% accurate as the seed
> region isn't perfectly predicted by the target region.
>
> Also, if one region has lower variance, then the weights for the gPPI beta
> and seed beta terms might be greater than than of the opposite direction.
> One potential solution would be to make all regions have a variance of 1.
> However, I don't think anyone has explored the effect of this on gPPI
> effects.
>
> One solution might be to look at the significance of the gPPI effects,
> rather than the amplitudes. This might provide a better relationship of the
> upper and lower triangles.
>
> One final thought. Although, gPPI is generally thought of as functionally
> connectivity as opposed to effective connectivity, there seems to be some
> information about the information about the directionality of the effects.
> More work is needed to determine if the directionality is true or an
> artifact of variance differences across regions.
>
> Hope this helps.
>
>
> Best Regards, Donald McLaren
> =================
> D.G. McLaren, Ph.D.
> Research Fellow, Department of Neurology, Massachusetts General Hospital and
> Harvard Medical School
> Postdoctoral Research Fellow, GRECC, Bedford VA
> Website: http://www.martinos.org/~mclaren
> Office: (773) 406-2464
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> On Mon, Apr 14, 2014 at 11:41 AM, Todd Thompson <[log in to unmask]> wrote:
>>
>> Hello, PPI experts,
>>
>> We're running a gPPI analysis and are noticing something we can't
>> quite get our heads around: the PPI regressor weights from seed A to
>> target B are often quite different than those from seed B to target A.
>>
>> In fact, if we run gPPIs for 20-odd seeds and generate the 20x20
>> correlation matrix among those seeds, then plot the A->B values from
>> the upper triangle against the B->A values from the lower triangle,
>> there is no significant statistical relationship between them.
>>
>> Is this expected behavior? If so, how should we think about it?
>>
>> Thanks much,
>> Todd
>
>
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