Good points, Tor.
I completely forgot about the scaling issue. Whether or not your beta
represents % change really does depend on the scaling.
If the data are not scaled at all, then the betas will not represent %
change. If 2 given voxels both change intensity by 1 signal unit, they will
both exhibit the same beta. However, they may differ significantly in
baseline signal intensity, and hence % change.
The way I scale my own data is to normalize (that is, divide) each voxel
either by a baseline time point, or even better, by the intercept of the
regression at each voxel. I do not know if this is what the global mean
scaling option in SPM does. This is equivalent to normalizing the response
function to 100% change at each voxel, similar to what you mention.
Multiplying by 100 turns the proportion into a percent. I think this can
either be applied to the raw time series or the betas themselves.
Michael
At 12:20 PM 4/16/2001 -0400, Tor Dessart Wager wrote:
>Hi everyone,
>
>I have to add my 2 cents to the discussion on percent signal change...I
>think that beta values are SOMETIMES equal to percent signal change, but
>not always. Betas can have arbitrary scaling, so they don't always give
>you % change, but they should give you something proportional to it.
>
>Even if your model has high error (high variance), the beta is always your
>best guess as to what the change in signal is. If the error variance is
>high, the beta might not be significantly different from zero - but this
>is a different question than "what is the % signal change." So, you might
>have a timeseries where you estimate the % change, and it's, say, .1%.
>If properly scaled, a beta of .1 = a % change of .1% - but whether one
>should infer that's a "real" change, or random noise, depends on the
>significance of the beta.
>
>About scaling: if you mean center your predictors, and then measure betas,
>you lose information about the baseline level of signal, so you lose info
>about % change from that baseline. I think - correct me - that if your
>HRF is normalized so that the height of the impulse response function is
>1% of the baseline signal, then a beta of 1 = 1% signal change. This
>isn't guaranteed to be the case. So I'm not sure right now how to
>normalize betas to get % change, but maybe someone can say...
>
>Anyway, about the issue of parametric maps: I think you have to have a
>statistical map so that you know what's significant. This is also good if
>you're trying to find reliable changes. If, however, you're more
>concerned with which are the LARGEST changes rather than which are the
>most reliable, you might want to make a % signal change map for
>significant voxels only. I think this would be a very useful way to
>summarize results.
>
>So please correct my faulty thinking on any of these points...
>
>Thanks,
>Tor
>
>
>_____________________________
>Tor Wager
>Department of Psychology
>University of Michigan
>Cognition and Perception Area
>525 East University
>Ann Arbor, MI 48109-1109
>
>Office: 734-936-1295
>Home: 734-995-8975
>Email: [log in to unmask]
>_____________________________
>
>On Mon, 16 Apr 2001, Stephen Fromm wrote:
>
> > Regarding the discussion on betas and % signal change, I'd be interested if
> > anyone had comments on the validity of looking at % signal change. I guess
> > I'm asking for comments as to why we (the community) use *statistical*
> > parametric maps, as opposed to *change* maps (like % signal change).
> >
> > My vague impression (I'm confining my remarks to fMRI):
> >
> > Pros: in the best possible world, there would be no noise. We could make
> > statements like "this task had a large effect on signal; this stimulus
> had a
> > small effect on signal". (Recall the point made in statistics texts that
> > you can have a statistically significant effect that is not important, in
> > that the amount of change induced is small---especially when the available
> > degrees of freedom is high.)
> >
> > Cons: we live in a world where there is lots of
> noise. Hence, statistical
> > images are a necessity. Furthermore (at least for fMRI), drawing
> > conclusions about % signal change implies that there is some kind of zero
> > baseline (in statistical language, that signal is a ratio measure, not just
> > an interval measure); and this isn't so clear. (I'd especially appreciate
> > comments on this last point. One might make some argument that, by
> > linearizing each step in the path from neuronal activity to raw fMRI data,
> > there *is* a ratio scale here, but I'm not so convinced.)
> >
> > Best wishes,
> >
> > Stephen Fromm, PhD
> > NIDCD/NIH
> >
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