(1) A-fixation and B-fixation would be sufficient for using as the DV and IV respectively. This would allow one to control for B (e.g. houses) when looking at the relation between cognitive score and A (e.g. faces). This allows addresses the issue of relationship being multiplicative as opposed to additive.
(2) The statement that this cannot be done in SPM and has to be done at the ROI level is wrong. Download the SPM extension Biological Parametric Mapping (
http://fmri.wfubmc.edu/software/Bpm) and you can build your multiple regression model with your cognitive measure and contrast B (e.g. houses) as IV that vary at each voxel.
Hope this helps.
Best Regards, Donald McLaren
=================
D.G. McLaren, Ph.D.
Postdoctoral Research Fellow, GRECC, Bedford VA
Research Fellow, Department of Neurology, Massachusetts General Hospital and
Harvard Medical School
Office: (773) 406-2464
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On Fri, Jul 8, 2011 at 7:15 AM, Roberto Viviani
<[log in to unmask]> wrote:
<...>
Our concern with this approach is related with using the contrast images at
the second level. We have realized that if we use a certain measure A, and
subtract a control task B from it, we end up with a measure that usually
correlates positively with A, but *correlates negatively* with B. Therefore,
when we use the contrast resulting from a subtraction of parameter estimates
at the first level, the values at each voxel are negatively correlated with
our control measure. We would like, however, to be able to use a measure
that is *independent* of B.
Under the null, the [A-B] constrast is uncorrelated with your individual variable; A and B in isolation are also uncorrelated, if they are centered. This can be shown agebraically. What you mean is that if the null is rejected at the regression of the individual variable on the contrast image, then you do not know if you have a positive association with A or a negative association with B.
Ideally, we would like to be able to look for the relationship of brain
response A to certain behavior while *regressing out* the brain responses to
B, and not subtracting those responses. It seems that only by doing this, we
would be able to effectively remove the influence of measure B. Would it be
possible to do this in SPM?
Treating A and B quantitatively, as you are proposing to do here, is difficult due to the non-quantitative nature of the BOLD-EPI signal. In other words, you cannot view A and B as separate measures of activity; only the difference is valid. Furthermore, it breaks the SPM approach (because the regressor now including B differs at each voxel -- so no, you can't do it with SPM). You could adjust for B, however, in a ROI-averaged signal where the ROI is selected by a contrast orthogonal to the factor with levels A B.
Apart from the limitations of BOLD-EPI, the issue you are raising bears some relation to interventional studies, where for example you test the effect of therapy (the 'control variable') on a pre- and post-therapy measurement (A and B). In this case, it is indeed common to adjust for pre- instead of regressing on [post - pre]. The reason is that the contrast [post - pre] is like having pre in the regression model with a fixed coefficient of one; if you adjust, instead, you estimate this coefficient from the data, i.e. the model is more general. The issue, however, is far from clearcut; much depends on the existence of a causal association between pre levels and your 'control variable'. If this is the case, then contrary to your reasoning you do introduce bias in the estimate of the control variable. See basic background in S. Greenland, J. Pearl, J. M. Robins 1999, ‘Causal diagrams for epidemiologic research’. Epidemiology, 1:37-48, and more specifically
M. M. Glymour, J. Weuve, L. F. Berkman, I. Kawachi, J. M. Robins 2005, When is baseline adjustment useful in analyses of change? An example with education and cognitive change’. American Journal of Epidemiology, 162:267-278.
A discussion of the generality of adjusting vs. regressing on the contrast is in the book by Hill & Gelman, Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge (UK): Cambridge University Press
The algebra of individual testing at the 2nd level is in doi:10.1016/j.neuroimage.2009.10.085
Best wishes,
Roberto Viviani
Dept. of Psychiatry
University of Ulm, Germany
I'm writing to ask if this problem has been considered before, and whether
you have any suggestion about how we can deal with it?
I'd be very grateful for any thoughts that you have about these issues.
With many thanks and kind regards,
Lucia Garrido