Dear Sukhi,
> I am unclear what the higher order polynomials represent in terms of likely
> relationship with BOLD response; and whether other people have used them
> with good effect.
With the parametric modulation in your block design you are testing whether
the mean activity in each block of your language task is well fit by some
polynomial function of rate. The order of the polynomial you select
determines how many columns are generated in the design matrix. There will
always be one column (a boxcar whose amplitude is identical across all
presentation rates) and in your case a second one (a boxcar whose amplitude
is modulated in a linear fashion by presentation rate). These boxcars are
fitting the mean and slope of any relationship between rate and BOLD. Areas
that correlate in a positive linear fashion with rate will be given by the
t-contrast [0 1].
A second order term (and above) will allow you to model nonlinear
relationships between the mean BOLD contrast in each epoch and the rate of
the language task (provided that they are well fit by a polynomial). For an
fMRI example of how this works see Christian's paper:
Büchel C, Holmes A, Rees G and Friston KJ Characterising stimulus response
functions using nonlinear regressors in parametric fMRI experiments
NeuroImage 8, 140-8 (1998)
Whether a higher order polynomial term is useful in your model will depend
on whether brain regions exist that show a response to rate that is well
modelled by a higher order polynomial.
What Jesper suggests (using an F test across the three categorical
regressors) is useful because some (linear) combination of the categorical
regressors can model any function relating BOLD to presentation rate
(whether polynomial or not). So this F contrast will tell you whether there
is some interesting relationship between rate and BOLD to model (whether
with a polynomial or not), and plotting the parameter estimates for A/B/C
will give you an idea of what sort of a function might relate BOLD and rate.
hope this helps!
best wishes,
Geraint
--
Dr. Geraint Rees
Wellcome Advanced Fellow, Lecturer,
Division of Biology 139-74, Institute of Neurology,
California Institute of Technology, University College London,
Pasadena CA 91125 London WC1N 3BG
voice 626-395-2880 020-7833-7472
fax 626-796-8876 020-7813-1420
web http://www.klab.caltech.edu/~geraint
--
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