On Thu, 11 Aug 2005 14:38:10 +0900, WATANABE Takamitsu <takawatanabe-
[log in to unmask]> wrote:
>Hello
>
>I have a question about independence between regressors in a modified
>FIR model.
>The modified FIR model means:
>
>SPM.xBF.length is the same as TR in order to avoid interference
>between neighbor scanning.
>Two conditions(e.g, A, B) And the order is one. >> Two regressors.
>No duration time, so the model is one of event-related designs.
>Every image can be classified to condition A or B.
>
>other settings are following:
>SPM.xBF.name = 'Finite Impulse Response';
>SPM.xBF.length = 14; % length in seconds
>SPM.xBF.order = 1; % order of basis set
>SPM.xBF.T = 16; % number of time bins per scan
>SPM.xBF.T0 = 1; % first time bin (see slice
>timing)
>SPM.xBF.UNITS = 'scans'; % OPTIONS: 'scans'|'secs' for
>onsets
>SPM.xBF.Volterra = 1; % OPTIONS: 1|2 = order of
>convolution
>
>In such analysis, the independence between the two regressors is
>assured? One of my colleagues said No because the sum of those
>regressors is almost 1 in every time point.
>
>But, in SPM2, there is no sign to doubt the independence. Even when
>SPM.xBF.T (# of time bins pre scan) was set as 1, SPM2 did not show
>any warning.
>
>Which is right, SPM2 or my colleague?
> I would appreciate your any comment.
I haven't used FIR models in SPM2, so my comment here only goes to the
independence issue.
It's not clear to me why summing to one is enough reason to doubt
independence.
For example, if there are 4 time points, then the vectors
[1 0 1 0]
[0 1 0 1]
sum to one at every time point, yet are "independent" in the sense that
they are orthogonal.
Of course, usually SPM adds a constant regressor for effect of session.
When this regressor is added, then the design is overparameterized if the
other regressors sum to one. But that doesn't matter, insofar as SPM can
handle overparameterized designs.
Caveat: if a design is truly, exactly overparameterized, SPM will
(properly) constrain the choice of contrasts to those that
are "estimable." However, it's often the case that designs are _nearly_
overparameterized (perhaps true here with your language that the sum
is "_almost_ 1"). In that case, SPM will allow you to choose contrasts
which, though nominally estimable, aren't estimable in the sense that
there would be lots of numerical instability.
>Thank you
>
>T.W.
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