Kenny,
I don't know if this will help further, but perhaps you are familiar
with sequential (hierarchical) regression? The issue of
orthogonalization is fundamentally related to sequential regression and
the selection of what is known as "Type I" (sequential) or "Type
III" (partial) sums of squares.
If you are interested, search the SAS documentation for "Hypothesis
Testing in PROC GLM" for info on the various types of hypothesis tests:
http://support.sas.com/onlinedoc/913/docMainpage.jsp
Orthogonalizing 2 wrt 3, and 1 wrt 2 and 3 is basically like a
sequential regression in the order 3-2-1. Typically one wants to work
with Type III sums of squares type-statistics, so as Eugene said, you
don't want to orthogonalize unless you know how to interpret the
orthogonalized regressors (and you specifically want to work with a
sequential type model).
cheers,
-Mike H.
On Mon, 2010-05-10 at 18:56 +0100, Eugene Duff wrote:
> Hi Kenny -
>
>
> On 10 May 2010 18:13, Kevin Denny <[log in to unmask]> wrote:
> > Hi FSL users,
> >
> > I have a question about the orthogonalise option for FEAT as there has been some confusion in my lab as to what it's doing and when to use it.
> >
> > I'm doing a resting-state functional connectivity analysis with 3 EVs - an ROI timecourse (1) and two regressors: average of ventricles (2) and whole brain mean timecourse (3). The way I understand it is that if I orthogonalise (1) wrt to (2) and (3) that is moving any similar components from (1) to (2) and (3) thereby allowing me to see only the ROI. First of all, am I correct here?
>
> Partly. Orthogonalising 1 wrt 2 and 3 removes variance explainable by
> 2 and 3 from 1, but it will have no effect on the fit of or statistics
> associated with EV 1, because in the fitting of this regressor's
> parameter estimate and estimate of this parameter's variance, the GLM
> algorithm in effect ignores the component of signal that can be
> explained by other regressors.
>
>
> > Secondly, is it necessary to orthogonalise (2) wrt to (3) and/or (3) wrt to (2)? I am under the assumption that this is unnecessary as it does not effect my ROI but others have said something about the shared variance between my two regressors having some ill effect if I do not orthogonalise them to each other.
>
> No. The GLM deals sensibly with the shared variance.
>
> >
> > And overall, is it even necessary to orthogonalise any of my EVs? The FSL documentation points out that most designs are already in this form but since this is strictly a resting-state analysis, is it necessary to do any or all of the above mentioned?
> >
>
> No, the documentation holds true here. Orthogonalisation effectively
> forces the model to assign the shared variance to one EV (the one not
> orthogonalised), which is usually not a good thing, as the fit of this
> regressor becomes difficult to interpret, and it's variance estimate
> will probably not be realistic.
>
> Cheers,
>
> Eugene
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