[Eeglablist] nested hypothesis testing to decide whether to use one or two dipoles to fit a component

[Scott Makeig]

MAX - Unfortunately, in general using two dipoles rather than one will
~always improve the fit. Even if the source is a pure single dipole, a
second dipole can be used to correct for noise or errors in the forward
head model. This is less always the case for the constrained
spatially-symmetric dipole pairs allowed by dipfit().  However, we have not
thought of an optimal way to decide between using one or (occasionally) two
dipoles to fit e.g. maps of ICA brain sources.  The goal would be to decide
whether the two-dipole version is fitting noise/forward model error vs
actual bilateral source generation...

Scott Makeig

On Thu, Aug 9, 2012 at 1:54 AM, Maximilien Chaumon <
maximilien.chaumon at gmail.com> wrote:

> Hello all,
>
> When fitting dipoles to components, we are all sooner or later puzzled by
> the question whether to use one or two symmetrical dipoles.
>
> Would it be correct to put the problems in terms of a nested hypothesis
> testing?
>
> We are fitting a scalp map with one or two parameters and get a residual
> variance after the fit.
> Could we not use this residual variance as a measure of the SSE and
> compute a F statistic to decide whether to use the more complex (with two
> dipoles) or simpler (with one dipole) of two nested models?
> If yes, then how would we decide on the number of degrees of freedom? How
> many free parameters do we have in each case? x,y,z,and two orientations
> per dipole? how does the imposed symmetry affect that number? Could we
> really map residual variance to SSE? How many "observations" do we have in
> that case (see formula below)?
>
> I found this formula, for F:
> F = (SSEF-SSER)/ (kF-kR) / ((1-SSEF)/(N-kF-1))
> where
> SSE is sum of squared errors,
> k is numbers of parameters,
> N is number of observations (? what in our case?)
> F and R indices for full and reduced model respectively (in our case two
> and one dipole).
>
>
> Thanks a lot for any comment!
> Best,
> Max
>
> dipfit
>
>
>
>
>
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-- 
Scott Makeig, Research Scientist and Director, Swartz Center for
Computational Neuroscience, Institute for Neural Computation; Prof. of
Neurosciences (Adj.), University of California San Diego, La Jolla CA
92093-0559, http://sccn.ucsd.edu/~scott
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