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

[Maximilien Chaumon]

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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