Dear Alexa/Rik/List,
we are considering to test the effect of inclusion of more basis
function on 2nd level RFX analyses, see my most recent email in this
thread on the list. Is it really the case that betas are not affected by
the inclusion of extra basis functions, even under OLS? When not
including them AND when HRF does not capture the BOLD response well,
the residuals have more structure, are not that independent anymore, and
hence the Beta estimates have a larger bias (e.g., are more different
from the 'real' beta), in the worst case? That would also affect 2nd
level stats on the betas of the HRF alone...
I am not a statistician, but one should be able to prove or disprove
that analytically to some extent.
But perhaps I am talking nonsense here.
Cheers,
Bas
Alexa Morcom schreef:
> Rik/Bas/List
>
> Has anybody actually tested in a quantitative way the impact of these
> somewhat (we know - but how much?) inefficient first level betas on a 2nd
> level inference?
>
> It also seems a recurring question how white one should wash one's
> residuals...
>
> Alexa
>
>>> In the absence of correlation, the inclusion of extra basis functions
>>> can reduce the residual error in 1st-level models, and hence improve
>>> T-contrasts on one basis function alone (eg the canonical HRF).
>>> However, the inclusion of such extra basis functions will not affect
>>> 2nd-level analyses on only one basis function in SPM99, or only
>>> minimally so in SPM2/5, because this orthogonality means that the
>>> parameter estimates are not affected under OLS, and only minimally
>>> under WLS. Thus it is a common misapprehension that including, eg the
>>> temporal derivative of the canonical HRF in 1st-level models somehow
>>> allows for latency differences in 2nd-level analyses on the canonical
>>> HRF alone. It does not. The answer is to take (contrasts of) all basis
>>> functions to 2nd-level analyses, and again perform F-contrasts.
>>>
>
>
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Dr. S.F.W. Neggers
Division of Brain Research
Rudolf Magnus Institute for Neuroscience
Utrecht University Medical Center
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