The orthogonalization of covariates issue is a real evergreen. A mail
on one or the other aspect of this appears on the list with
regularity, say every two or three months. The automatic
orthogonalization of parts of the design matrix appears to be
unsettling to many.
If a covariate is a nuisance covariate, it makes no sense to
orthogonalize it. Orthogonalization makes sure that any nuisance
effect is present intact in the effect estimate of the covariate of
interest, thus defeating the purpose of the concept of nuisance.
In other cases, adding an orthogonalized regressor changes the
estimate of residual variance. I'd be relaxed about this if this
happens at the first level, my argument being that it won't impact
much second-level inference. It might improve the REML estimate of an
autoregressive term, but I am sceptical about the practical
consequences of this -- the indirect consequences on effect estimates
will be tiny, I'd think.
Roberto Viviani
Psychiatry III Ulm Germany
Quoting DDW <[log in to unmask]>:
> Thanks for the reply.
>
> It still seems to me that explicitly orthogonalizing within-trial
> can lead to more problems than good. Although, if any multiple
> regression experts want to chime in, I'm all ears.
>
> In the case of FIR models, it seems like orthogonalizing each
> successive regressor with respect to the first (or is it done with
> respect to the preceding regressor?) would introduce bias. Moreover,
> in most of the FIR designs I've looked at, the correlation between
> each successive time bin is usually negligible (0.02 to 0.1).
>
> In the case of parametric designs, I've yet to see a situation where
> the event defining regressor (convolved with the HRF) is correlated
> with the parametric modulator. I think you would have to be very
> unlucky to chance upon a parametric modulator that is correlated
> with the regressor defining your events.
>
> If memory serves, the addition of within-trial orthogonalisation
> occurred between spm2 and spm5 (or perhaps it was spm5 and spm8) do
> any of the developers remember why? I'm a little antsy about
> disabling something that may be essential.
>
> Cheers.
>
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