With this option, if I am not mistaken, one gets an unmodulated regressor that represents the average for a condition and then a parametric modulated regressor. Is this regressor orthogonalized with respect to the condition regressor it is paired with in a timing file? Also, I am under the impression if you include more than one parametric modulator they are not orthogonalized with respect to each other. Is this statement correct?

With this option, if I am not mistaken, one gets an unmodulated regressor that represents the average
for a condition and then a parametric modulated regressor.

Instead of “unmodulated regresssor”, personally I prefer to call the corresponding effect as the effect associated with the average modulation value.

Is this regressor orthogonalized with respect to the condition regressor it is paired with in a timing file?

No, typically there is no point performing orthogonalization. The situation is pretty much like a simple regression model

y ~ a + b*x

in which we don’t orthogonalize between x and the intercept regressor of (1, 1, …, 1).

Also, I am under the impression if you include more than one parametric modulator they are not orthogonalized with
respect to each other. Is this statement correct?

In the typical case, the modulation regressor should be at
least very close to being orthogonal to the main one, since
unless the user specifies otherwise, the modulation terms
are demeaned.

No, typically there is no point performing orthogonalization. The situation is pretty much like a simple regression model y ~ a + b*x

Okay but if you have multiple conditions each with their own parametric modulator this option does not produce separate design matrices it puts them all into a single model (one design matrix)? Is each modulator in this case interpreted as the deviation from the average for the paired condition?

Yes, I was under the impression that AFNI centered to the mean across runs for the paired condition. If I have multiple conditions each with a parametric modulators I assume I should interpret each parametric modulator as deviation from the average of the paired condition induced by the given predictor. Is this correct or is there something I am overlooking?

Yes, that is right. Unless you specify otherwise (setting
the environment variable AFNI_3dDeconvolve_rawAM2
to YES, or by specifying the exact value to subtract from
each modulator), 3dDeconvolve will demean each set of
auxiliary parameters.

As with a typical regression, there is no additional attempt
to orthogonalize terms.

if you have multiple conditions each with their own parametric modulator this option does not produce
separate design matrices it puts them all into a single model (one design matrix)? Is each modulator in
this case interpreted as the deviation from the average for the paired condition?

Multiple modulators would be similar to multiple regression

y ~ a + b1 * x1 + b2 * x2 + …

with x1, x2, … centered (e.g. around their respective means). The effect associated with each modulator is interpreted with the effects from other modulators being accounted for.

The
National Institute of Mental Health (NIMH) is part of the National Institutes of
Health (NIH), a component of the U.S. Department of Health and Human
Services.