Amplitude Modulation AM2

AFNI Message Board
1

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?

Thanks

2

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?

Correct.

3

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.

  • rick
4

Thanks for your input

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?

5

Thanks for your response

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?

6

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.

  • rick
7

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.