I’d only add this:
Correlation with the 6 realignment parameters (trans_x trans_y trans_z rot_x rot_y rot_z) is an explicit criterion in the AROMA classifier; components that are more correlated with motion are more likely to be classified as nuisance by ICA-AROMA.* Furthermore, in the aggressive model, the nuisance components aren’t competing with signal-of-interest components to explain variance in the dataset; thus, all of the variance that can be explained by nuisance components should be removed in the regression step.
For the above reasons, there is likely to be substantial collinearity between nuisance components and realignment parameters; fitting realignment parameters in a separate model could be redundant or could remove additional temporal degrees of freedom from the data for little benefit. The original implementation of ICA-AROMA recommended supplementing the ICA-based denoising procedure with a confound model that incorporated mean signal from white matter and cerebrospinal fluid compartments (white_matter and csf in fmriprep), but didn’t include the 6 motion parameters. We’ve found, along with others, that adding the mean global signal into the model can also substantially improve denoising performance, but some reviewers might still find it controversial.
So, in short, in addition to Oscar’s warning about potential reintroduction of artefactual variance, there might be other reasons not to include the realignment parameters in the nuisance regression.
*Technically, the criterion uses a linear discriminant analysis on a 2D feature space including (i) the maximum temporal correlation with any of the motion parameters and (ii) spatial overlap with a mask indicating voxels at the edge of the brain. The details are in Fig 2A in the original Pruim article.