In this answer it was discussed that when terms are being deleted for the purposes of model simplification, it's best to delete terms "by chunk". That is, in an x1 * x2 * x3 * x4 scenario we'd contemplating deleting the fourth order term, and if we did that we might consider removing all the third order terms, and so on.
I often see people ignoring this advice and removing particular interaction terms at a level. For that reason, I asked why it was recommended to remove interaction terms as a chunk.
@frank-harrell wrote here that
If you have a completely pre-specified order that was not determined by looking at the data, then you may be OK to do that. In general you will have co-linearity and multiplicity problems when making multiple decisions using multiple P-values.
Can anyone provide some more detail about why these problems occur? When, if ever, is it valid to delete individual interaction terms at a particular level?
