When does choice of scale for contrast coding matter?

[yjunechoe]

For sum coding (and probably also for other types of contrast coding), I've seen variants like:

• -1 vs. 1
• -0.5 vs. 0.5
• -2 vs. 2

I understand that these affect the interpretation of the coefficient, but do the choice of these values affect any technical aspects of the model (like the model fitting process, PCA, etc.)? Or are we free to choose whatever number as long as they sum up to 0 (for sum coding)?

[yjunechoe]

Answered - notes:

• 1s is probably good default for sum coding. 1/2s can be get confusing when not reasoning about the interaction contrasts explicitly (may be surprised by 1/4s or smaller for interactions).
• For Helmer coding, it's can be good to normalize the max of row to 1 because then the coefficients represent the same unit of distance between means.

These kinds of transformations do not affect the ratio of coefficient to SE. The ratio (beta/SE) does not change.