Transformed Interactions in Regression

[mandy_a41]

Hi all,

I have a quick (but surprisingly difficult) question to ask regarding transformed variables in an interaction term when conducting regression.

This question was asked previously (as below) however, the answer was slightly incorrect as there are assumptions for multiple regression and one of those is that the data are normally distributed.

I have searched high and low for the answer so any insight or references on this issue would be greatly appreciated.


QUESTION:

I'm performing a multiple regression analysis and have a question about transforming variables.

I am using two IVs to see if there are interaction effects on the DV. I understand its often best to center the IVs before running the regression. Problem is one of my IVs needs to be transformed. So, do I first center the two IVs, and then do the transformation?

thanks so much...

ANSWER:
It is not necessary. I guess it is a cross section data. There is no distribution assumption is required (for IVs) to build multiple regression.

[CowboyBear]

Sorry if I'm being dense, but what exactly do you mean by centering the IV's? Do you mean standardise the variables?

[mandy_a41]

Yes...subtracting the mean from the IVs to make the mean 0.

[CowboyBear]

Hmm... Standardising requires dividing (case score - mean) by the standard deviation. I'm not sure what benefit there'd be in just subtracting the mean, I've never seen this done in a published study. Standardisation isn't always best - it'd be useful if one of your IV's has a much bigger variance than the other, which could lead to it having a proportionally larger influence in the unstandardised regression equation. But each transformation or standardisation leads to the interpretation of what the regression coefficients actually mean becoming increasingly more difficult.

Anyway, to answer your question, I'd suggest transforming first and then standardising. If you standardise first you end up with a bunch of negative case values which then can't be transformed via popular transformations like logarithm and square root. There are probably ways around this, but I can't see what the benefit would of doing it this way round.