[posting inverted compared to the SPSSX-List ordinary order. ]
Date: Sat, 27 Sep 2014 08:39:15 +0400
From:
[hidden email]Subject: Re: Factor analysis & Interaction terms
To:
[hidden email] quoting me>
--> notion that two near-identical variables
do not form an "orthogonal basis set" (Is that the
mathematical term?)
where their sum and difference do.
Kirill>
Are you referring to that when X and Y are of equal variances then r
b\w X+Y and X-Y is 0, whatever r b\w X and Y?
[snip, rest of my post]
Yes. And if X and Y are not of equal variance, you can get the same result -- that is,
creating r=0 *exactly* for the two derived variables -- by using weighted sum and difference.
By the way, in regard to this process: Technically, I think of this as dealing with "confounding"
by finding un-confounded variables to use in modeling; and I think that this is better terminology
for statisticians than "interaction terms." "Interaction" tends to be reserved by statisticians
for terms computed as X*Y.
I do have some sympathy for the common-sense collapsing of confounding and interaction,
which is how I recognized the question in the first place. - Consider that X*Y is expressed as
a sum after you take logs, and X/Y is X*(1/Y), which is a difference after logs. So when
arbitrary re-scaling is available, "fixing" a model may look either like dealing with interaction
(multiplication) or with confounding (sum and difference).
--
Rich Ulrich