Okay, after reading a few responses - I get it.
The key here is to use
the notion of "highly correlated" as the starting point. And
then, you
think of "interaction" as the broader idea of, "What information
is here
that is not measured directly?"
Given two variables that are *very* highly correlated, like two
protein
or hormone levels or two economic indicators, it is *usually*
useful and
meaningful to compute and use their ratio (or the log of their
ratio) or
their simple difference. - Only use a simple difference, A
minus B, if you
have made sure that the scaling is compatible for A and B.
This does not arise very often, but it is (unfortunately) likely
to be
overlooked when it does. When do you need to define the set of
variables to use, and how to transform them? Answer: - "at the
start."
Do you, as analyst, always use the variables as they are handed
to you,
or do you argue for a basic set of measures that are
individually
well-distributed have other good properties? - by "good
properties",
I am thinking precisely of the notion that two near-identical
variables
do not form an "orthogonal basis set" (Is that the mathematical
term?)
where their sum and difference do.
So, in answer to your question -- I think it is fine to replace
(A,B) that are
highly correlated with (A, f(A,B)) that are nearly
uncorrelated. Your
mention of factor analysis was a bit of a distraction, since I
would have
probably considered the change before I got that far. But if
that is when
you notice that variables are too mutually-confounding to be
useful... sure,
reformulate the set of variables and start over. You don't want
two near-
identical variables in later analyses. For the sort of measures
that I used
as examples, I would pick A or B to go along with their
"difference" function.
For rating scales, I would consider using their sum or average.
--
Rich Ulrich
> Date: Fri, 26 Sep 2014 06:18:50 -0700
> From:
[hidden email]
> Subject: Factor analysis & Interaction terms
> To:
[hidden email]
>
> Hi everyone,
>
> Is it possible to include interaction terms in a factor
analysis.
> Specifically, if we find that a few variables are highly
correlated, can we
> create an interaction (between those two highly
correlated variables) and
> re-run the factor analysis with it (the interaction
term)?
>
> Any advice is greatly appreciated.
>
> thanks!
> Mike
>