Ch. 11. Confounding and Interaction in Regression
I. Introduction
A. Confounding
1. Regression coefficients developed with a set of X
variables are invariant because they are computed
with Type II SS.
2. If the addition of extra X variable(s)
dramatically changes the existing coefficients,
then the extra X variable(s) is called
confounding.
3. The criterion for "dramatic change" is
subjective.
4. The X variable(s) which is NOT a part of
interaction effect should be considered for
confounding.
B. Interaction
1. The unique effect of the combination of two or
more X variables independent of the effect of
individual X variables.
2. The effect of one X variable depends on the level
of the other X variable (e.g.).
3. We can test any type of interaction effects in
regression.
II. Interaction Effect
A. For a given number of X variables (p), we can have a
maximum of (2p - 1) - p interaction effects if the
number is smaller than n - 1 where n is sample size.
B. If we have four(4) X variables (X1-X4), we may have 11
interaction effects assuming we have over 16 subjects.
Fist order: X1X2, X1X3, X1X4, X2X3, X2X4, X3X4
Second order: X1X2X3, X1X2X4, X2X3X4
Third order: X1X2X3X4
C. In practice, it is very difficult to interpret any
interaction effects beyond the second order.
D. Using human judgment we typically select some of the
interaction effects for testing.
E. For model testing, use PROC GLM and test for X1*X2 or
any other product form.
F. For model development, use PROC REG and create a new
variable for the product form (e.g., create X12=X1*X2
and use X12 for X1*X2).
G. We test the highest order interaction effect first, if
it is significant, we are in trouble. If it is NOT
significant, then, go ahead to test the next highest
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