Interpretation of Statistical Interactions in
Multiple Regression
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Y= b0 + b1
(X1)
+b2(X2) +b3(X1
X2)
How do you interpret the estimates of an interactive
model?
The equation outlined above will serve as the model
interpreted here. In order to interpret the effect of X
1 on Y at other values of
X2 it is
necessary to employ an idea presented by Friedrich (1982) and Aiken
and West (1991). The impact of X1 on Y can be produced using the following equation:
Metric effect for X1
: b
1 +
(b3
X2)
There are two components in the equation:
b1
and the product of b3*X
2. To derive the metric effect of
X1 on Y conditioned on
X2, sum
b1
and the product of b3 times
some value of X2.
This computation can be used for any value of the independent variable
(in this example X2).
It is recommended that you select values of X2 that hold some type of substantive meaning. For
example, if X2 represents
a percentage it may be useful to use quartile values. The result
generated by the equation above provide estimates of
the conditional effect of X1 at the specified
value of X2.(Numerical Example)
The same equation can be used to calculate the impact of X2 on Y:
Metric effect for X2
: b
2 +
(b3
X1)
To derive the metric effect of
X2 on Y conditioned on
X1, sum the coefficient
b2
and b3* X1.
What do b1
and b2 in
the interaction model mean?
b1 is the measure of the
effect X1 on Y when
X2 equals zero and b2 is the measure of the effect of X2
on Y when X1 equals zero. In interpreting
the effect of X1 on Y there maybe instances in
which X2 may never equal zero. For
example, a state’s GNP would never equal zero. In this case, one would not want to
interpret the effect of X1 under this
condition. The same holds true for X2.
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Last updated: August 16, 1999