Introduction to Statistical Interactions
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What is a statistical interaction in the
context of OLS regression?
An interaction is a conditional relationship between an independent
variable and the dependent variable. Generally, this type of conditional relationship
refers to a case where the relationship between X1 and Y, varies
according to the value of X2.
What is an interactive model?, How does one test for an interaction?, and When should one include a product term in a
model?
Y= b
0 +
b1
(X1)
+b2
(X2)
+b3
(X1
X2)
A) The equation above is an example of an interactive model.
b3
represents the interaction between the X1 and X2, which is referred to here as the "product
term". In a traditional linear regression model
(without a
product term),
the slope of Y on X1 has a
constant value across all values of X2. The inclusion of a product
term--b3(X1X2)--indicates the presence of a
conditional multiplicative relationship between the two independent
variables. In other words, the regression of Y on X1 is conditional upon the specific value of
X2(Aiken and West 1991).
B) It is possible, using OLS regression, to test for relevant
interactions by including
a product term in the model estimation. First, create the
product term
by multiplying the relevant variables and
then estimate the model including the new "product term" variable
in the regression equation. The p-value provided for the t-test
indicates the level of significance of the
product term. If the product term is significant one can conclude that the
hypothesized interaction actually exists in the data.
C) The suspicion that an interaction may exist in a certain data set can
arise from apriori information or from theorizing. When one suspects that
an interaction may exist in the data, the interaction should be included.
For an example of a statitical interaction click here: (Statistical Interaction Example).
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Last updated: August 16, 1999