Numerical Example of the Metric
Effect
To help demonstrate the metric effect of a statistical interaction the
previous example is utilized. The following represents the
relationship of an
interaction between sex and age on the response variable, salary. X1 represents age and
X2 represents sex. The general
model estimated is:
Y= 2 + 6 (X1
)
+1 (X2
) +1
(X1
X2)
The metric effect of age (X1
) on salary (Y) at values of sex (X2
):
Sex Group 1 (Males): 6 + 1 (1)= 7
Sex Group 0 (Females): 6 + 1 (0)= 6
The metric effect of sex (X2)
on salary (Y) at values of age (X1):
Age 30: 1 + 1(30)= 31
Age 40: 1 + 1(40) = 41
Age 50: 1 + 1(50) = 51
The results provided above represent the estimate of the conditional
effect of sex at specified values of age. It is possible to determine the
relationship between sex and salary at values of age for both males and
females. In this case, the independent variable of interest is a
dummy variable. The metric effect results can be multiplied by values of
the sex variable.
The metric effect of males on salary at the age of
30:
Age 30 and Sex Group 1 (males): (1 + 1(30))1 = 31
The metric effect of females on salary at
the age of 30:
Age 30 and Sex Group 0 (females): (1 + 1(30))0 = 0
Substantively, 30 year old males average just over 3 thousand dollars more
than do 30 year old females.
Back to Interpretation
Revised: August 17, 1999.