Suppressor Variables


(Taken from the work of Kristin Woolley)
Most researchers determine the worth of a predictor variable by its correlation with the dependent variable. However, sometimes a variable can raise the total R2 even though it has a negligible correlation with the dependent variable and a strong correlation with the other predictor variables (Hinkle, Wiersma & Jurs, 1994; Pedhazur, 1982). A variable that when added as another predictor increases the total R2 is called a suppressor variable. Horst (1966, p. 363) explained:

A suppressor variable may be defined as those predictor variables which do not measure variance in the criterion measures, but which do measure some of the variance in the predictor measures which is not found in the criterion measure. They measure invalid variance in the predictor measures and serve to suppress this invalid variance. "

There may be cases when you select a predictor that does not have a relationship with the outcome variable (DV) but increases the multiple R.
Suppose that both IV1 and IV2 are positively correlated with DV. That means that if either of those variables increases, we expect to see Y increase. But suppose that the regression equation comes out as

Y = 12.78 + 1.3X1 - 2.4X2   

[Taken from the work of David Howell]

"Cohen's classic example (Maybe it was Darlington), is of a speeded test of history. We want to predict knowledge of historical facts. We give a test which supposedly tests that. But some people will do badly just because they read very slowly, and don't get through the exam. Others read very quickly, and do all of the questions. We don't think that reading speed has anything to do with how much history you know, but it does affect your score. We want to "adjust" scores for reading speed, which is like saying "The correlation between true historical knowledge and test score, controlling for reading speed."

Suppression Examples

X1=Amount of psychotherapy
X2=Degree of depression
Y=Number of prior suicide attempts

Classical Suppressor Example [Dataset] X1 is the suppressor

Two Practical Examples of Suppressor Variables can be found here.