Classical and Cooperative Suppression – Simplified

Suppressing error variance

Suppression analysis

Having a good understanding of mediation helps. A bit. But for me, mediation made sense pretty quickly… Suppression did not. So, let’s walk through this. Specifically, we’ll talk about classical and cooperative (reciprocal) suppression. I’ll also give you a basic toolkit for suppression analyses.

It’s like the opposite of a mediation effect…

Let’s break down this “opposite of mediation” explanation. When there is a mediation effect, a third variable decreases the strength of the relationship between X and Y. This occurs because the mediator has taken the stage. A suppression effect is opposite because a third variable increases the relationship between X and Y.

Okay, hold on. If relationship strength increases, why is it called suppression? Well, a third variable, called a suppressor, suppresses irrelevant variance in X. This enables a stronger effect of X on Y. Suppressors suppress error variance in X. Thus, suppressors indirectly increase the independent variable’s predictive ability of Y, even though suppressors have little to no relationship with Y.

What we typically see before a third variable enters the model is that independent variables are weakly related to the dependent variable. In other words, we may see little or no total effect.

Before the suppressor enters the model, X and Y have a non-significant or weak relationship.

Suppression analysis comes with a lot of relationship rules. Very high maintenance. These rules tell us how variables typically relate to each other in a suppression analysis. Although rules may break down a suppression, it’s difficult to simply memorise these rules. I’m going to use models to put these rules into more context. Now, let’s go through classical and cooperative suppression individually.

Classical suppression

Let’s try to understand classical suppression – the “opposite of mediation”. Below I made a diagram to resemble a mediation path analysis. However, notice the faded, grey lines? These indicate weak/no relationship. There’s also some error getting in the way of X and Y. As mentioned before, the independent variables (X& S) share some variance. The independent variables share little variance with Y.

Classical suppression model
  • S & Y – little to no shared variance
  • S & X – moderate shared variance
  • X & Y – little shared variance

Now let’s get rid of the grey lines – zero lines for a zero correlation. We’ll also show a classic suppression effect. The suppressor increases X‘s relationship with Y. We can use a bold line to show the revealed relationship for X and Y.

In classic suppression, a third variable leads to an ‘appearance’ or increase in the strength of the relationship between X and Y. That’s the work of a suppressor. The suppressor continues to have no relationship with Y.

Cooperative suppression

Cooperative or reciprocal suppression starts the same as classical suppression. Independent variables are weakly correlated Y. The difference is that both independent variables are suppressors. The suppression effect is mutual.

When both independent variables are in the regression model they suppress each other.

Here are some patterns in the correlations of cooperative suppression.

  • X1 & X2 – positively correlated
  • Opposite correlations with Y
  • X1 & X2 – negatively correlated
  • Positive correlations with Y

Your toolkit for observing suppression effects

Standardised beta-weights – β

The standardised beta-weights indicate the strength and direction of a relationship between two variables (e.g., X and Y). We now know that suppression leads to the ‘appearance‘ or strengthening of a relationship between two variables. So, if the beta-weights of the direct effect are larger than the beta-weights of the total effect – this suggests suppression.

Squared Correlations

How big was our effect? To understand this, we’re interested in two types of correlations. Zero-order correlations are simple correlations between two variables (e.g., bivariate regression, Pearson correlation). Semi-partial correlations show the unique effect of X on Y.

Now let’s square these correlations. Why? Squaring a correlation gets you the coefficient of determination. Remember? The percentage of shared variance between X and Y. When you subtract the squared zero-order correlations from the squared semi-partial correlations, you can get the suppression effect size.

squared semi-partial correlations – squared zero-order correlations = effect size (%)

Sources

Cheyenne Chooi, PhD Student (Neuropsychology)

Cheyenne is a graduate of the University of Western Australia where she received a Bachelor's degree in Science, and a Bachelor's degree in Science with Honours in psychology. She is currently a third year PhD Student researching factors related to Alzheimer's disease. Her current research focuses on the concept of cognitive reserve.

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