**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**.

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*.

*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**.

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*

*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

- Gaylord-Harden, N. K., Cunningham, J. A., Holmbeck, G. N., & Grant, K. E. (2010). Suppressor effects in coping research with African American adolescents from low-income communities.
*Journal of Consulting and Clinical Psychology*,*78*(6), 843. doi:10.1037/a0020063 - Lancaster, B. P. (1999). Defining and interpreting suppressor effects: Advantages and limitations.
- Semipartial (part) and partial correlation. (2020). Retrieved from https://www3.nd.edu/~rwilliam/stats1/x93.pdf
- Partial and semi-partial correlation. (2020). Retrieved from http://faculty.cas.usf.edu/mbrannick/regression/Partial.html
- Statisticshowto (2020). Partial correlation & semi-partial: Definition & example. Retrieved from https://www.statisticshowto.com/partial-correlation/
- Statisticshowto (2020). Zero-order correlation: Definition, examples. Retrieved from https://www.statisticshowto.com/zero-order-correlation/
- Watson, D., Clark, L. A., & Kotov, R. (2014). The value of suppressor effects in explicating the construct validity of symptom measures.
*Psychological Assessment*,*25*(3), 929–941. https://doi.org/10.1037/a0032781. - Wikiversity (2018). Semi-partial correlation. Retrieved from https://en.wikiversity.org/wiki/Semi-partial_correlation