Suppressors Demystified: The Silent Influencers of Data in Statistical Modeling

Suppressors Demystified: The Silent Influencers of Data in Statistical Modeling
by Audrey Guinn, Ph.D.

Suppressors are rarely talked about in the marketing research community. They are viewed as the “red-headed stepchild” of statistics: rejected, neglected, and outcast.
Sometimes, it seems as though researchers believe ignoring the problem will make it go away. Unfortunately, however, no amount of ignoring will make suppressors disappear. They are like a persistent former friend, showing up unexpectedly, casting doubt, and ruining our well-thought-out plans.

Suppressors are variables that when added to a regression model, change the original relationship between X (a predictor) and Y (the outcome) by making it stronger, weaker, or no longer significant—or even reversing the direction of the relationship (i.e., changing a positive relationship into a negative one).

This may be more easily understood within the context of human relationships. For example, we have a simple regression with X1 predicting Y1, or in terms of human couplings, we have a relationship between two people, X1 and Y1 (see the very popular meme to the left for illustration). When we examine this relationship by itself, it is a positive and significant relationship. X1 really digs Y1, and Y1 really digs X1. When we add the suppressor variable into the mix (X2), the relationship between X1 and Y1 no longer has the same positive and significant outcome. Depending on the suppressor (X2), the relationship between X1 and Y1 could become weaker, where X1 and Y1 are unsure if they want to continue their relationship. Or, their relationship could become negative, although still significant (X1 and Y1 stay together but fight all the time). Another possible outcome is that the relationship between X1 and Y1 ends (becomes non-significant). Lastly, sometimes, the relationship between X1 and Y1 becomes stronger when X2 is introduced into the relationship.

What I’ve learned by working with suppressors is that they can enhance relationships or destroy them. Suppressors act as saviors when they increase the relationship between X1 and Y1. Their addition to the regression strengthens the relationship, increasing the significance and effect size. Typically, when this outcome occurs, we researchers shrug and chalk it up to our expectations. We often don’t notice suppressors when they are saviors because they are helping our regression analyses, not hurting them.

On the other hand, when suppressors destroy relationships, we take notice, mostly because we are shocked to find outcomes contrary to our expectations. When relationships we know should be positive turn out to be negative, or when we expect to find a significant relationship but it is not significant, this is when we pause and ask ourselves, “What is going on here?!” After a little digging, we finally realize that we have a destroyer among our data.

Although I could get into the nitty gritty of the types of suppressors and the relationships between all the variables and explain it all using Venn diagrams, I will spare you. All you really need to know is that suppression effects are due to the collinearity (relationship) between the predictor variables. Any time two or more predictor variables are correlated, the outcome between X1 and Y1 will change with each addition of another predictor (X2, X3, X4, etc.) into the model.

What is intriguing—or frightening—is that there are such things as suppressor factors. I experienced this recently while working on a large project using structural equation modeling. When I ran the model, some of the latent predictor (factor) variables had a negative relationship with the outcome. This absolutely did not make sense. The variables were expected to be positively related to the outcome. After a little investigating, multiple suppressor factors were revealed. Yes, multiple. That is another issue that isn’t really discussed either. It is possible to have many suppressors in the same model.

What can researchers do when encountering problem suppressors? There are a couple of possible solutions.

For Suppressors in Regression:
- Combine predictor variables that are highly correlated.
- Run a factor analysis on the predictors and use their factor scores as the predicting variables.
- Find the suppressors and remove them from the analyses.
For Factor Suppressors in Structural Equation Modeling:
- Re-examine your factor structure to make sure it has good fit.
- Compare your factor structure with Harman’s Single Factor.
- Combine factors that are highly correlated to each other.
- Find the factor suppressor(s) and remove them from the model.
- Examine the factor suppressor(s) in isolation in their own model(s).

Although suppressors can be surprising and seemingly problematic, researchers should not ignore them. Understanding what suppressors are is a valuable tool for the marketing researcher. They tell us important information about the relationship between multiple variables, and they offer potential causes for problematic regression models.

Instead, researchers should explore their data to locate the suppressors. Once identified, researchers can examine possible solutions to remedy the problem. In some scenarios, the best option may be to remove the suppressors from the analyses. In other situations, the best course of action may be to examine the suppressors in their own models. Sometimes, to answer a client’s question, the best solution may be to conduct the regression using factor scores. Either way, knowing what the problem is and how to manage it will allow researchers to reach their end goal: presenting viable results to the client.

About the Author

Audrey Guinn, Ph.D. (aguinn@decisionanalyst.com) is a Statistical Consultant in the Advanced Analytics Group at Decision Analyst. She may be reached at 1-800-262-5974 or 1-817-640-6166.

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