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I am analyzing data using path analysis and I am hoping someone here can help.

In my model, I am looking at predictors of a variable, $Y$. In the path model, $Y$ has 4 significant predictors lets call them $A$, $B$, $C$, and $X$ (path coefficient $X$ to $Y$ is $-.16$ which is significant). Of importance, $X$ is not significantly correlated with $Y$ when tested as a bivariate correlation ($r = .105$, ns). I feared that suppression may be present and so I ran the partial correlation controlling for $A$, $B$, and $C$. The partial correlation between $X$ and $Y$ was $-.209$, which is significant.

Does this rule out suppression and instead suggest incidental / accidental cancellation may be more likely the issue, or am I missing something? Are there other ways to determine if suppression is the issue?

gung - Reinstate Monica
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SLL
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2 Answers2

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Simply because the coefficient switched signs and became significant from the bivariate analysis to the multivariate analysis does not guarantee that $X$ is a suppressor. It certainly could be, what you have is the signature effect of suppression, but there are other possibilities as well. For example, $X$ could be confounded with another of the variables in the model, causing the sign to change, but the inclusion of the remaining variables accounts for enough of the residual variance as to make the effect significant. In general, it is hard to ultimately know for sure what the exact relationships are between variables. The best way to determine if $X$ is a suppressor would be to run a new experiment in which you manipulate $X$ and see if there is an effect on $Y$. If it is a suppressor, there will be no effect. (Note that this is an equivalence test, which is more subtle than the prototypical hypothesis testing situation.)

For more information about these topics, you may want to read the following CV threads:

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gung - Reinstate Monica
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I may be mistaken, but suppression typically refers to a multivariate analysis that reduces the effect of one of the variables in the equation. In this case, it seems the univariate relationship is not significant, while the variable is significant in the multivariate analysis. If anything, this is the opposite of suppression. In essence, it appears that removing error associated with A, B, and C led to an increase in variance in Y attributable to X, which lead to it becoming a significant predictor.

Note that the significance of the partial correlation and the path coefficient should be identical, unless I am mistaken.

Behacad
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  • Thanks for the reply! I will double check the significance as I think you point about equivalence makes sense. I have dealt with suppressors before (primarily seen in sign switching when negative correlation becomes pos. predictor). If I am understanding you correctly, the current results are interpretable and I dont have to worry about removing this X variable from the model? Thanks again! – SLL Apr 26 '13 at 13:21
  • I don't think you need to remove X. Indeed, if all the predictors are significant in the equation, then certainly know I think. – Behacad Apr 26 '13 at 16:10
  • Seems you inverted it. A suppressor variable decreases the effect of a predictor when *excluded* from the model of the DV. Hence adding the suppressor variable to the predictive model will *increase* the effect size of the suppressed predictor (and thus its significance). – Nick Stauner Jan 26 '14 at 05:48