# What if path c’ has a negative coefficient, but X - > Y share a moderate to high Spearman correlation?

I am running a mediation model including the variables $$X$$, $$M$$, and $$Y$$.

The Spearman correlation between $$X$$ and $$Y$$ is +0.4, while the direct path c’ between $$X$$ and $$Y$$ has a negative coefficient of -0.206.

Further notes: All variables, that is, $$X$$, $$M$$, and $$Y$$, are the same kind of measurement. Hence, they do not operate on different scales or intervals. Also, I did not demean the data before running the moderation model.

Question: I cannot make sense of this result because it seems like a contradiction to me. Also, why does the direct path c’ yield a negative coefficient of -0.206 when a linear regression between X and Y, as shown in the image below, is positive? Am I confusing the direct path c’ with the total path c here?

It's quite easy for something like this to occur. First, note that a correlation only captures the covariance between two variables. It does not partial out the effects present from other predictors. After conditioning on other variables, this can greatly influence your regression coefficients (see for example suppression effects, which pushes a coefficient to essentially zero even with correlations seemingly "strong" enough). Here you are fitting two regression paths which use $$X$$ as a predictor. Therefore the variance that is tied up in $$X$$ that would normally only go to $$Y$$ is now being shared with $$M$$. There is also a strong correlation between $$M$$ and $$Y$$, which means more of the variance in $$Y$$ is being soaked up by $$M$$. This could be contributing in some way. You may want to think on what is contributing to that from a theoretical lens.
• Thank you. It is much more clear to me now. I also have a theoretical reason why M way better explains the variance in Y than X. Explaining this goes way beyond my question here though. You are also right about pointing out the two blobs. I know the reason for that, but I cannot really disentangle that in the data analysis (again, explaining this goes beyond my topic here). So thank you, I will accept your answer! Commented Jun 20 at 8:55