I have a logistic model, say Category B vs Category A. I run a basemodel, with some controls and my variable of interest $X_1$ (continuous, standardised), which is slightly negative and non-significant.

Then in model $2$ I add variable $X_2$ (again, continuous and standardised), which is positive (beta coeff. $+1.3$) and significant, $X_1$ keeps being negative but with a much larger coefficient (beta coeff. from $-0.1$ to $-0.7$), which is now highly significant. (There is no change in the sample in moving from model $1$ to model $2$)

$X_2$ is fairly correlated with $X_1$ ($r= 0.45$) in Category A (the baseline of the model), whereas in Category B the correlation is much smaller ($r=0.10$). Indeed there is a trend of $X_2$ among the various categories of the baseline, whereas among the "1s" its value is quite stable. Overall we have $r=0.34$

And yes, $X_2$ could be on the causal pathway between $X_1$ and $Y$. Now I understand what is going on, I have more difficulties in labelling it, let's say. Maybe I am wrong, but I would rule out a confounding effect of $X_2$ between $X_1$ and $Y$, cause there is a causal pathway (something that should be missing in the case of a confounder). So I would go for a mediator effect. But does this apply also in case like that, where the effect of $X_2$ increases the magnitude of the relationship between $X_1$ and $Y$? Maybe is it a case of a suppressor?


1 Answer 1


You seem to be on the right track.

You are correct that if $X_2$ is on the causal path between $X_1$ and $Y$ then it is a mediator, not a confounder, and if you are interested in the total causal effect of $X_1$ on $Y$ then you should not include $X_2$.

Regarding the situation where the inclusion of $X_2$ increases the magnitude of the $X_1 \rightarrow Y$ estimate, I can't see any reason why that is not plausible.

You may find this post to be of some use:
How do DAGs help to reduce bias in causal inference?


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