For example, I am interested in the influence of X on Y via Z and W, and the path(s) look like:
X>Z>Y and X>W>Z
Here Z is the possible collider variable - I say 'possible' because its parents (X and W) are associated. Given that X influences W, then is it ok to control for Z ?
Hello Tanya,
Without knowing your rationale for wanting to control for a downstream/collider variable, it's hard to offer constructive advice.
Attempts to invoke control over collider variables can result in biased estimations of relationships among the variables under investigation. Sampling, especially for non-experimental studies, can induce a control (especially if too restrictive a sample frame) over the collider variable. See this explanation: https://catalogofbias.org/biases/collider-bias/
If you have a compelling reason to presume that there should be sampling, experimental, and/or statistical control over a collider variable, perhaps you could explain it in a bit more detail (along with your variables X, W, Y, Z). You'd likely get a more focused recommendation.
Good luck with your work.
Hi Tanya,
the question is in what specific equation you control/adjust for other variables. If your target equation is X --> Y, controlling for Z does not introduce collider bias but would block the mediator effect.
If your target equation is, in contrast, X --> W, you would not control for Z (which is a common effect of both X and W) as this would lead to a collider bias.
Of course, specifying an overall SEM with your structure does address all of this and give you all the wanted effects.
All the best,
--Holger
Hi David and Holger,
Thank you so much for your helpful answers. The issue is, that I am interested in identifying both X --> W and X -->Z and X --> Y.
To be specific, X is a fisheries co-management intervention, and Y=state of fisheries after intervention. We know that X --> W (increased participation of local community members in decision-making), and it also causes Z (improved management). Finally, we have good reason to expect that W --> Z.
So even though we know that X --> W, would controlling for Z induce bias? This is problematic for my purpose, because I need to uncover the influence of X on W, Z and Y.
Have you any recommendations for how to recover the various pathways of interest without inducing collider bias?
Thanks again!!
Hi Tanya,
simply do not control for Z in the X-->W regression.
The options in total are
1) Conduct two sets of regression analyses: The first set aims at the mediator effect (tested by bootstrapping of the indirect effect). In this set, you would NOT control for W (as it partially mediates the X->Z effect). The second set aims for the X --> W or the partial mediation of X via W on Z by the same means. In this case, Z would be the outcome, not a control variable
2) Estimate a SEM with the whole model in one step. This model has the advantage that you test for endogeneity of the Z --> Y link.
All the best,
--Holger
Hi Holger,
Thanks! Just to clarify: what do you mean by "This model has the advantage that you test for endogeneity of the Z --> Y link" ? How exactly do I test this?
Best,
Tanya
Hi
an SEM has an omnibus chi square test that tests all exclusion restrictions of the model. In your case, the model as the implication that
a) X is independent on Y given Z and
b) W is independent of Y given Z.
If the true model has an unobserved confounding effect of an unobserved cause of Z and Y, these implications fail. The same is true if Y causes Z.
In econometrics, this is known as the Sargan test.
Best,
--Holger
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