confoundingepidemiologymediationmultiple regressionregression
Given a large dataset, one cannot possibly check every model. In particular, it does not seem clear to me that one can check confounding or mediation in either cases.
How does one check confounding/mediation in large data context? I am no epidemiologist. Does the question even make sense in tons spurious relationship due to large data? If there are 5 variables, there might be hope. I could not see hope in data with 100 variables.
The bootstrap shouldn’t care if the data is normally distributed. What bootstrapping basically does is to generate a custom distribution around your data and then test for the significance of your results against that custom-made distribution. If you are concerned about assumptions involving indirect effect, bootstrapping shouldn’t be terribly affected by it, but you might want to try using RMA regression rather than OLS regression in that case. Bootstrapping is just effective in both cases.
Rephrasing the opposite of a confounder: It is definitely possible that an unobserved variable yields the impression that there is no relationship, when there is one.
Confounding usually refers to a situation where an unobserved variable yields the illusion that there exists a relationship between two variables where there is none:
This is a special case of omitted-variable bias, which more generally refers to any situation wherein an unobserved variable biases the observed relationship:
It's easy to imagine a scenario where this would have a canceling effect on the estimate instead:
(I wrote $\rho=0$ for the illustration, but the unobserved relationship does not have to be linear.)
You could call this phenomenon omitted-variable bias, cancellation, or masking. Confounding usually refers to the kind of causal relationship shown in the first figure.
Best Answer
The size of the dataset only helps a little. The only way I know to check confounding is to convene a large number of experts in the subject matter area and in operations and procedures related to subject matter and to have them list all of the factors they feel may be used in the decision making process related to the exposure or treatment you are interested in. Then see if those factors (or ones highly correlated with them) happen to be collected in your dataset and are measured accurately enough without too many missing values.