Metadata
- Author: Julia Rohrer
- Full Title:: 2 thoughts on “If you have two measures of the same confounder, you can just include both of them in your regression model”
- Category:: 🗞️Articles
- Document Tags:: statistics,
- URL:: https://www.the100.ci/2025/10/13/if-you-have-two-measures-of-the-same-confounder-you-can-just-include-both-of-them-in-your-regression-model/?utm_campaign=Data_Elixir&utm_source=Data_Elixir_545
- Read date:: 2025-10-23
Highlights
Recall that in a multiple regression analysis, every coefficient makes a statement about what happens to the outcome when all other predictors are held constant. So, if covariate 1 increases by one point, but covariate 2 is held constant, what happens to the outcome? Both usually go up together, given that they are supposed to measure the same thing—a person who scores high on one test of cognitive abilities will also tend to score high on another one—and so this is a hard question for our model to answer. There just isn’t much information in the data about what happens when they vary independently. So, the model returns the numerical equivalent of a shruggie: wide standard errors. This wouldn’t have happened if you had listened to your parents included only one covariate, in which case you would have asked your model an easier question, resulting in narrower standard errors. (View Highlight)
But what happens beyond that? What does it mean for the thing that we are actually interested in, the coefficient of X? Nothing bad, actually. If you think of your model as a lean, mean prediction machine,[2] it’s still working perfectly fine. While the model is uncertain whether it’s covariate 1 or covariate 2 or a combination of them that does the heavy lifting, this uncertainty actually doesn’t matter for the rest of the model. That’s because when one of the covariates goes up, the other one does so, too. So, it doesn’t matter how precisely any predicted increase in the outcome is split between the two of them, in the end you come out at the same place.[3] (View Highlight)