# Should I incorporate sex as a control variable or use multi-level modelling?

I'm doing a linear regression model to look at how socio-economic status impacts children's height. My dataset will be survey data for both males and females.

To me, it makes sense to control for sex, as boys and girls obviously have different growth patterns. However, I've been told that with regression models you should only control for confounding variables - those that are associated with both the independent and dependent variables and could therefore create a spurious relationship.

So, should I instead be controlling for confounders, then using multi-level modelling to look at the relationship on both a male and female level? Or would I just collect info about sex in the survey and filter the dataframe by sex to run models for each? Or should I approach it a different way? OR should I in fact be including sex as a control variable?

Any help would be very very much appreciated!

Thank you!

• As a point of interest, the term "adjust" should be used in place of "control" in observational studies. Jennifer Hill makes this point, arguing that "control" should only be used in cases for which the variable is "literally under our control". For observation studies like this for which no variables are influenced by the investigator, "adjust" is a more appropriate and honest term. Jan 11 at 3:47

My two cents: Adjust your estimate for sex by adding it into the model. Justification is below...

you should only control for confounding variables

This is not completely accurate.

If your goal is to estimate causal relationships, then adjusting for confounders is a good thing -- indeed its a must! However, the estimate can actually be improved by conditioning on a variable which is associated with the outcome but does not lay on the causal pathway between the exposure and the outcome. By adjusting for these related covariates, the residual variance is decreased thereby increasing the efficiency of the causal estimate.

Its simple to demonstrate via simulation. I'm going to simulate data from this causal graph. Note that $$w$$ is not a confounder of the causal effect of $$x$$ on $$y$$. However $$z$$ is. We will repeatedly simulate data, fit two models -- one with $$w$$ and one without it -- and compare the disrtribution of estimated effects. The result is shown below.

Note that the distribution of effects for $$x$$ when not conditioning on $$w$$ is much wider. This results in lower statistical power. Since $$w$$ effects $$y$$ and does not lay on the causal pathway, it is a good idea to adjust for it.

As to if you should or should not adjust for sex, it really depends on your causal graph. I agree that a child's sex partly causes their height, and I see no way in which a child's sex could cause SES so I don't see it as a confounder. I'm open to different interpretations should there be any.