Mediators

I one of my previous blogs, we saw Omitted Variable Bias. In this blog, we’ll do mediation analysis using the same example. Please revise that before continuing.

In brief, we tried to estimate the effect of Area of the house on its price. We saw that when “crime” variable correlates with both Area and Price, then omitting crime variable in the model led to bias in estimating the effect of area on price.

But, if you try to turn the above causal diagram, you’ll see a causal diagram that refers to mediators.

There is absolutely no difference between both the diagrams!

It is ‘generally’ suggested that Mediators should be removed to avoid bias. Should we remove Area variable then? Let’s do that and check with the data where crime and area are correlated (more about this data is explained in the OVB blog.)

We see that houses in Crime1 area have 31k less price on average.

When we add Area variable. We reproduced this result in the OVB blog as well.

You can observe that the coefficient of crime reduced from -31k to -12k. Did the effect of crime reduce?

Remember that the dataset was created in such a way that high crime regions do not have large house areas. I ensured 0.4 correlation between area and crime. So, Crime reduces area → small homes cost less. This is the mediation. Some of the effect of Crime on Price is mediated through the reduction in Area.

Why is this mediation a concern?

If correlation between crime and area is further increased, then adding both variables to the model would give us negligible coefficient to the crime variable. Will we then say crime has no effect on prices and recommend reduction of police budgets?

Hence, to get the true effect of crime on prices, we remove the mediator (Area). This encapsulates the mediating effect of crime on area → area on price as well.

However, from the OVB blog, we saw that adding both variables to the model will give us the correct estimate for the effect of area. Thus, we report all the models that we specify when we present our results. The changes in the coefficients as we add/remove variables have a story to tell — stories of mediations, selection bias/colliders and confounders.

Bottom line:

Both variables will be needed to get the unbiased effect of the Mediator. Mediator should be removed to get the unbiased effect of Confounder.