Week 11: Causal Inference

Multilevel Causal Inference

Week Learning Objectives

By the end of this module, you will be able to

• Define causal effect from a causal inference framework
• Describe what a confounder is using a directed acyclic graph (DAG)
• Explain how randomized experiments control for confounders
• Explain when and how statistical adjustment can potentially remove confounding
• Explain how including cluster means can remove confounders at level 2

Task List

1. Review the resources (lecture videos and slides)
2. Complete the assigned readings
   • Rhoads & Li (2022) (to be shared on Slack)
   • Feller & Gelman (2015)
3. Attend the Tuesday session on last week’s exercise (cross-lagged models)
4. Attend the Thursday session and participate in the class exercise
5. Complete Homework 9

Lecture

Slides

PDF version

Overview

Causal Inference Frameworks

Check your learning

In a study of the association between chocolate consumption and number of Nobel laureates, what would be considered a causal effect?

The difference in the number of Nobel laureates between countries with high and low per capita chocolate consumptions
The difference in the number of Nobel laureates between people, in the same age group, with high and low average chocolate consumptions
The change in the number of Nobel laureates if everyone in the US ate more chocolate while keeping everything else constant

Check your learning

A potential outcome for a person i is

The outcome value the same person would have obtained if they were in a particular treatment condition
The average outcome value of everyone similar to person i
What person i could have obtained if the treatment is made stronger

Confounding

Check your learning

In the graph above, which variable is a confounder?

U1 U2 U3 U4

Check your learning

In an experiment, why do we only get an average treatment effect (ATE), instead of causal effects of individuals?

Because the average is more accurate than individual scores
Because we only observe one potential outcome for each individual
Because the counterfactual score of each person in the treatment group is the same as the mean of the control group

Statistical Adjustment

Check your learning

`geom_smooth()` using formula 'y ~ x'
`geom_smooth()` using formula 'y ~ x'

Which of the following is closest to the effect of x on y, adjusting for m?

0 0.5 -1

Check your learning

In the graph above, which variable is a mediator?

U1 U2 U3 U4

Multilevel Causal Inference

Berkeley admission example

The role of cluster means

Check your learning

From a causal inference perspective, why is including the cluster mean beneficial?

Because confounding variables at the cluster level have effects on the cluster mean, which is held constant by including in the model
Because the cluster mean is a mediator variable
Because the between-cluster and within-cluster effects can be decomposed