Causal Concepts Midterm Review

Exam Review

• Just some reminders of stuff we have covered

Describing Variables

• Continuous and Discrete Distributions
• Summary statistics - mean, percentiles, skew
• Theoretical distributions and our attempts to learn about them from data
• Sampling variation messing up our ability to do so

Describing Relationships

• Conditional means
• Explaining one variable with another
• Conditional distributions, contrasting distributions, scatterplots
• Local means, fitting shapes with regressions, adding controls for conditional conditional means
• Interaction terms

Identification

• We are isolating the variation we are interested in
• That’s the “good variation”
• Bad variation can get in the way
• We need a model of how the world works to figure out what the bad variation is so we can sweep it out

Causal Diagrams

1. Consider all the variables that are likely to be important in the data generating process (this includes variables you can’t observe)
2. For simplicity, combine them together or prune the ones least likely to be important
3. Consider which variables are likely to affect which other variables and draw arrows from one to the other
4. (Bonus: Test some implications of the model to see if you have the right one)

Causal Diagrams

Identifying X -> Y by closing back doors:

1. Find all the paths from X to Y on the diagram
2. Determine which are “front doors” (start with X ->) and which are “back doors” (start with X <-)
3. Determine which are already closed by colliders (X -> C <- Y)
4. Then, identify the effect by finding which variables you need to control for to close all back doors (careful - don’t close the front doors, or open back up paths with colliders!)

Controlling

• One way to close back doors is by controlling
• Control for W by seeing what W explains (perhaps with a regression) and taking it out

library(Ecdat)
data(BudgetFood)
BudgetFood <- BudgetFood %>% mutate(totexp = totexp/1000000)
m1 <- lm(wfood ~ totexp, data = BudgetFood)
m2 <- lm(wfood_r ~ totexp_r, data = BudgetFood %>% mutate(wfood_r = resid(lm(wfood~age)),
                                                          totexp_r = resid(lm(totexp~age))))
m3 <- lm(wfood ~ totexp + age, data = BudgetFood)

Controlling

	Model 1	Model 2	Model 3
(Intercept)	0.495***	0.000	0.406***
	(0.002)	(0.001)	(0.004)
totexp	-0.135***		-0.125***
	(0.001)		(0.001)
totexp_r		-0.125***
		(0.001)
age			0.002***
			(0.000)
Num.Obs.	23972	23972	23972
R2	0.263	0.228	0.282
* p < 0.1, ** p < 0.05, *** p < 0.01