DAGs and the causal revolution

# DAGs and the Causal Revolution

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# Types of data

.box-inv-6.medium[Experimental]

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.box-inv-6.medium[Observational]

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.box-inv-6.medium.sp-before[Which kind lets you prove causation?]

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# Causation with observational data

.box-inv-6.medium.sp-after[Can you prove causation with observational data?]

.box-inv-6.medium[Why is it so controversial to use observational data?]

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# The causal revolution

.pull-left-narrow[
<figure>
 <img src="img/01/book-of-why.jpg" alt="The Book of Why" title="The Book of Why" width="100%">
</figure>
]

.pull-right-wide.center[
<figure>
 <img src="img/01/judea-pearl.jpg" alt="Judea Pearl" title="Judea Pearl" width="90%">
</figure>
]

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# Causal diagrams

.box-inv-6.medium[Directed acyclic graphs (DAGs)]

.box-6.SMALL[Graphical model of the process that generates the data]

.box-6.SMALL[Maps your philosophical model]

.box-6.SMALL[Fancy math ("*do*-calculus") tells you what to control for to isolate and identify causation]

]

]

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# How to draw a DAG

.box-inv-6.medium[What is the causal effect of an additional year of education on earnings?]

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# 1. List variables

.box-6.sp-after[Education (treatment) → Earnings (outcome)]

.center.float-left.sp-after-half[
.box-inv-6[Location]&ensp;.box-inv-6[Ability]&ensp;.box-inv-6[Demographics]
]

.center.float-left.sp-after-half[
.box-inv-6[Socioeonomic status]&ensp;.box-inv-6[Year of birth]
]

.center.float-left[
.box-inv-6[Compulsory schooling laws]&ensp;.box-inv-6[Job connections]
]

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# 2. Simplify

.box-6.sp-after[Education (treatment) → Earnings (outcome)]

.center.float-left.sp-after-half[
.box-inv-6[Location]&ensp;.box-inv-3[Ability]&ensp;.box-inv-3[Demographics]
]

.center.float-left.sp-after-half[
.box-inv-3[Socioeonomic status]&ensp;.box-inv-6[Year of birth]
]

.center.float-left[
.box-inv-6[Compulsory schooling laws]&ensp;.box-inv-6[Job connections]
]

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# 3. Draw arrows

]

]

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# 3. Draw arrows

.box-inv-6[Background, year of birth, location, job connections, and school requirements all cause education]

]

]

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# 3. Draw arrows

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]

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# 3. Draw arrows

]

]

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# 3. Draw arrows

.box-inv-6[Location and background are probably related, but neither causes the other. Something unobservable (U1) does that.]

]

]

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# Your turn #1

.box-inv-6.medium[Does a longer night's sleep extend your lifespan?]

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# Causal identification

]

![](01_dags_files/figure-html/edu-earn-full-1.png)

]

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# Causal identification

.box-inv-6.medium[A causal effect is *identified* if the association between treatment and outcome is propertly stripped and isolated]

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# Paths and associations

.box-inv-6.medium[Arrows in a DAG transmit associations]

.box-inv-6.medium[You can redirect and control those paths by "adjusting" or "conditioning"]

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# Three types of associations

.box-inv-6.small[Common cause]
]

.box-inv-6.small[Mediation]
]

.box-inv-6.small[Selection / endogeneity]
]

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# Confounding

.pull-left-wide[
<img src="01_dags_files/figure-html/confounding-dag-big-1.png" width="100%" style="display: block; margin: auto;" />
]

.box-inv-6.medium[But **Z** causes both **X** and **Y**]

.box-inv-6.medium[**Z** * confounds* the **X** → **Y** association]
]

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# Paths

.box-inv-6.medium[**Z** is a *backdoor*]
]

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# *d*-connection

.pull-right-narrow[
.box-inv-6[**X** and **Y** are "*d*-connected" because associations can pass through **Z**]

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# Effect of money on elections

.box-inv-6.medium[What are the paths between **money** and **win margin**?]

.pull-left[
<img src="01_dags_files/figure-html/money-elections-1.png" width="100%" style="display: block; margin: auto;" />
]

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# Closing doors

.pull-left[
<img src="01_dags_files/figure-html/confounding-dag-adjusted-1.png" width="100%" style="display: block; margin: auto;" />
]

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# Closing doors

.pull-left[
.box-inv-6.small[Find the part of campaign money that is explained by quality, subtract it out. This is the residual part of money.]

.box-inv-6.small[Find the part of win margin that is explained by quality, subtract it out. This is the residual part of win margin.]

.box-inv-6.small[Find the relationship between the residual part of money and residual part of win margin. **This is the causal effect**.]
]

.pull-right[
<img src="01_dags_files/figure-html/money-elections-adjusted-1.png" width="100%" style="display: block; margin: auto;" />
]

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# Closing doors

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# How to adjust

.box-inv-6.medium[Include term in regression]

$$
`\begin{aligned}
\text{Win margin} =& \beta_0 + \beta_1 \text{Campaign money} +\\
& \beta_2 \text{Candidate quality} + \varepsilon
\end{aligned}`
$$

.center.float-left[
.box-inv-6.medium[Matching]&ensp;.box-inv-6.medium[Stratifying]

.box-inv-6.medium.sp-before-half[Inverse probability weighting]
]

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# *d*-separation

.pull-right[
.box-inv-6.medium[If we control for **Z**, **X** and **Y** are now "*d*-separated" and the association is isolated!]

]

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# Closing backdoors

.pull-left-narrow[
.box-inv-6[Block all backdoor paths to identify the main pathway you care about]
]

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# All paths

.pull-left.left[
.box-6.smaller[Education → Earnings]

.box-6.smaller[Education → Job connections → Earnings]

.box-2.smaller[Education ← Background → Earnings]

.box-2.smaller[Education ← Background ← U1 → Location → Earnings]

.box-2.smaller[Education ← Location → Earnings]

.box-2.smaller[Education ← Location ← U1 → Background → Earnings]

.box-2.smaller[Education ← Year → Earnings]
]

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# All paths

.pull-left-narrow[
.box-inv-6[Adjust for **Location**, **Background** and **Year** to isolate the **Education → Earnings** causal effect]
]

.pull-right-wide[
<img src="01_dags_files/figure-html/edu-earn-adjust-1.png" width="100%" style="display: block; margin: auto;" />
]

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# Let the computer do this!

.box-inv-6.large[dagitty.net]

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# How do you know if this is right?

.pull-left-narrow[
.box-inv-6[You can test the implications of the model to see if they're right in your data]

$$
X \perp Y\ |\ Z
$$

.box-6.small[X is independent of Y, given Z]
]

.pull-right-wide[
<figure>
 <img src="img/01/dagitty-implications.png" alt="Dagitty implications" title="Dagitty implications" width="100%">
</figure>
]

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# Your turn #2

.box-6.medium[Go to andhs.co/nyt and skim the article]

.box-6.medium[Pick one of the causal claims in the article]

.box-6.medium[Draw a DAG for that causal claim]

.box-6.medium[Determine what needs to be adjusted to identify the effect]

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# Causation

.pull-left-wide[
<img src="01_dags_files/figure-html/causation-dag-big-1.png" width="100%" style="display: block; margin: auto;" />
]

.box-inv-6.medium[**X** causes **Z** which causes **Y**]

.box-6.medium[Should you control for **Z**?]
]

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# Causation

.box-inv-6.medium[No!]

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# Causation and overcontrolling

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# Colliders

.pull-left-wide[
<img src="01_dags_files/figure-html/collider-dag-big-1.png" width="100%" style="display: block; margin: auto;" />
]

.box-inv-6.medium[**Y** causes **Z**]

.box-6.medium[Should you control for **Z**?]
]

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# Programming and social skills

.box-inv-6.medium[Do programming skills reduce social skills?]

.pull-left[
<img src="01_dags_files/figure-html/programming-social-skills-1.png" width="100%" style="display: block; margin: auto;" />
]

.pull-right[
.box-6[You go to a tech company and conduct a survey. You find a negative relationship! Is it real?]
]

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# Programming and social skills

.box-inv-6.medium[Do programming skills reduce social skills?]

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# Colliders and selection bias

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# Three types of associations

![](01_dags_files/figure-html/confounding-dag-1.png)

.box-inv-6.small[Common cause]
]

![](01_dags_files/figure-html/mediation-dag-1.png)

.box-inv-6.small[Mediation]
]

![](01_dags_files/figure-html/collision-dag-1.png)

.box-inv-6.small[Selection / endogeneity]
]

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# Next up

&nbsp;

.box-inv-6.medium[How to analyze RCTs]