Class 5: DAGs, do()ing stuff, and measuring stuff

# In-person session 5

**September 20, 2021**

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# Plan for today

.box-5.medium.sp-after-half[Colliders]

.box-2.medium.sp-after-half[Potential outcomes vs. do() notation]

.box-4.medium.sp-after-half[do-calculus, adjustment, and CATEs]

.box-6.medium.sp-after-half[Logic models, DAGs, and measurement]

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layout: false
name: colliders
class: center middle section-title section-title-5 animated fadeIn

# Colliders

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.box-5.less-medium.sp-after[How do I know which of these is which?]

.center[
<figure>
 <img src="img/05-class/dag-associations.png" alt="DAG associations" title="DAG associations" width="100%">
</figure>
]

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.box-5.medium[But what does that mean, "opening a backdoor path"?]

.box-5.medium[How does statistical association get passed through paths?]

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.pull-left[
<figure>
 <img src="img/04-class/slider-switch-plain-80.jpg" alt="Switch and slider" title="Switch and slider" width="100%">
</figure>
]

.pull-right[
<img src="05-class_files/figure-html/confounding-dag-alone-1.png" width="100%" style="display: block; margin: auto;" />
]

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.pull-left[
<figure>
 <img src="img/04-class/slider-switch-plain-80.jpg" alt="Switch and slider" title="Switch and slider" width="100%">
</figure>
]

.pull-right[
<img src="05-class_files/figure-html/mediating-dag-alone-1.png" width="100%" style="display: block; margin: auto;" />
]

---

.pull-left[
<figure>
 <img src="img/04-class/slider-switch-plain-80.jpg" alt="Switch and slider" title="Switch and slider" width="100%">
</figure>
]

.pull-right[
<img src="05-class_files/figure-html/colliding-dag-alone-1.png" width="100%" style="display: block; margin: auto;" />
]

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d-separation

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.box-5.medium[How can you be sure you include everything in a DAG?]

.box-5.medium[Is there a rule of thumb for the number of nodes?]

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.box-5.large[How exactly do colliders mess up your results?]

.box-5.medium[It looks like you can still get the effect of X on Y]

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.center[
<figure>
 <img src="img/04-class/facebook.png" alt="Facebook collider" title="Facebook collider" width="55%">
</figure>
]

???

<https://www.businessinsider.com/facebook-sent-incomplete-misinformation-data-flawed-researchers-2021-9>

<https://www.nytimes.com/live/2020/2020-election-misinformation-distortions#facebook-sent-flawed-data-to-misinformation-researchers>

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# Does niceness improve appearance?

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# Collider distorts the true effect!

]

]

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.box-5.large[Effect of race on police use of force using administrative data]

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.box-5.medium[Effect of race on police use of force using administrative data]

.pull-left[
<figure>
 <img src="img/05-class/klm-dag.png" alt="Use of force" title="Use of force" width="100%">
</figure>
]

.pull-right[
<figure>
 <img src="img/05-class/klm.png" alt="Use of force" title="Use of force" width="100%">
</figure>
]

---

layout: false
name: po-do
class: center middle section-title section-title-2 animated fadeIn

# Potential outcomes vs. do() notation

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`$$\operatorname{E}(\cdot), \mathbf{E}(\cdot), \mathbb{E}(\cdot) \quad \text{vs.}\quad \operatorname{P}(\cdot)$$`

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# Causal effects with potential outcomes

$$
`\begin{aligned}
& \textbf{Potential outcomes notation:} \\
\delta\ =& {\textstyle \frac{1}{n} \sum_{i=1}^n} Y_i (1) - Y_i (0) \\
& \\
& \text{or alternatively with } \textbf{E} \\
\delta\ =& \textbf{E} [Y_i (1) - Y_i (0)] \\
\end{aligned}`
$$

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# Causal effects with do()

$$
`\begin{aligned}
& \textbf{Pearl notation:} \\
\delta\ =& \textbf{E}[Y_i \mid \operatorname{do}(X = 1) - Y_i \mid \operatorname{do}(X = 0)] \\
& \\
& \text{or more simply} \\
\delta\ =& \textbf{E} [Y_i \mid \operatorname{do}(X)] \\
\end{aligned}`
$$

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$$
\delta \quad = \quad \textbf{E} [Y_i \mid \operatorname{do}(X)] \quad = \quad \textbf{E} [Y_i (1) - Y_i (0)]
$$

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.box-2.medium[We can't see this]

`$$\textbf{E} [Y_i \mid \operatorname{do}(X)] \quad \text{or} \quad \textbf{E} [Y_i (1) - Y_i (0)]$$`

.box-2.medium[So we find the average causal effect (ACE)]

$$
\hat{\delta} = \textbf{E} [Y_i \mid X = 1] - \textbf{E} [Y_i \mid X = 0]
$$

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.center[
<figure>
 <img src="img/05-class/cor-not-cause.png" alt="Correlation is not causation" title="Correlation is not causation" width="100%">
</figure>
]

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layout: false
name: po-do
class: center middle section-title section-title-4 animated fadeIn

# do-calculus, adjustment, and CATEs

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.box-4.medium[
How can you create a DAG/transform the expression and do all the backdoor adjustments to determine causality if you can't possibly think of all variables that may impact your outcome variable?
]

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.box-4.medium[Where can we learn more about *do*-calculus?]

.center[
<figure>
 <img src="img/05-class/do-calculus-math.png" alt="Do-calculus" title="Do-calculus" width="70%">
</figure>
]

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.box-4.medium[Adjusting for backdoor confounding]

.center[
<figure>
 <img src="img/05-class/backdoor.png" alt="Backdoor adjustment" title="Backdoor adjustment" width="100%">
</figure>
]

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.box-4.medium[Adjusting for frontdoor confounding]

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.box-4.medium[When you're making groups for CATE, how do you decide what groups to put people in?]

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layout: false
name: logic-dag
class: center middle section-title section-title-6 animated fadeIn

# Logic models, DAGs, and measurement

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.box-6.large[What's the difference between logic models and DAGs?]

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# DAGs vs. Logic models

.box-6.large[DAGs are a *statistical* tool]

.box-6.large.sp-before[Logic models are a *managerial* tool]

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.pull-left[
<figure>
 <img src="img/04-class/greenspace-eater.png" alt="Green space in Berkeley" title="Green space in Berkeley" width="100%">
</figure>
]

.pull-right[
<figure>
 <img src="img/04-class/greenspace-conversation.png" alt="Covid green spaces" title="Covid green spaces" width="100%">
</figure>
]

???

<https://theconversation.com/how-cities-can-add-accessible-green-space-in-a-post-coronavirus-world-139194>

<https://sf.eater.com/2020/5/14/21258980/berkeley-coronavirus-covid-19-jesse-arreguin-street-closures>