hw3.Rmd

```{r hw3_setup, include=FALSE}
knitr::opts_chunk$set(echo=TRUE, eval=FALSE)
```

# Homework 3 {-}

## General instructions {-}

Due: Friday, February 17 at midnight CST. (Note that we're skipping a week in our prior weekly HW cadence.)

- Continue using the same Google Doc from HW1.

<br>

**You do not need to complete all parts (except the Metacognitive Reflection).** Just complete the parts that align with your learning goals and would be most helpful in developing strong understanding.

**If you're interested in working on something not listed here, I'm very open to that too.** Talk with me about what you're thinking, and we'll come up with a good collection of work to further your goals.


<br><br>


## Revisions {-}

If you would like to make revisions to any parts of prior assignments, please do the following:

- Keep all old writing and feedback intact
- Un-highlight yellow text that has already been addressed with feedback and revisions
- Write an updated response just below your previous response and highlight the new writing in yellow


<br><br>


## Clarifying the big picture {-}

Tell a story/give a summary of our course up to this point by writing a piece that connects the following ideas:

- Potential outcomes and causal effects
- Exchangeability
- Causal graphs
- Causal and noncausal paths
- D-separation
- Building causal graphs in practice for applied analyses

**Audience:** If you have a personal website or would like to create one, what you write here has the potential to make for a great blog post. If this appeals to you, think of who you would want to read such a piece (e.g., a potential employer, a friend, a family member), and write for them.

**Note:** As we continue to move forward with new ideas in the course, you may find it helpful to continue incorporating the new ideas into what you write here.


<br><br>


## The smoking-birthweight paradox {-}

Write a piece summarizing the arguments and key takeaway messages from our discussion of the [The Birth Weight "Paradox" Uncovered?](https://doi.org/10.1093/aje/kwj275).

If you're curious about even further commentary on that article, read [Commentary: Resolutions of the birthweight paradox: competing explanations and analytical insights](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4190521/), and incorporate your synthesis of the arguments in this paper.

**Audience:** If you have a personal website or would like to create one, what you write here has the potential to make for a great blog post. If this appeals to you, think of who you would want to read such a piece (e.g., a potential employer, a friend, a family member), and write for them.


<br><br>


## Exchangeability: Computation {-}

Suppose that the treatment ($A$) groups are exchangeable conditional on $Z$. Given the table of information below, compute the following average causal effects (showing your work):

- Overall ACE: $E[Y^{a=1} - Y^{a=0}]$
- ACE within $Z = A$: $E[Y^{a=1} - Y^{a=0} \mid Z = A]$
- ACE within $Z = B$: $E[Y^{a=1} - Y^{a=0} \mid Z = B]$

($Z$ and $A$ are binary, and $Y$ is quantitative. $n$ indicates the sample size for the 4 groups.)

 $n$   $Z$   $A$   $E[Y\mid A, Z]$
----- ----- ----- -----------------
  80    A     1         40
  20    A     0         20
  20    B     1         30
  80    B     0         20


<br><br>


## Exchangeability: explaining via causal graphs {-}

Causal graphs and the ideas of causal/noncausal paths can help clarify the concept of exchangeability. Use a causal graph to generate a numeric example of a potential outcomes table (containing information on covariate(s), treatment, and both potential outcomes) in which marginal exchangeability does not hold but conditional exchangeability does.

If you would like to keep going, also use a causal graph to create a numeric example where marginal exchangeability does hold but conditional exchangeability does not.


<br><br>


## Simulation, d-separation, and exchangeability {-}

Pick any causal graphs from our in-class exercises or textbooks (WHATIF and/or PRIMER) that surprised or perplexed you.

For a given graph:

- Use d-separation to identify appropriate conditioning set(s) of variables that would allow for valid estimation of the average causal effect.
- Check that those conditioning set(s) actually result in conditional exchangeability by performing a simulation study. (It is important to perform many runs of the simulation. Check the Topic 5 Solutions on Moodle for guidance.)


<br><br>


## Study designs: examples of applied studies {-}

If you would like to see more examples of how study designs are used in applied research, find some applied papers and read enough of each to get a sense for how the study was conducted. Summarize your findings here.


<br><br>


## Metacognitive Reflection {-}

- How do you feel about your level of understanding of prior topics and new topics (causal/noncausal paths, d-separation, building causal graphs in practice)?

- What were some notable themes in self- and peer-noticings?

- How do these reflections inform your next steps for developing stronger understanding? What support and resources would best help you?