Multiple Regression & Fundamentals of Causal Inference

class: center, middle, inverse, title-slide

.title[
# Multiple Regression & Fundamentals of Causal Inference
]
.subtitle[
## 1. Introduction
]
.author[
### Merlin Schaeffer Department of Sociology
]
.date[
### 2024-09-03
]

---

# Course structure

.left-column[

| TA       | Fridays  | Room       |
|:---------|:---------|:-----------|
| Adna     | 8  am    | CSS 2-1-02 |
| Josefine | 8  am    | CSS 4-1-30 |
| Elias    | 10 am    | CSS 2-2-55 |
| Jonas    | 10 am    | CSS 2-1-55 |
]

.right-column[
<img src="./img/Structure.png" width="100%" style="display: block; margin: auto;" />
]

---
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background-image: url("https://stanfordbloodcenter.org/wp-content/uploads/2021/01/iStock-1208283967.jpg")
background-position: center
background-size: cover

.font160[
**My research agenda**
]
.font200[
**How Does International Immigration Transform our Societies?**
]

---
layout: true
# Some of my current work

---

.left-column[
<img src="https://www.templehealth.org/sites/default/files/styles/without_crop/public/2021-01/man-wearing-mask-coughing-into-shoulder.jpg?itok=Z6mUgWPd" width="100%" style="display: block; margin: auto;" />
]

.right-column[
<img src="./img/Paired_Vignette.png" width="100%" style="display: block; margin: auto;" />
.center[.backgrnote[*Source*: Schaeffer and Haderup Larsen (2023)]]
]

---

<img src="./img/jcac025f1.jpeg" width="80%" style="display: block; margin: auto;" />
.center[.backgrnote[*Source*: Schaeffer and Haderup Larsen (2023)]]

---

<img src="./img/Krzysz.png" width="42%" style="display: block; margin: auto;" />
.center[.backgrnote[*Source*: Krakowski, Schaeffer, Romarri, and Rosenberg (2022)]]

---

<img src="./img/IT-Healthcare.png" width="95%" style="display: block; margin: auto;" />
.center[.backgrnote[*Source*: Krakowski, Schaeffer, Romarri et al. (2022)]]

---

<img src="./img/Wiedner.png" width="45%" style="display: block; margin: auto;" />
.center[.backgrnote[*Source*: Wiedner, Schaeffer, Carol, and Böller (2023)]]
 
---
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class: inverse middle center
# Explanatory Sociology

---
# 4 Types of research questions

.push-left[
**(1) Ontological**: What is the nature of .alert[X]?
  + What is power?
  + What is gender; how is it different from race?
  + What is a state? .backgrnote[
> A human community that (successfully) claims the monopoly of the legitimate use of physical force within a given territory

> -- Max Weber, "Politics as a Vocation" 1918]

**(2) Critical**: Is .alert[X] (un-)just?
  + Is home office exploitation?
  + Is the color-blind ideology a new form of racism?
]

.push-right[
**(3) Descriptive**: What types of .alert[X] exist and how frequent are they?
 + What are the survival strategies of the poor?
 + How did Danes structure their days during the COVID-19 lockdowns?

**(4) Explanatory**: What is the effect of .alert[X]?
 - What are the consequences of anomie? .backgrnote[Why does the suicide rate vary across societies?]
 - How does capitalism affect us?
 - How does urbanization affect us?
 - .backgrnote[Why do people obey power?]
 - .backgrnote[How does a state gain legitimacy over the use of physical force?]
]

.content-box-green[
.center[
Think of the last exam you wrote. What type of research question did it enage with?
]]

---
# 4 Types of research questions

> -- Max Weber, "Politics as a Vocation" 1918]

**(2) Critical**: Is .alert[X] (un-)just?
  + Is home office exploitation?
  + Is the color-blind ideology a new form of racism?
]

.content-box-red[
**(4) Explanatory**: What is the effect of `\(X\)`?
 - What are the consequences of anomie? .backgrnote[Why does the suicide rate vary across societies?]
 - How does capitalism affect us?
 - How does urbanization affect us?
 - .backgrnote[Why do people obey power?]
 - .backgrnote[How does a state gain legitimacy over the use of physical force?]
]]

---
# Goal of empirical sociology

.font130[.center[Use data to discover patterns, and the .alert[social mechanisms that bring them about.]]]

---
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# Three learning goals

---
# Three learning goals

.push-left[
**(1) Multiple OLS regression**
  + Multiple predictors & confounder adjustment,
  + Interaction effects,
  + Polynomials.

**(2) Visualization of regression results**
  + Model predictions,
  + Coefficient plots.

<img src="https://www.journals.uchicago.edu/cms/10.1086/686942/asset/images/medium/fg3.gif" width="65%" style="display: block; margin: auto;" />
.backgrnote[.center[*Source:* Legewie and Schaeffer (2016)]]

]

.push-right[
**(3) Fundamentals of causal inference**
  + Potential outcomes and directed acyclical graphs,
  + Randomized Controlled Trials,
  + Intention to treat & instrument variable regression,
  + Multiple regression,
  + 2-SLS instrument variable regression,
  + Regression discontinuity designs.

<img src="1-Introduction_files/figure-html/DAG1-1.png" width="45%" style="display: block; margin: auto;" />
]

---
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class: clear
# Example: Regression discontinuity design

.push-left[
<img src="https://pbs.twimg.com/media/FOH1FlhWUAIqbN1.jpg:large" width="62%" style="display: block; margin: auto;" />
]

.push-right[
<img src="https://pbs.twimg.com/media/FZIn0ymXgAAOopA.jpg:large" width="100%" style="display: block; margin: auto;" />
]

---
class: clear
# Example: Regression discontinuity design

.push-left[
<img src="https://pbs.twimg.com/media/FOH1FlhWUAIqbN1.jpg:large" width="62%" style="display: block; margin: auto;" />
]

.push-right[
.center[Municipalities where far-right candidates *ran*
versus where they *won*]
<img src="./img/Map_Italy.png" width="100%" style="display: block; margin: auto;" />
.backgrnote[.center[*Source:* Romarri (2020)]]
]

---
class: clear
# Example: Regression discontinuity design

<img src="./img/Romarri.png" width="50%" style="display: block; margin: auto;" />
.backgrnote[.center[*Source:* Romarri (2020)]]

---
class: clear
# Example: Regression discontinuity design

.left-column[
<img src="./img/Krzysz.png" width="100%" style="display: block; margin: auto;" />
]

.right-column[
<img src="./img/Figure2a-1.png" width="100%" style="display: block; margin: auto;" />
.backgrnote[.center[*Source:* Krakowski, Schaeffer, Romarri et al. (2022)]]
]

---
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# Break

---
# Course structure

.right-column[
<img src="./img/Structure.png" width="100%" style="display: block; margin: auto;" />
]

.left-column[
.center[**Recommendations**]
- Activate email notifications on Absalon.

- Regularly check your KU email or forward it to your personal email.

- Ask and answer questions in the [t-R-ouble forum](https://absalon.ku.dk/courses/70545/discussion_topics/563046?module_item_id=2037268) on Absalon.
]

---
class: clear

<img src="./img/Quizz1.png" width="60%" style="display: block; margin: auto;" /><img src="./img/Quizz2.png" width="60%" style="display: block; margin: auto;" /><img src="./img/Quizz3.png" width="60%" style="display: block; margin: auto;" />
---
# Weekly Absalon Online Quizzes

.left-column[
- 13 Online Quizzes on Absalon designed by [Epinion](https://epinionglobal.com/) & Adna.

- Based on data Epinion collects for municipality of Copenhagen, DR, Skat, etc.

- .alert[Submit at least 10 completed quizzes] to qualify for the integrated exam with "Velfærd, ulighed og mobilitet"!

- .alert[Submit individually and within two weeks] after they are made available online (i.e., Wednesdays after the lecture).
]

.right-column[
<img src="./img/Quizz1.png" width="80%" style="display: block; margin: auto;" /><img src="./img/Quizz2.png" width="80%" style="display: block; margin: auto;" /><img src="./img/Quizz3.png" width="80%" style="display: block; margin: auto;" />
]

---
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# Consequently, this course assumes

1. You have basic R coding skills and know how to use RStudio.

2. You know basic statistics:
  + Descriptive statistics: `\(\%\)`, `\(\bar{x}\)`, `\(\text{SD}(x)\)`.
  + Associations: 
      + Correlation: `\(r_{y,x}\)`,
      + OLS regression: `\(y_{i} = \alpha + \beta x_{i} + \epsilon_{i}\)`.
  + Inference: Confidence intervals, `\(t\)`-values & `\(p\)`-values.

---
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# Two textbooks

`\(\rightarrow\)` Both textbooks are accessible at Academic Books and are available at the university library.

.push-left[
.center[The first textbook, carried over from last semester, serves as a reference for regression and statistical inference.]

<img src="https://imgcdn.saxo.com/_9781292362328" width="40%" style="display: block; margin: auto;" />
.backgrnote[.center[Veaux, Velleman, and Bock (2021)]]
]

.push-right[
.center[To deepen our understanding of how regression analysis can be applied to identify causal effects, we will heavily rely on Angrist and Pischke's textbook]

<img src="https://imgcdn.saxo.com/_9780691152844" width="35%" style="display: block; margin: auto;" />
.backgrnote[.center[Angrist and Pischke (2014)]]
]

---
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# Questions

---
# Task 1

1. Get a [recent version of R (>= 4.3.0)](https://mirrors.dotsrc.org/cran/).

2. [Install RStudio](https://posit.co/download/rstudio-desktop/), or update to the most recent version.

---
# Task 2 .font70[Open RStudio and follow these instructions]

---
# Task 3 .font70[Set R Studio preferences]

.left-column[
Set these preferences to improve *reproducibility*! 
 `\(\rightarrow\)` RStudio/Tools/Global options.
]

.right-column[
<img src="https://d33wubrfki0l68.cloudfront.net/7fa44a5471d40025344176ede4169c5ad3159482/1577f/screenshots/rstudio-workspace.png" width="70%" style="display: block; margin: auto;" />
]

---
# R Studio workflow

.left-column[
1. Use **Projects** to manage all files (scripts, data, figures and tables) belonging to the same project.

2. Always start your RStudio session by clicking on the **Project** for this course.

2. Use the editor the write as many **R scripts** as you like, save them in the same folder as your **Project**. Thereby you can reproduce your results.
]

.right-column[
<img src="https://d33wubrfki0l68.cloudfront.net/8a64bb047429d7ae0e2acae35c40e421e6439bf6/80e5d/diagrams/rstudio-editor.png" width="85%" style="display: block; margin: auto;" />
]

---
# Set up your "Stats_II" project

.left-column[
- Click on the Project button.
]

.right-column[
<img src="./img/RProject1.png" width="40%" style="display: block; margin: auto;" />
]

---
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# Set up your "Stats_II" project
.left-column[
Set up a new project in R Studio. 
  1. "New Directory"
  2. "New Project"
  3. Finally, a name for the folder and under "Browse" where you want that folder to be located. I call mine Stats_II. 
    + This will also generate a folder with the name you chose. Use that folder for everything related to this course.

**Done!** Now you should find an empty folder under the path your wanted it to be set up.

.alert[In the future, always start RStudio by double clicking on the project icon in your folder for this course.]
]

---

.right-column[
<img src="./img/RProject2.png" width="90%" style="display: block; margin: auto;" />
]

---

.right-column[
<img src="./img/RProject3.png" width="90%" style="display: block; margin: auto;" />
]

---

.right-column[
<img src="./img/RProject4.png" width="90%" style="display: block; margin: auto;" />
]

---

.right-column[
<img src="./img/RProject5.png" width="90%" style="display: block; margin: auto;" />
]

---
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layout: true
# R Scripts
---

.left-column[
1. Open a new R Script.
2. Save it in your new folder.
  + Find it under "Files".
]

.right-column[
<img src="./img/Rscript1.png" width="100%" style="display: block; margin: auto;" />
]

---

.left-column[
1. Type the lines shon in the screenshot on the right.
2. Save the file by clicking on the flopy disc icon;
  - I called mine "Lecture.R".
3. Mark all code and click "run".
]

.right-column[
<img src="./img/Rscript3.png" width="100%" style="display: block; margin: auto;" />
]

---

.left-column[
OK, you are good to go!

**Pro tip:** *Use the R Script to take notes during the lecture!*

A `#` defines a comment. So use it to take notes and code in one single document per lecture.
]

.right-column[
<img src="./img/Rscript4.png" width="100%" style="display: block; margin: auto;" />
]

---
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class: clear
# AI & Large Language Models like ChatGPT

.push-left[
1. **Privacy**: .alert[Don't use AI/LLMs to process sensitive information!]
2. **Learning**: Use AI/LLMs to *explain, comment, debug, and improve* R code that you drafted. Also use AI/LLMs to get *summaries* of text passages and concepts that you do not understand. This will help you to read complex texts and better understand difficult topics. You can also use use AI/LLMs to *discuss* your understanding of the course materials and ask things that confuse you.

3. **Generation**: Don't use AI/LLMs to *generate, draft, and write* your R code. .alert[You need to learn how to code to assess whether ChatGPT coded what you asked for.]
]

.push-right[
<img src="https://media1.giphy.com/media/iiSb58oATiANL65Dd2/giphy.gif?cid=ecf05e470i00dk1kq5bvalzh4irqygm4pieeqkdyz9vk76ht&ep=v1_gifs_search&rid=giphy.gif&ct=g" width="100%" style="display: block; margin: auto;" />
]

---
# References

.push-left[
.font70[
Angrist, J. D. and J. Pischke (2014). _Mastering 'Metrics: The Path from Cause to Effect_. Princeton
University Press.

Krakowski, K., M. Schaeffer, A. Romarri, et al. (2022). "Populist Right-Wing Governors, Healthcare
Chauvinism, and Public Health in the Time of the Global Pandemic". In: _Unpublished manuscript_.

Legewie, J. and M. Schaeffer (2016). "Contested Boundaries: Explaining Where Ethnoracial Diversity
Provokes Neighborhood Conflict". In: _American Journal of Sociology_, pp. 125-161.

Romarri, A. (2020). _Do Far-Right Mayors Increase the Probability of Hate Crimes? Evidence From
Italy_. SSRN Scholarly Paper ID 3506811. Rochester, NY: Social Science Research Network.

Schaeffer, M. and M. Haderup Larsen (2023). "Who Should Get Vaccinated First? Limits of Solidarity
during the First Week of the Danish Vaccination Programme". In: _European Sociological Review_, pp.
1-13.
]]

.push-right[
.font70[
Veaux, D., Velleman, and Bock (2021). _Stats: Data and Models, Global Edition_. Pearson Higher Ed.

Wiedner, J., M. Schaeffer, S. Carol, et al. (2023). "Ethno-Religious Minority Infrastructures: Why Do
Some Immigrant Minorities Build Dense Organizational Infrastructures While Others Do not?" In:
_Unpublished manuscript_.
]]