Week 3 Dear Prudence, Help! I may be cheating with my X

Interactions and the logic of causal inference

Description

Much of what we do in quantitative data analysis is about examining relationships. We are often interested in proposing and testing models of relationships between two or more variables. Sometimes our variables cry out to us begging for help, and we turn into agony aunts and uncles to our data. Other times we must psychoanalyse our data to uncover hidden associations and interactions. This is not an easy task. Do it carelessly, and you may unwittingly cheat yourself and the readers of your research. This week we’ll build some intuition for detecting complex and uneasy relationships within the design matrix X - that promiscuous commune on the right-hand-side of our regression equations. We’ll expand on the linear additive models that we looked at in the previous week by considering interactions among our predictor variables, we’ll explore the possibilities and challenges of asking causal questions of observational data, and we’ll think about ways to avoid what evolutionary anthropologist Richard McElreath calls ‘causal salad’. We may get an uncomfortable feeling that we may have cheated with our Xs in the past, but we’ll look towards the future. By the way, Dear Prudence is Slate magazine’s advice column; I like the name because being prudent really is essential in data analysis and interpretation. If you’re done with the readings for this week, you may indulge in some Prudie advice on matters more serious than statistics.

Readings

Statistics

• ROS: Chapters 10-12, 18-20

Coding

• TSD: Chapter 14

Application

• Österman, Marcus. 2021. ‘Can We Trust Education for Fostering Trust? Quasi-Experimental Evidence on the Effect of Education and Tracking on Social Trust’. Social Indicators Research 154(1):211–33 - (online)

References

David, F. N. 1955. “Studies in the History of Probability and Statistics i. Dicing and Gaming (a Note on the History of Probability).” Biometrika 42 (1/2): 1–15. https://doi.org/10.2307/2333419.

El-Shagi, Makram, and Alexander Jung. 2015. “Have Minutes Helped Markets to Predict the MPC’s Monetary Policy Decisions?” European Journal of Political Economy 39 (September): 222–34. https://doi.org/10.1016/j.ejpoleco.2015.05.004.

Gelman, Andrew, Jennifer Hill, and Aki Vehtari. 2020. Regression and other stories. Cambridge: Cambridge University Press. https://doi.org/10.1017/9781139161879.

Lord, R. D. 1958. “Studies in the History of Probability and Statistics.: VIII. De Morgan and the Statistical Study of Literary Style.” Biometrika 45 (1/2): 282–82. https://doi.org/10.2307/2333072.

McElreath, Richard. 2020. Statistical Rethinking: A Bayesian Course with Examples in R and Stan. Second. CRC Texts in Statistical Science. Boca Raton: Taylor and Francis, CRC Press.

Mulvin, Dylan. 2021. Proxies: The Cultural Work of Standing in. Infrastructures Series. Cambridge, Massachusetts: The MIT Press.

Senn, Stephen. 2003. “A Conversation with John Nelder.” Statistical Science 18 (1): 118–31. https://doi.org/10.1214/ss/1056397489.