Week 6 Challenging hierarchies

Multilevel models

Description
By now we got a sense that every new thing we learn about turns out to be merely a specific case of a larger class of things. So, all the models we covered so far are specific, single-level, versions of multilevel models, in which our cases can be seen as clustered within larger entities. Sometimes they are part of several cross-cutting clusters and/or the clusters are themselves clustered. In general terms, we must acknowledge that there are dependencies in our data that may influence their behaviour. It turns out that data about humans living in societies look somewhat like humans living in societies. The importance of including information about hierarchical dependencies in our models is probably emphasised by no one else more than McElreath (2020, 15), who wants “to convince the reader of something that appears unreasonable: multilevel regression deserves to be the default form of regression. Papers that do not use multilevel models should have to justify not using a multilevel approach.” We will encounter some of the uses and challenges of multilevel modelling.

Readings

Textbook

  • ARM: Chapters 11 (pp. 237-249) and 12 (pp. 251-278)
  • TSD: Chapter section 15.2

Application

  • Valentino et al. (2017) Economic and cultural drivers of immigrant support worldwide. British Journal of Political Science, 49(4), 1201–1226. (The accepted manuscript version can be downloaded from here; Note: this version of the article also contains a brief “response to reviewers” by the authors, which you may find interesting)

Further readings

  • ARM: Chapters 13 (pp. 279-299), 14 (pp. 301-323) and 15 (pp. 325-342)

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.