Week 4 The Y question

Generalised linear models

Description
It wasn’t until the last quarter of the 20th century that a unified vision of statistical modelling emerged, allowing practitioners to see how the general linear model we have explored so far is only a specific case of a more general class of models. We could have had a fancy, memorable name for this class of models - as John Nelder, one of its inventors, acknowledged later in life (Senn 2003, 127) - but back then academics were not required to undertake marketing training on the tweetabilty-factor of the chosen names for their theories; so we ended up with “generalised linear models”. These models can be applied to explananda (“explained”, “response”, “outcome”, “dependent” etc. variables, our ys) whose possible values have certain constraints (such as being limited by a lower bound or constrained to discreet choices) that makes the parameters of the Gaussian (‘normal’) distribution inefficient in describing them. Instead, they follow some of the other “exponential distributions” (and not only the exponential: cf. Gelman, Hill, and Vehtari (2020, 264)), of which the Poisson, gamma, beta, binomial and multinomial are probably the most common in human and social sciences research. Their “generalised linear modelling” involves mapping them unto a linear model using a so-called “link function”. We will explore what all of this means in practice and how it can be applied to data that we are interested in most in our respective fields of study.

Readings

Statistics

  • ROS: Chapters 13-15

Coding

  • TSD: Chapter 13

Application

  1. Ladd, Jonathan McDonald, and Gabriel S. Lenz. 2009. ‘Exploiting a Rare Communication Shift to Document the Persuasive Power of the News Media’. American Journal of Political Science 53(2):394–410. doi: 10.1111/j.1540-5907.2009.00377.x.(published version should be accessible with university login; additional Appendix available here)

  2. Weiss, Alexa, Corinna Michels, Pascal Burgmer, Thomas Mussweiler, Axel Ockenfels, and Wilhelm Hofmann. 2021. ‘Trust in Everyday Life’. Journal of Personality and Social Psychology 121:95–114. doi: 10.1037/pspi0000334 (access preprint version here)

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.