Week 3 Curves

Logistic regression and other 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

  • Connelly, Roxanne, Vernon Gayle, and Paul S. Lambert. 2016. ‘Statistical Modelling of Key Variables in Social Survey Data Analysis’. Methodological Innovations 9:205979911663800. Library access

Coding

  • TSD: Chapter 13

Application

  1. Wu, Cary. 2021. ‘Education and Social Trust in Global Perspective’. Sociological Perspectives 64(6):1166–86. Available here: Library access

  2. Dingemans, Ellen, and Erik Van Ingen. 2015. ‘Does Religion Breed Trust? A Cross-National Study of the Effects of Religious Involvement, Religious Faith, and Religious Context on Social Trust’. Journal for the Scientific Study of Religion 54(4):739–55. Library access

References

Gelman, Andrew, Jennifer Hill, and Aki Vehtari. 2020. Regression and other stories. Cambridge: Cambridge University Press. https://doi.org/10.1017/9781139161879.
Senn, Stephen. 2003. “A Conversation with John Nelder.” Statistical Science 18 (1): 118–31. https://doi.org/10.1214/ss/1056397489.