Modelling dichotomous outcomes

In the social sciences we are often confronted with phenomena and concepts measured not on a numeric scale but on a categorical scale. Linear regression analysis has provided us with a general approach which can be generalised to categorical dependent variables, but this generalisation relies on a mathematical transformation of the dependent variable using the natural logarithm. Luckily, we have powerful software to take care of these transformations for us, and we can instead focus on understanding the sociological importance of estimating the probability of cases (people) with certain characteristics to belong to one outcome category as opposed to another.  We will focus on the basic case where there are only two (dichotomous, binary) outcome categories, which can be modelled using logistic regression, another versatile and foundational statistical method that is probably the most commonly employed in sociological research.

Essential readings

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1. Spiegelhalter (2020) The Art of Statistics:
   • CHAPTER 5 | Modelling Relationships Using Regression
     • read from section Different Types of Response Variable
   • CHAPTER 6 | Algorithms, Analytics and Prediction
   • CHAPTER 8 | Probability – the Language of Uncertainty and Variability
2. Goss-Sampson (2025) Statistical Analysis in JASP:
   • LOGISTIC REGRESSION (pp. 88-92)

Application:

• Delhey & Newton (2003) Who Trusts?

Further readings

Statistics:

• Çetinkaya-Rundel & Hardin (2024) Introduction to Modern Statistics:
  • Chapter 9 (“Logistic regression”)
• Connelly, Roxanne, Vernon Gayle, and Paul S. Lambert (2016) “Statistical Modelling of Key Variables in Social Survey Data Analysis”. Methodological Innovations 9:205979911663800.

Advanced topics:

• Mood, Carina (2010) “Logistic Regression: Why We Cannot Do What We Think We Can Do, and What We Can Do About It.” European Sociological Review 26(1): 67–82.

• Breen, Richard, Kristian Bernt Karlson, and Anders Holm (2018) “Interpreting and Understanding Logits, Probits, and Other Nonlinear Probability Models.” Annual Review of Sociology 44(1): 39–54.