Tasha Fairfield is an Associate Professor at the London School of Economics and Political Science. Dr. Fairfield spoke about her methodological research, which examines the Bayesian logic of inference in qualitative social science, drawing on her recent paper on case selection: A Bayesian Perspective on Case Selection (adapted from an upcoming book).
What is the Value of a Bayesian Perspective on Case Selection?
Fairfield introduced her work in contrast to frequentist approaches, focused on randomized sampling and enumerating populations, which is the framework that either explicitly or implicitly underpins much of the literature on case selection. Fairfield argued that frequentist approaches are ill-suited for qualitative research in diverse geographical areas. Instead, she draws on Bayesian reasoning from the natural sciences to provide a methodological foundation for qualitative research. She argues that Bayesian perspectives offer qualitative researchers alternative guidelines that shift the focus away from representative sampling and toward the principle of maximizing expected information gain.
Fairfield is a pioneer in bringing the Bayesian perspective to case selection. She first explained how Bayesian reasoning works. It allows us to come up with some potential explanations (hypothesis) for whatever we are studying, and then our background knowledge gives us an initial sense of how plausible each explanation is (our “prior” view). Once we gather evidence, we assess how well that evidence fits with each hypothesis, which in Bayesian terms is evaluation the “likelihood” of the evidence, and finally, we come up with a view about which explanation is most plausible (“posterior view”). At any point in this approach, we can refine the hypothesis or come up with a new one, returning to the initial stages of Bayesian reasoning. Next, Fairfield provided a foundation of Bayes’ rule and explained the different applications between the natural sciences, where you would have a strong theory and well-characterized error model, and qualitative research where things are more subjective. While calculating expected information gain will be prohibitive in qualitative research, the mathematical properties show us that from the outset, we expect to learn from any case that we study, and even suboptimal cases will take us closer to the truth.
After establishing the foundation of logical Bayesianism, Fairfield discussed the advantages of using this approach for qualitative research. Bayesianism helps us look at limited events, analyze limited amounts of data, and analyze non-stochastic data.
Case Selection Guidelines
Fairfield provided some case selection guidelines given Bayesian rationale, many of which run counter to the current case selection literature. In principle, the goal is to maximize expected information gain that will help invent, compare and/or revise hypotheses. At the early stages of research, any information-rich case will be useful. The idea is that we want to choose cases that will help us home in on the best explanation as efficiently as possible, and in many instances, random selection is actually a sub-optimal strategy.
In practice, Fairfield recommends the following:
- No need to begin by enumerating every case or listing every case within the scope of the hypothesis. What we did not learn in the cases we didn’t study has no bearing on what we learned in the cases that we actually studied. This allows for the iterative process between theory development and data collection and analysis
- Still need to provide the rationale for case selection to make it easier to facilitate scrutiny about argument’s scope and for follow-up research.
- Seek diversity among cases to obtain logically independent evidence to gain more information about the truth of rival hypotheses.
- Similarities across cases can also yield strong tests, such as seeking variation on one variable but not on other potential variations.
- No need to avoid cases with multiple plausible causes or confounders. We can still learn from these cases.
- To adjudicate between different causal mechanisms that may underpin an established model, H = X causes Y, select model-conforming cases.
- Retire the notion of most/least-likely cases. There is no consistent definition of what most likely or least likely case is. Instead, a much better approach is to look at expected information gain as the measure for how critical the case is.
Fairfield’s encouraged the participants that there are no cookie-cutter rules for case selection, though you need to invest some careful thought, and to worry less about case selection because you can expect to learn from any case you choose. She reminded participants, however, that even though this perspective does not need a large number of cases, it does not mean studying a small amount of data. This approach also forces us to be more explicit about our theories and our priors.