Qualitative Comparative Analysis and Fuzzy Sets

First week, taught by Ioana-Elena (Nena) Oana

The central aim of week 1 is to familiarise you with the formal logic of set-theoretic methods and to introduce QCA as an approach, its main assumptions, the technical environment (software) and the standard procedures and operations.

I will put particular emphasis on a thorough understanding of the notions of necessity and sufficiency, because they are the nuts and bolts of QCA that set it apart from the majority of other cross-case comparative techniques.

On day 1 I will introduce the course topic, the content and sequence of the sessions, and the resources. We touch upon the basics of set-theoretic methods, the epistemology of QCA, its different variants, and how it compares to other standard qualitative and quantitative social scientific research designs. The centrepiece of this first session will be a demonstration of QCA on the basis of a recently published study.

On day 2, we turn to the methodological foundations of QCA including a thorough discussion of the basic mathematical concepts of QCA, which are derived from set theory. The session begins by with an outline of sets and set membership, including the notion of fuzzy sets as opposed to crisp sets. Once these essentials are in place, we turn to Boolean and fuzzy algebra, formal logic and operations on complex expressions.

On day 3, we will start by revisiting notions of causal complexity with a focus on INUS and SUIN causes. Afterwards we address the question of how to prepare observational data to perform QCA, i.e. how to calibrate. In doing so, we will cover various modes of calibrating raw data for crisp-set, multi-value and fuzzy-set QCA. We will go through various calibration techniques using R and discuss the consequences of different calibration decisions.

On day 4, we will define the notion of a truth table in crisp-set and fuzzy-set QCA and how it differs from a data matrix. We will show how to analyse truth tables with respect to necessary and sufficient conditions in order to derive solution formulas. This includes the Quine-McCluskey Algorithm for the logical minimisation of the sufficiency statements in a truth table.

On day 5, we will turn to the so-called parameters of fit that are central to any QCA study, i.e. the measures of consistency and coverage for necessary and sufficient conditions. We will further discuss some methodological issues that are related to the parameters of fit. The first week concludes with an informal course evaluation and a consideration of topics that you would like to see covered in more depth in the second week.

Second week, taught by Carsten Q. Schneider

The purpose of week two is fourfold:

1. to revisit the core points of QCA addressed in week 1 (calibration, tests of necessity and sufficiency, truth tables, parameters of fit);
2. to elaborate on further issues that arise when neat formal logical tools and concepts, such as necessity, sufficiency, and truth tables, are applied to social science data (mainly the issues of limited diversity and the challenge to make good counterfactuals on so-called logical remainders);
3. to get better acquainted with the standards of good practice, both in its fundamental aspects and in using the relevant software programmes;
4. to discuss general methodological issues such as robustness and theory evaluation from a set-theoretic point of view.

On day 6, we will start by briefly reviewing what we learned in week 1, above all with regard to the basics of the analysis of necessary and sufficient conditions and how truth tables are used to reveal the latter. Putting everything together, we explain how the Truth Table algorithm, the standard mode for analysing crisp and fuzzy sets in QCA, works. We will recap the notions of parameters of fit, problematise some of their properties, and elaborate on potential improvements of these formulas. Since several of the problems have their roots in what could be called skewed set membership scores, we will be looking into this issue more closely.

On day 7, we will discuss the second problem of incomplete truth tables: logical remainder rows. We will explain how this phenomenon of limited diversity arises and which basic strategies are at the researcher’s disposal to mitigate its impact on drawing inferences. Above all, we will show how counterfactual thinking can be used to resolve problems of limited diversity. This leads to the development of 'intermediate solutions' in a so-called standard analysis.

On day 8, we continue with the issue of limited diversity and introduce several amendments to the standard analysis. In addition to distinguishing between easy and difficult counterfactuals, we introduce the notion of tenable and untenable assumptions on remainders.

On day 9, we introduce various perspectives on the ‘robustness’ or ‘sensitivity’ of results obtained with QCA. We discuss against which analytic decisions a result ought to be robust and how we see if and when a result can be considered robust (enough). Along these lines, we also discuss strategies for confronting situations when the data at hand contains potentially relevant clusters. These clusters can be of any kind, such as temporal, geographic, or substantive clusters, and we explain how to probe whether the result obtained for the pooled (i.e. across clusters) data holds for all clustered separately.

On day 10, we put together the material of the entire course by spelling out the Truth Table algorithm, i.e. the process from turning the data matrix into a truth table, then logically minimising the table, allowing for different strategies vis-à-vis the logical remainders, and calculating the parameters of fit for each solution formula. On this day, I will ask you to apply the knowledge gained during this course to different published data sets and/or your own data.

Throughout the course, we will analyse fake and real data in the computer lab, using the R software environment and its QCA package.

In addition to prepared datasets, which will be made available, we encourage you to bring your own raw data (even if still tentative), for lab exercises and project work.

Instructors and teaching assistants will be available for individual appointments to discuss your research projects, questions regarding the design of a QCA study, the ‘formatting' of raw data to be compatible with QCA, and similar issues.

You don't need any prior knowledge of QCA or the R software environment and the package relevant for set-theoretic methods.

However, you would profit from prior empirical-comparative training and we strongly encourage you to read the recommended literature in advance, to familiarise yourself with the basic principles of the method.

Knowledge of the basic functions of R and RStudio would be useful to start working with the software from day one. 

To get off to the best start, we strongly recommend signing up for the short course Introduction to Case-Based Research and Set-Theoretic Thinking, which includes a brief introduction to set-theoretic methods, and to R.