Qualitative Comparative Analysis and Fuzzy Sets

The central aim of week 1 (P.A. Mello) is to familiarize the participants 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. Particular emphasis is put on a thorough understanding of the notions of necessity and sufficiency, as they are the nuts and bolts of QCA that set it apart from the majority of other available cross-case comparative techniques.

• On day 1, participants will be introduced to the course topic, the content and sequence of the course sessions, as well as the course resources. We will also 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 the 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 minimization 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 will be concluded with an informal course evaluation and a consideration of topics that the participants would like to see covered in more depth in week 2.

The purpose of week 2 (C.Q. Schneider) is fourfold: (1) to re-visit 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, problematize 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 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 minimizing the table, allowing for different strategies vis-à-vis the logical remainders, and calculating the parameters of fit for each solution formula. During this day, participants are asked to apply their knowledge gained during the course to different published data sets and/or their own data.
• Day 10 will be devoted to deepening our knowledge on how to perform a QCA. In addition, we spell out the principles of Set-Theoretic Multi-Method Research, that is, how to combine cross-case analyses using QCA with within-case analyses using process tracing.

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, participants are encouraged to bring their own raw data (even if this data is still tentative), which can be used for lab exercises and project work. Instructors and teaching assistants will be available for individual appointments with course participants to discuss research projects, questions regarding the design of a QCA study, the “formatting” of raw data to be compatible with QCA, and similar issues.

Participants are not required to have any prior knowledge of QCA or the R software environment and the package relevant for set-theoretic methods. However, they would profit from prior empirical-comparative training and we strongly encourage advance familiarization with the basic principles of the method by reading the recommended literature as specified in the reading list. A previous introduction to the basic functions of R and RStudio will be useful to start working with the software from day 1.