Advanced Topics in Set-Theoretic Methods and QCA

Participants who are in good command of all the issues addressed above under “prerequisite knowledge” can expect from this course a deepened understanding of potentials and pitfalls of set-theoretic methods. This should enable them to be both more critical and assertive if and when they choose or reject set-theoretic methods as the most appropriate research method for their research project. Successfully completing the course will also enable participants to produce QCA studies of a quality and level of sophistication beyond the current mainstream and thus yield substantive results that are more compelling both for themselves and their (critical) audience. Since much of the course explores the boundaries of the still relatively young family of set-theoretic methods, it will be unavoidable that some of our debates will have to remain inconclusive. Participants should therefore be prepared to not always be provided ready-made and fool-proof answers and procedures for all the issues that they will face when trying to implement a high-quality QCA. Rather, this course invites students to think critically about set-theoretic methods, and, by extension, also about other data analysis techniques that they will have to choose when doing empirical comparative research.

This course is the result of two developments. First, the toolbox of set-theoretic methods is quickly expanding. Second, there are renewed and forceful critiques that question the fundamental logic of set-theoretic methods and QCA and the way it is put into practice in applied research. This course deals with these two, partially overlapping, recent developments. We proceed as follows.

In order to set the stage, we discuss several recent writings that are heavily critical of set-theoretic methods and QCA. From this debate, we distil the most important issues of contention. These are, among others, the question of how robust QCA results are and how (not) concerned QCA scholars are about this issue; the unrecognized assumptions incorporated in a QCA and the preconditions that are thus required in order to meaningfully apply QCA; the status of fuzzy sets, especially their alleged distinctiveness vis-à-vis variables; and the connection between QCA and proper within-case analyses. Days 2 and 3 are dedicated to discussing these critiques. On day 2, we read and discuss contrasting arguments about the distinctiveness of STM vis-à-vis quantitative techniques. On day 3, we engage with the notion of robustness in set-theoretic methods and try to systematize the debate by specifying the analytic decisions to be made against which QCA results should be expected to be robust. Along these lines, we aim at formulating criteria for meaningful robustness tests and, based on these criteria, evaluate existing, simulation-based robustness test. On day 4, we introduce set-theoretic multi-method research as an attempt at specifying just how QCA should be combined with within-case process tracing. We define the meaning of typical and deviant cases after a QCA, spell out the different rationales for studying each of them, and provide formulas for selecting the best available cases for (comparative) within-case analysis after a QCA.

Unless student demand dictates otherwise, on day 5, we tackle two issues. First, we discuss the principles and computer-assisted practice of set-theoretic theory evaluation. Second, we present strategies for including notions of time into set-theoretic analyses. Along these lines, we discuss calibration strategies, sequence elaboration, and temporal QCA, the same as an analytic tool for analysing set-theoretic panel data.

Participants of the course should not expect to be provided a general introduction to the basics of set-theoretic methods and QCA. We will also not introduce into the very basics of the R software environment.

Participants are expected to have a firm command of basic formal logic, Boolean algebra, and set-theory. Participants also need to be familiar with the basic protocol of Qualitative Comparative Analysis (QCA), including the following topics:

• the difference between sets and variables;
• the notion of set calibration;
• the meaning of set relations (sufficiency, necessity, INUS, SUIN);
• the construction and logical minimization of a truth table;
• the calculation and interpretation of the parameters of fit (consistency and coverage);
• the treatment of logical remainders as done by the Standard Analysis.

In short, participants should check whether they are in command of all the issues addressed in Schneider/Wagemann (2012) “Set-Theoretic Methods for the Social Sciences”, chapters 1-7. In case of doubt, students are encouraged to consult the online appendix of the book, which contains exercises and test questions for all these chapters. Participants are further expected to be familiar with the basics of the R software environment as we will use the R packages relevant for performing set-theoretic analyses (QCA, QCAGUI, and SetMethods) during the course. Students who have attended the two-week course on Set-Theoretic Methods and QCA at the ECPR Summer School in Ljubljana should be well prepared for this advanced course.