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Advanced Topics in Set-Theoretic Methods and QCA

Carsten Q. Schneider

Central European University

Carsten Q. Schneider is Professor of Political Science at Central European University Budapest.

His research focuses on regime transitions, autocratic regimes, the qualities of democracies, and the link between social and political inequalities. He also works in the field of comparative methodology, especially on set-theoretic methods.

Carsten has published articles in several peer-reviewed journals, and three books, among them Set-Theoretic Methods for the Social Sciences (Cambridge University Press, 2012) co-authored with Claudius Wagemann.


Course Dates and Times

Monday 6 to Friday 10 March 2017
Generally classes are either 09:00-12:30 or 14:00-17:30
15 hours over 5 days

Prerequisite Knowledge

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 should be well prepared for this advanced course.

Short Outline

This course addresses advanced issues that arise if and when scholars embrace notions of sets and their relations. While it is a course about set-theoretic methods writ large, most of the time, we will discuss issues that are specific to Qualitative Comparative Analysis (QCA). Although much effort has been put into developing standards of good practice, still many important issues remain unresolved, and even sometimes unaddressed. This has given rise to a recent wave of literature sceptical of set-methods, in general, and QCA, in particular. In this course we not only discuss the issues raised by theses critiques, but go beyond them and explore the hitherto under-used potentials of set-theoretic methods. Depending on needs and interests of participants, we choose among the following topics: set-theoretic multi-method research; robustness and uncertainty; set-theoretic theory evaluation; enhanced Standard Analysis; time and set-theoretic methods; model ambiguity; and/or two-step QCA.

Long Course Outline

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-prove 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.

Day 1 is dedicated to discussing these critiques. During day 1, we also go through the standard protocol of a QCA, using R. On day 2, we cover a set of relatively unrelated, yet interesting and important issues. Depending on the interest of participants, we focus on one or two of the following topics in more detail: Enhanced Standard Analysis; skewed sets and their analytic consequences; multi-value QCA. 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 analyzing 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.

Day Topic Details
1 Set-Theoretic Methods and QCA in a Nutshell; Critiques of STM I

120’ seminar:

- the standard QCA protocol

- overview of criticisms (robustness, hidden assumptions, the status of (fuzzy) sets, the detachment from cases, the superiority of non-set methods).

60’ lab:

- implementation of standard QCA protocol in R.

2 Potpourri: - Enhanced Standard Analysis - Skewed Sets - multi-value QCA

120’ lecture:

- how to avoid untenable assumptions on logical remainders

- how to avoid analytic pitfalls that stem from skewed sets

- the logic of multi-value QCA

60’ lab:

- implementation of Enhanced Standard Analysis and multi-value QCA

- diagnostics for skewed sets

3 Robustness and sensitivity

90’ lecture:

- what can and cannot be the meaning of robust results in set-theoretic methods?

- robustness against what?

- the inherently inductive nature of QCA

- designing meaningful robustness tests.

90’ lab:

- applying set-theoretic robustness tests to published QCA studies

4 Set-theoretic multi-method research

90’ lecture:

- how to select cases after a QCA

- how to make use of the insights gained from these (comparative) within-case analyses

90’ lab:

- applying the post-QCA case selection principles to examples of published QCA studies

5 - set-theoretic theory evaluation - the inclusion of time into set-theoretic analyses (panel data)

90’ lecture:

- how to evaluate theories (rather than testing hypotheses) with set-theoretic methods

- the intrinsic challenges of including notions of time as causally relevant

90’ lab:

- applying the Enhanced Standard Analysis to examples of published QCA studies

- implementing analysis of set-theoretic panel data

Day Readings
Day 1 Standard QCA Protocol; Critiques of STM I - Overview

Collier, David. 2014. “Symposium. The Set-Theoretic Comparative Method: Critical Assements and the Search for Alternatives.” Qualitative & Multi-Method Research Newsletter 12(1): 1–52

Rohlfing, Ingo, and Carsten Q Schneider. 2014. “Clarifying Misunderstandings , Moving Forward: Towards Standards and Tools for Set-Theoretic Methods.” Qualitative & Multi-Method Research Newsletter 12(2): 27–34



Fiss, Peer C, Axel Marx, and Benoît Rihoux. 2014. “Getting QCA Right: Some Comments on Lucas and Szatrowski.” Sociological Methodology 44.

Lucas, Samuel R, and Alisa Szatrowski. 2014. “Qualitative Comparative Analysis in Critical Perspective.” Sociological Methodology 44, DOI: 10.1177/0081175014532763.

Mahoney, James. 2014. „Set Diagrams and Qualitative Research.“ Comparative Political Studies. DOI 10.1177/0010414013519410

Paine, Jack. 2015. “Set-Theoretic Comparative Methods: Less Distinctive Than Claimed.” Comparative Political Studies 49(6), 703-741

Ragin, Charles C. 2014. “Lucas and Szatrowski (2014) in Critical Perspective.” Sociological Methodology 44.

Thiem, Alrik, Michael Baumgartner, and Damien Bol. 2015. “Still Lost in Translation! A Correction of Three Misunderstandings between Configurational Comparativists and Regressional Analysts.” Comparative Political Studies, 49(6): 742-774

Schneider, Carsten Q. 2016. “Real Differences and Overlooked Similarities. A Reply to Paine (2015).” Comparative Political Studies 49(6): 781-792

Skaaning, Svend-Erik. 2011. “Assessing the Robustness of Crisp-Set and Fuzzy-Set QCA Results.” Sociological Methods & Research 40(2): 391–408.

Vaisey, Stephen. 2014. “Why I ’ m Still Using QCA - Comment on Lucas and Szatrowski.” Sociological Methodology 44.


Day 2 Potpourri: Enhanced Standard Analysis / Skewed Sets / mvQCA

Haesebrouck, Tim. 2016. “The Added Value of Multi-Value Qualitative Comparative Analysis.” Forum: Qualitative Social Research 17(1)

Schneider, Carsten Q., and Claudius Wagemann. 2012. Set-Theoretic Methods for the Social Sciences: A Guide to Qualitative Comparative Analysis. Cambridge: Cambridge University Press, chapters 8, 9, 10.2



Cooper, Barry, and Judith Glaesser. 2011. “Paradoxes and Pitfalls in Using Fuzzy Set QCA: Illustrations from a Critical Review of a Study of Educational Inequality.” Sociological Research Online 16(3).

Cooper, Barry, and Judith Glaesser. 2016. “Analysing Necessity and Sufficiency with Qualitative Comparative Analysis: How Do Results Vary as Case Weights Change?” Quality and Quantity 50(1): 327–46.

Cronqvist, Lasse, and Dirk Berg-Schlosser. 2009. “Multi-Value QCA (mvQCA).” In Configurational Comparative Methods. Qualitative Comparative Analysis (QCA) and Related Techniques, eds. Benoit Rihoux and Charles C Ragin. Thousand Oaks/London: Sage. CHAP, 69–86.

Thiem, Alrik. 2015. “Parameters of Fit and Intermediate Solutions in Multi-Value Qualitative Comparative Analysis.” Quality & Quantity 49: 657–74. (March 12, 2014).

Thiem, Alrik. 2013. “Clearly Crisp, and Not Fuzzy: A Reassessment of the (Putative) Pitfalls of Multi-Value QCA.” Field Methods 25(2): 197–207. (March 29, 2013).

Thiem, Alrik. 2013. “Unifying Configurational Comparative Methodology: Generalized-Set Qualitative Comparative Analysis.” Sociological Methods & Research 43(2): 313–37.

Vink, M. P., and O. van Vliet. 2009. “Not Quite Crisp, Not Yet Fuzzy? Assessing the Potentials and Pitfalls of Multi-Value QCA.” Field Methods 21(3): 265–89. (May 3, 2011).


Day 3 Robustness and Sensitivity

Baumgartner, Michael, and A. Thiem. 2015. “Model Ambiguities in Configurational Comparative Research.” Sociological Methods & Research: 1/34.

Rohlfing, Ingo. 2015. “Why Simulations are Appropriate for Evaluating Qualitative Comparative Analysis.” Quality and Quantity, online first. DOI: 10.1007/s11135-015-0251-8

Rohlfing, Ingo. 2015. “Mind the gap: A review of simulation designs for Qualitative Comparative Analysis.” Research and Politics, October-December, 1-4

Schneider, Carsten Q., and Claudius Wagemann. 2012. Set-Theoretic Methods for the Social Sciences: A Guide to Qualitative Comparative Analysis. Cambridge: Cambridge University Press, chapters 11.2



Braumoeller, Bear. 2015. “Guarding Against False Positives in Qualitative Comparative Analysis.” Political Analysis, online first. DOI: 10.1093/pan/mpv017

Collier, D. 2014. “Comment: QCA Should Set Aside the Algorithms.” Sociological Methodology. (August 12, 2014)

Hug, S. 2013. “Qualitative Comparative Analysis: How Inductive Use and Measurement Error Lead to Problematic Inference.” Political Analysis 21(2): 252–65.

Krogslund, Chris, Donghyun Danny Choi, and Mathias Poertner. 2014. “Fuzzy Sets on Shaky Ground : Parametric and Specification Sensitivity in fsQCA.” Political Analysis, 23(1), 21-41.

Schneider, Carsten Q., and Claudius Wagemann. 2012. Set-Theoretic Methods for the Social Sciences: A Guide to Qualitative Comparative Analysis. Cambridge: Cambridge University Press, chapters 11.2

Seawright, Jason. 2014. “Comment: Limited Diversity and the Unreliability of QCA.” Sociological Methodology, 44(1), 118-121.

Thiem, A. (2014). Mill's Methods, Induction and Case Sensitivity in Qualitative Comparative Analysis: A Comment on Hug (2013). Qualitative & Multi-Method Research, 12(2), 19-24

Thiem, Alrik, Reto Spöhel, and Adrian Duşa. 2015. “Enhancing Sensitivity Diagnostics for Qualitative Comparative Analysis: A Combinatorial Approach.” Political Analysis: 1–17.

Day 4 Set-Theoretic Multi-Method Research

Schneider, Carsten Q., and Ingo Rohlfing. 2013. “Set-Theoretic Methods and Process Tracing in Multi-Method Research: Principles of Case Selection after QCA.” Sociological Methods and Research, 42(4), 559-597

Rohlfing, Ingo, and Carsten Q. Schneider. 2016. “A Unifying Framework for Causal Analysis in Set-Theoretic Multi-Method Research”. Sociological Methods and Research, online first, DOI: 10.1177/0049124115626170



Mikkelsen, Kim Sass. “Fuzzy-Set Case Studies.” 2015. Sociological Methods and Research. online first. DOI: 10.1177/0049124115578032

Mikkelsen, Kim Sass. “Negative Case Selection: Justifications and Consequences for Set-Theoretic MMR.” Sociological Methods and Research. online first. DOI: 10.1177/0049124115591015

Ragin, Charles C. and Garrett Andrew Schneider. 2011. “Case-Oriented Theory Building and Theory Testing.” In The SAGE Handbook of Innovations in Social Research Methods, ed. Malcolm; Vogt Williams W. Paul. London, 150–66.

Rihoux, Benoit, and Bojana Lobe. 2009. “The Case for Qualitative Comparative Analysis (QCA): Adding Leverage for Thick Cross-Case Comparison.” In Sage Handbook Of Case-Based Methods, eds. David Byrne and Charles C Ragin. London: Sage, 222–42.

Rohlfing, Ingo, and Carsten Q. Schneider. 2013. “Combining QCA With Process Tracing in Analyses of Necessity.” Political Research Quarterly 66(1): 220–35.

Schneider, C. Q., and I. Rohlfing. 2016. “Case Studies Nested in Fuzzy-Set QCA on Sufficiency: Formalizing Case Selection and Causal Inference.” Sociological Methods & Research 45(3): 526–68.

Day 5 Theory Evaluation/ Inclusion of Time


Baumgartner, Michael and Ruedi Epple. 2014. “A Coincidence Analysis of a Causal Chain: The Swiss Minaret Vote.” Sociological Methods and Research, 43(2), 280-312.

García-Castro, Roberto, and Miguel A. Arino. 2013. “A General Approach to Panel Data Set-Theoretic Research.” Compasss Working Paper, WP2013-76; 1–27.

Schneider, Carsten Q., and Claudius Wagemann. 2012. Set-Theoretic Methods for the Social Sciences: A Guide to Qualitative Comparative Analysis. Cambridge: Cambridge University Press, chapters 10.3

Thiem, Alrik. 2015. “Using Qualitative Comparative Analysis for Identifying Causal Chains in Configurational Data: A Methodological Commentary on Baumgartner and Epple (2014).” Sociological Methods and Research, online first. DOI: 10.1177/0049124115589032.


Theory evaluation:

Ragin, Charles C. 1987. The Comparative Method: Moving Beyond Qualitative and Quantitative Strategies, University of California Press, pp. 118-121

Schneider, Carsten Q., and Claudius Wagemann. 2012. Set-Theoretic Methods for the Social Sciences: A Guide to Qualitative Comparative Analysis. Cambridge: Cambridge University Press, chapters 11.3



Baumgartner, Michael, and Alrik Thiem. 2015. “Identifying Complex Causal Dependencies in Configurational Data with Coincidence Analysis.” The R Journal: 1–9.

Caren, Neal, and Aaron Panofsky. 2005. “TQCA. a Technique for Adding Temporality to Qualitative Comparative Analysis.” Sociological Methods & Research 34(2): 147–72.

Ragin, Charles C, and Sarah Strand. 2008. “Using Qualitative Comparative Analysis to Study Causal Order. Comment on Caren and Panofsky (2005).” Sociological Methods & Research 36(4): 431–41.

Rihoux, Benoît. 2012. “It’s About Time. Which Best Strategies to Articulate Sequence and Process with QCA?” Paper prepared for workshop nr3 on “Methodological Advances, Bridges and Limits in the Application of Qualitative Comparative Analysis”, ECPR Joint Sessions of Workshops, Antwerp, 11-14 April 2012: 1–27

Schneider, Carsten Q, and Claudius Wagemann. 2006. “Reducing Complexity in Qualitative Comparative Analysis (QCA): Remote and Proximate Factors and the Consolidation of Democracy.” European Journal of Political Research 45(5): 751–86.

Software Requirements

- R, R packages QCA, QCAGUI, SetMethods, and all their dependencies

- RStudio

Hardware Requirements

Participants are expected to bring their own laptop


Goertz, Gary, and James Mahoney. 2012. A Tale of Two Cultures: Contrasting Qualitative and Quantitative Paradigms. Princeton, N.J: Princeton University Press

Ragin, Charles C. 2008. Redesigning Social Inquiry: Fuzzy Sets and Beyond. Chicago: University of Chicago Press

Schneider, Carsten Q., and Claudius Wagemann. 2012. Set-Theoretic Methods for the Social Sciences: A Guide to Qualitative Comparative Analysis. Cambridge: Cambridge University Press

Recommended Courses to Cover Before this One

<p>Summer School</p> <ul> <li>Set-Theoretic Methods: Qualitative Comparative Analysis and Related Approaches</li> <li>Introduction to R</li> </ul>

Recommended Courses to Cover After this One

<p>Summer School</p> <ul> <li>Case Study Research &ndash; Method and Practice</li> </ul>

Additional Information


This course description may be subject to subsequent adaptations (e.g. taking into account new developments in the field, participant demands, group size, etc). Registered participants will be informed in due time.

Note from the Academic Conveners

By registering for this course, you confirm that you possess the knowledge required to follow it. The instructor will not teach these prerequisite items. If in doubt, contact the instructor before registering.