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Advanced Topics in Set-Theoretic Methods and QCA

Course Dates and Times

Monday 5 to Friday 9 March 2018
15 hours over 5 days

Carsten Q. Schneider

Central European University

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; data structures and set-theoretic methods, including temporal ordering, multi-level structures, and two-step QCA; model ambiguity; and/or multi-value QCA.


Tasks for ECTS Credits

  • Participants attending the course: 2 credits (pass/fail grade) The workload for the calculation of ECTS credits is based on the assumption that students attend classes and carry out the necessary reading and/or other work prior to, and after, classes.
  • Participants attending the course and completing one task (see below): 3 credits (to be graded)
  • Participants attending the course, and completing two tasks (see below): 4 credits (to be graded)

The task(s) to be assessed by the instructor and required to acquire credits are the following:

  1. Daily assignments
    • graded daily, without feedback, as 0 - Did not submit, 1 - Insufficient, 2 - Sufficient, 3 - Excellent.
    • These assignments will consist of performing your own data analysis in R, using the functions and concepts learned in class.
  2. Take-home paper
    • Participants will receive a published QCA study plus its data and are asked to, first, replicate and, second, expand the analysis.
    • Deadline for submitting the roughly 15 page long paper plus clean R code is three weeks after the end of the course.


Instructor Bio

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 in leading political science journals, and he is the author three books, among them Set-Theoretic Methods for the Social Sciences (Cambridge University Press, 2012).

The book Qualitative Comparative Analysis (QCA) using R: A Gentle Introduction, co-authored with Ioana-Elena Oana and Eva Thomann, appeared in 2021 with Cambridge University Press and his book Set-Theoretic Multi-Method Research: A Guide to Combining QCA and Case Studies is forthcoming with the same publisher.


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.

During day 1, we refresh our knowledge and go through the standard protocol of a QCA, using the relevant R packages. In addition, 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 2, 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. 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. In addition, we discuss the principles and computer-assisted practice of set-theoretic theory evaluation. On days 4 and 5, we address issues that arise from various forms of structures in the data. On day 4, we mainly focus on different temporal structures in the data and discuss various strategies, such as, calibration temporal QCA (tQCA), and cluster diagnostics. On day 5, we focus on causal chains detexted via Coincidence Analysis (cna), multi-level structures and also discuss an updated version of the two-step QCA approach.

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 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. 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 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.

Each course includes pre-course assignments, including readings and pre-recorded videos, as well as daily live lectures totalling at least three hours. The instructor will conduct live Q&A sessions and offer designated office hours for one-to-one consultations.

Please check your course format before registering.

Online courses

Live classes will be held daily for three hours on a video meeting platform, allowing you to interact with both the instructor and other participants in real-time. To avoid online fatigue, the course employs a pedagogy that includes small-group work, short and focused tasks, as well as troubleshooting exercises that utilise a variety of online applications to facilitate collaboration and engagement with the course content.

In-person courses

In-person courses will consist of daily three-hour classroom sessions, featuring a range of interactive in-class activities including short lectures, peer feedback, group exercises, and presentations.


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 at the time of change.

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, please contact us before registering.

Day Topic Details
1 Set-Theoretic Methods and QCA in a Nutshell; Potpourri: - Enhanced Standard Analysis - Skewed Sets - multi-value QCA

120’ seminar:

- the standard QCA protocol

- 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 standard QCA protocol in R

- implementation of Enhanced Standard Analysis and multi-value QCA

- diagnostics for skewed sets in R

2 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

3 - Robustness and sensitivity - set-theoretic theory evaluation

90’ lecture:

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

- robustness against what?

- designing meaningful robustness tests

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

90’ lab:

- applying set-theoretic robustness tests to published QCA studies

- applying Theory Evaluation to examples of published QCA studies

4 Data Structures I - the inclusion of time into set-theoretic analyses - panel data diagnostics - temporal QCA (tQCA)

90’ lecture:

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

- diagnosing clusters in the data

- simple sequences via tQCA

90’ lab:

- applying tQCA and the cluster diagnostic functions to examples of published QCA studies

5 Data Structures II - Coincidence Analysis (can) - two-step QCA updated - multi-level structures

90’ lecture:

- more complex sequences detected via cna

- the (ir)relevance of multi-level structures

- an updated version of the two-step QCA approach

90’ lab:

- applying cna to published QCA studies

- implementation of the updated two-step QCA approach

Day Readings
Day 1 Standard QCA protocol; Potpourri: Enhanced Standard Analysis / Skewed sets / mvQCA

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


QCA basics refresher:

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

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 1-7

QCA critics and rejoinder:

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

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

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

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


Cooper, Barry, and Judith Glaesser. 2016. “Qualitative Comparative Analysis, Necessary Conditions, and Limited Diversity.” Field Methods 28(3): 300–315.

Schneider, Carsten Q., and Claudius Wagemann. 2016. “Assessing ESA on What It Is Designed for: A Reply to Cooper and Glaesser.” Field Methods 28(3): 316–21.

Skewed sets:

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.

Multi-Value QCA:

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 2 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 3 Robustness and sensitivity - Theory Evaluation


Baumgartner, Michael, and Alrik Thiem. 2017. “Often Trusted But Never (Properly) Tested: Evaluating Qualitative Comparative Analysis.” Sociological Methods & Research: 1–33

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

Theory evaluation:

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

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

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.

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

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

Rohlfing, Ingo. 2016. “Why Simulations Are Appropriate for Evaluating Qualitative Comparative Analysis.” Quality & Quantity 50: 2073–2208

Sager, Fritz, and Eva Thomann. 2017. “Multiple Streams in Member State Implementation: Politics, Problem Construction and Policy Paths in Swiss Asylum Policy.” Journal of Public Policy 37(3): 287–314

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.

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

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. 2016. “Enhancing Sensitivity Diagnostics for Qualitative Comparative Analysis: A Combinatorial Approach.” Political Analysis 24(1): 104–20.

Day 4 Data structures I: - time, small sequences, and cluster diagnostics

García-Castro, Roberto, and Miguel A. Arino. 2016. “A General Approach to Panel Data Set-Theoretic Research.” Journal of Advances in Management Sciences & Information Systems 2: 63–76

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


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

Williams, Timothy, and Sergio M. Gemperle. 2016. “Sequence Will Tell! Integrating Temporality into Set-Theoretic Multi-Method Research Combining Comparative Process Tracing and Qualitative Comparative Analysis.” International Journal of Social Research Methodology 5579(March): 1–15

Day 5 Data structures II: - chains - multi-level - two-step

Baumgartner, Michael. 2013. “Detecting Causal Chains in Small-N Data.” Field Methods 25(1): 3–24

Thiem, Alrik. 2016. “Analyzing Multilevel Data with QCA: Yet Another Straightforward Procedure.” Quality and Quantity 50(1): 121–28



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

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.

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.


Mannewitz, Tom. 2011. Two-Level Theories in QCA: A Discussion of Schneider and Wagemann’s Two-Step Approach

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.


Denk, Thomas. 2010. “Comparative Multilevel Analysis: Proposal for a Methodology.” International Journal of Social Research Methodology 13(1): 29–39

Denk, Thomas, and Sarah Lehtinen. 2014. “Contextual Analyses with QCA-Methods.” Quality and Quantity 48(6): 3475–87

Rohlfing, Ingo. 2011. “Analyzing Multilevel Data With QCA – A Straightforward Procedure.” International Journal of Social Research Methodology 49(0): 1–23

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

Summer School

  • Set-Theoretic Methods: Qualitative Comparative Analysis and Related Approaches
  • Introduction to R

Winter School

  • Comparative Research Designs

Recommended Courses to Cover After this One

Summer School

  • Case Study Research – Method and Practice
  • Machine Learning

Winter School

  • Advanced Multi-Method Research