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Advanced Topics in Set-Theoretic Methods and QCA

Course Dates and Times

Monday 25 February – Friday 1 March, 14:00 – 17:30 (finishing slightly earlier on Friday)
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 specific to QCA.

Although much effort has been put into developing standards of good practice, 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 discuss the issues raised by theses critiques, and go beyond them to explore the hitherto under-used potentials of set-theoretic methods.

We will try and address all the following topics but, depending on participants' needs and interests, we can put more emphasis on some:

  • set-theoretic multi-method research
  • robustness and sensitivity
  • set-theoretic theory evaluation
  • enhanced Standard Analysis
  • data structures and set-theoretic methods, including temporal ordering and two-step QCA
  • model ambiguity
  • multi-value QCA.

Tasks for ECTS credits

2 credits (pass/fail grade) Attend at least 90% of the course hours, participate fully in in-class activities, and carry out the necessary reading and/or other work prior to, and after, classes.

3 credits (to be graded) As above, plus complete daily assignments which involve performing data analysis in R, using the functions and concepts learned in class.

4 credits (to be graded) As above, plus complete a take-home paper of roughly 15 pages. You will receive a published QCA study plus its data. You must, first, replicate and, second, expand the analysis. Deadline for submission of the paper, along with 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.


If you have good knowledge of all the elements listed under 'Prerequisite knowledge', above, this course will deepen your understanding of the potentials and pitfalls of set-theoretic methods. The skills you gain will enable you to be more critical and assertive if and when you choose or reject set-theoretic methods as the most appropriate research method for your research project.

By the end of this course, you will be able to produce QCA studies of a quality and level of sophistication beyond the current mainstream and thus yield substantive results that are more compelling for you and for your (critical) audience.

Much of the course explores the boundaries of the still-relatively-young family of set-theoretic methods. Unavoidably, some of our debates will remain inconclusive. You won't always get ready-made, foolproof answers and procedures for all the issues you will face when trying to implement a high-quality QCA. Rather, this course invites you to think critically about set-theoretic methods, and, by extension, also about other data analysis techniques you will have to choose when doing empirical comparative research. 

Day 1
We refresh our knowledge and go through the standard protocol of a QCA, using the relevant R packages. We cover a set of relatively unrelated, yet interesting and important issues. We focus on one or two of the following topics in more detail, depending on participants' interest:

  • Enhanced Standard Analysis
  • skewed sets and their analytic consequences
  • multi-value QCA.

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. We discuss the principles and computer-assisted practice of set-theoretic theory evaluation.

Day 3
We engage with the notion of robustness in set-theoretic methods and try to systematise the debate by specifying the analytic decisions against which QCA results should be expected to be robust. Along these lines, we aim to formulate criteria for meaningful robustness tests and, based on these criteria, to evaluate existing, simulation-based robustness tests. (On days 4 and 5, we address issues that arise from various forms of structures in the data.)

Day 4
We focus on different temporal structures in the data and discuss strategies such as calibration, temporal QCA (tQCA), and cluster diagnostics.

Day 5
We focus on causal chains detected via Coincidence Analysis (cna) and discuss an updated version of the two-step QCA approach.

This is an advanced course. Don't expect a general introduction to the basics of set-theoretic methods and QCA, or an introduction to the basics of the R software environment.

You should have a firm command of basic formal logic, Boolean algebra, and set-theory.

You must be familiar with the basic protocol of Qualitative Comparative Analysis (QCA), including:

  • the difference between sets and variables
  • the notion of set calibration
  • the meaning of set relations (sufficiency, necessity, INUS, SUIN)
  • the construction and logical minimisation 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.

Check whether you are in command of all the questions addressed in Schneider/Wagemann (2012) Set-Theoretic Methods for the Social Sciences, chapters 1–7.

You should be familiar with the basics of the R software environment because we will use R packages relevant for performing set-theoretic analyses.

If you attended the two-week course on Set-Theoretic Methods and QCA at the ECPR Summer School, you are 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
Day 1 Set-Theoretic Methods and QCA in a Nutshell; Potpourri - Enhanced Standard Analysis - Skewed Sets - multi-value QCA

Two-hour 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

One-hour lab

  • implementation of standard QCA protocol in R
  • implementation of Enhanced Standard Analysis and multi-value QCA
  • diagnostics for skewed sets in R
Day 2 Set-theoretic multi-method research Set-theoretic theory evaluation

90-minute lecture

  • how to select cases after a QCA
  • how to make use of the insights gained from these (comparative) within-case analyses
  • how to evaluate theories (rather than testing hypotheses) with set-theoretic methods

90-minute lab

  • applying the post-QCA case selection principles to examples of published QCA studies
  • applying Theory Evaluation to examples of published QCA studies
Day 3 Robustness and sensitivity

90-minute lecture

  • what can and cannot be the meaning of robust results in set-theoretic methods?
  • robustness against what?
  • designing meaningful robustness tests

90-minute lab

  • applying set-theoretic robustness tests to published QCA studies
Day 4 Data Structures I - the inclusion of time into set-theoretic analyses - panel data diagnostics - temporal QCA (tQCA)

90-minute lecture

  • the intrinsic challenges of including notions of time as causally relevant
  • diagnosing clusters in the data
  • simple sequences via tQCA

90-minute lab

  • applying tQCA and the cluster diagnostic functions to examples of published QCA studies
Day 5 Data Structures II - Coincidence Analysis (cna) - two-step QCA updated

90-minute lecture

  • more complex sequences detected via cna
  • an updated version of the two-step QCA approach

90-minute 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

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


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), 703741

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. Benoît 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.  (accessed 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. (accessed 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. (accessed May 3, 2011)

Day 2 - SMMR - Theory Evaluation

Set-Theoretic Multi-Method Research (SMMR):

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

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


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, Benoît, 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.

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

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


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


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.

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

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 - two-step

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

Schneider, Carsten Q. 2018. 'Two-Step QCA Revisited: The Necessity of Context Conditions.' manuscript.



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.

Software Requirements

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


Hardware Requirements

Bring your 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

Machine Learning
Advanced Multi-Method Research