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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.

Ioana-Elena Oana

Central European University

Nena I.E. Oana is a Research Fellow at the European University Institute, Florence, where she is currently working on the POLCON project, directed by Hanspeter Kriesi. She finished her PhD in Comparative Politics at Central European University, Budapest, on policy responsiveness to collective mobilisation.

She is the main developer of the R package SetMethods and has extensive experience in teaching applied QCA using R, having assisted and taught for the ECPR Summer and Winter School QCA courses for the past six years.

Besides research methodology, Nena's main research interests include political participation and representation, political behaviour, and political psychology.



Course Dates and Times

Monday 17 – Friday 21February 2019, 14:00 – 17:30 (finishing slightly earlier on Friday)
15 hours over five days

Prerequisite Knowledge

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.

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 specific to QCA.

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.

Long Course Outline

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: Refresher Potpourri
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: SMMRI I
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: SMMR II, plus Theory Evaluation

Day 4: Sensitivity Analysis and Data Structures I
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 practice recent software implementations for robustness tests.  

Day 5: Sensitivity Analysis and Data Structures II
As part of the sensitivity analysis, we focus on different structures in the data. We discuss various strategies for detecting such structures via calibration, temporal QCA (tQCA), cluster diagnostics, Coincidence Analysis (cna), and the 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.

Day Topic Details
Day 1 Set-Theoretic Methods and QCA in a nutshell; Potpourri - Enhanced Standard Analysis - Skewed Sets - Multi-Value QCA

120-minute 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-minute lab session

  • 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

90-minute lecture

  • how to select cases after a QCA
  • how to make use of the insights gained from these (comparative) within-case analyses

90-minute lab session

  • applying the post-QCA case selection principles to examples of published QCA studies
Day 3 Set-theoretic multi-method research and Set-theoretic theory evaluation

90-minute lecture

  • More on selection cases for within-case analysis based on a QCA result
  • How to evaluate theories (rather than testing hypotheses) with set-theoretic methods 
  • What can and cannot be the meaning of robust results in set-theoretic methods?
  • Robustness against what?
  • Designing meaningful robustness tests

90-minute lab session

  • Applying the post-QCA case selection principles to examples of published QCA studies
  • Applying Theory Evaluation to examples of published QCA studies
  • Applying set-theoretic robustness tests to published QCA studies
Day 4 Sensitivity and Data Structures I - robustness principles and practices - the inclusionof time into set-theoretic analyses - panel data diagnostics - temporal QCA (tQCA)

90-minute lecture

  • How to see robust results in QCA
  • The intrinsic challenges of including notions of time as causally relevant
  • Diagnosing clusters in the data
  • Simple sequences via tQCA

90-minute lab session

  • Applying robustness functions to published QCA studies
  • Applying tQCA and the cluster diagnostic functions to examples of published QCA studies
Day 5 Sensitivity and 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 session

  • Applying cna to publshed 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 Studie

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 Assessments 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. pp, 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 I

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

Schneider, Carsten Q., and Ingo Rohlfing. Forthcoming
Corridors and Conjunctions for Case Selection in Set-theoretic Multi-Method Research
Swiss Political Science Review


Mikkelsen, Kim Sass
Fuzzy-Set Case Studies
Sociological Methods and Research. 2015, online first

Mikkelsen, Kim Sass
Negative Case Selection: Justifications and Consequences for Set-Theoretic MMR
Sociological Methods and Research. online first

Ragin, Charles C. and Garrett Andrew Schneider. 2011
Case-Oriented Theory Building and Theory Testing, pp. 150–166
In Sage Handbook of Innovations in Social Research Methods, ed. Malcolm; Vogt Williams W. Paul
London: Sage

Rihoux, Benoît, and Bojana Lobe. 2009
The Case for Qualitative Comparative Analysis (QCA): Adding Leverage for Thick Cross-Case Comparison, pp. 222–242
In Sage Handbook Of Case-Based Methods, eds. David Byrne and Charles C Ragin
London: Sage

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

Rohlfing, Ingo, and Carsten Q. Schneider. 2013
Combining QCA With Process Tracing in Analyses of Necessity
Political Research Quarterly 66(1): 220–235

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): 526–568

Day 3 – SMMR II – Theory Evaluation

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

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

Oana, Nena, and Carsten Q. Schneider
Case orientation and parameters of _t orientation. A proposal for systematized robustness tests in QCA using R

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


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

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

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

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

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

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

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

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

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

Thiem, Alrik, Reto Spöhel, and Adrian Duşa. 2016
Enhancing Sensitivity Diagnostics for Qualitative Comparative Analysis: A Combinatorial Approach
Political Analysis 24(1): 104–20


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


Haesebrouck, T. (2019)
An alternative update of the two-step QCA procedure
Quality & Quantity

Schneider, C. Q. (2019)
Two-Step QCA Revisited: The Necessity of Context Conditions
Quality & Quantity, 53(3), 1109–1126



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


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

<p><strong>Summer School</strong></p> <p>Set-Theoretic Methods: Qualitative Comparative Analysis and Related Approaches<br /> Introduction to R</p> <p><strong>Winter School</strong></p> <p>Comparative Research Designs</p>

Recommended Courses to Cover After this One

<p><strong>Summer School</strong></p> <p>Case Study Research &ndash; Method and Practice<br /> Machine Learning</p> <p><strong>Winter School</strong></p> <p>Machine Learning<br /> Advanced Multi-Method Research</p>

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.