Quality & Quantity

, Volume 49, Issue 2, pp 657–674 | Cite as

Parameters of fit and intermediate solutions in multi-value Qualitative Comparative Analysis

  • Alrik Thiem


Multi-value Qualitative Comparative Analysis (mvQCA) is a variant of QCA that continues to exist under the shadow of crisp and fuzzy-set QCA. The lack of support for parameters of fit and intermediate solutions has contributed to this undeserved status. This article introduces two innovations that put mvQCA on a par with its two sister variants. First, consistency and coverage as the two most important parameters of fit are generalized. Second, the concepts of easy and difficult counterfactuals for deriving intermediate solutions are imported. I demonstrate how to leverage these features in the QCA software package for the R environment. For researchers who do not use QCA, I explain how to exploit Veitch–Karnaugh maps instead for solving set-theoretic minimization problems of low to moderate complexity.


Configurational comparative methods Consistency Coverage csQCA fsQCA mvQCA QCA Qualitative Comparative Analysis 



I am grateful to Michael Baumgartner, Tim Haesebrouck and the two anonymous reviewers for very helpful comments and suggestions.


  1. Ackrén, M., Olausson, P.M.: Condition(s) for island autonomy. Int. J. Minor. Gr. Rights 15(2–3), 227–258 (2008)CrossRefGoogle Scholar
  2. Balthasar, A.: The effects of institutional design on the utilization of evaluation. Evaluation 12(3), 353–371 (2006)CrossRefGoogle Scholar
  3. Baumgartner, M.: Inferring causal complexity. Sociol. Methods Res. 38(1), 71–101 (2009)CrossRefGoogle Scholar
  4. Berg-Schlosser, D.: Determinants of democratic successes and failures in Africa. Eur. J. Polit. Res. 47(3), 269–306 (2008)CrossRefGoogle Scholar
  5. Cronqvist, L.: Tosmana: Tool for small-n analysis, version [computer programme]. University of Trier, Trier, (2011)Google Scholar
  6. Cronqvist, L., Berg-Schlosser, D.: Multi-value QCA (mvQCA). In: Rihoux, B., Ragin, C.C. (eds.) Configurational Comparative Methods: Qualitative Comparative Analysis (QCA) and Related Techniques, pp. 69–86. Sage, London (2009)CrossRefGoogle Scholar
  7. Delhi, V.S.K., Mahalingam, A., Palukuri, S.: Governance issues in BOT based PPP infrastructure projects in India. Built Environ. Proj. Asset. Manag. 2(2), 234–249 (2012)CrossRefGoogle Scholar
  8. Denk, T.: Comparative multilevel analysis: proposal for a methodology. Int. J. Soc. Res. Method. 13(1), 29–39 (2010)CrossRefGoogle Scholar
  9. Dubrova, E.: Multiple-valued logic synthesis and optimization. In: Hassoun, S., Sasao, T. (eds.) Logic Synthesis and Verification, pp. 89–114. Springer Science+Business Media, New York (2002)CrossRefGoogle Scholar
  10. Eliason, S.R., Stryker, R.: Goodness-of-fit tests and descriptive measures in fuzzy-set analysis. Sociol. Methods Res. 38(1), 102–146 (2009)CrossRefGoogle Scholar
  11. Gross, M., Garvin, M.: Structuring PPP toll-road contracts to achieve public pricing objectives. Eng. Proj. Organ. J. 1(2), 143–156 (2011)CrossRefGoogle Scholar
  12. Hartmann, C., Kemmerzell, J.: Understanding variations in party bans in Africa. Democratization 17(4), 642–665 (2010)CrossRefGoogle Scholar
  13. Herrmann, A.M., Cronqvist, L.: When dichotomisation becomes a problem for the analysis of middle-sized datasets. Int. J. Soc. Res. Method. 12(1), 33–50 (2009)CrossRefGoogle Scholar
  14. Hohn, F.E.: Applied Boolean Algebra: An Elementary Introduction, 2nd edn. Macmillan, New York (1966)Google Scholar
  15. Huntjens, P., Pahl-Wostl, C., Rihoux, B., Schlüter, M., Flachner, Z., Neto, S., Koskova, R., Dickens, C.: Adaptive water management and policy learning in a changing climate: a formal comparative analysis of eight water management regimes in Europe, Africa and Asia. Environ. Policy Gov. 21(3), 145–163 (2011)CrossRefGoogle Scholar
  16. Jordan, E., Gross, M.E., Javernick-Will, A.N., Garvin, M.J.: Use and misuse of Qualitative Comparative Analysis. Constr. Manag. Econ. 29(11), 1159–1173 (2011)CrossRefGoogle Scholar
  17. Klüver, H.: Europeanization of lobbying activities: when national interest groups spill over to the European level. J. Eur. Integr. 32(2), 175–191 (2010)Google Scholar
  18. Mannewitz, T.: Alte Bekannte im neuen System: Gründe für die Aufstiege und Niedergänge der mittelosteuropäischen Postkommunisten seit 1990. Zeitschrift für Vergleichende Politikwissenschaft 4(2), 261–293 (2010)Google Scholar
  19. McCluskey, E.J.: Introduction to the Theory of Switching Circuits. Princeton University Press, Princeton (1965)Google Scholar
  20. R Development Core Team.: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2013)Google Scholar
  21. Ragin, C.C.: The Comparative Method: Moving Beyond Qualitative and Quantitative Strategies. University of California Press, Berkeley (1987)Google Scholar
  22. Ragin, C.C.: Fuzzy-Set Social Science. University of Chicago Press, Chicago (2000)Google Scholar
  23. Ragin, C.C.: Set relations in social research: evaluating their consistency and coverage. Polit. Anal. 14(3), 291–310 (2006)CrossRefGoogle Scholar
  24. Ragin, C.C.: Redesigning Social Inquiry: Fuzzy Sets and Beyond. University of Chicago Press, Chicago (2008)CrossRefGoogle Scholar
  25. Ragin, C.C., Davey, S.: fs/QCA: Fuzzy-set/Qualitative Comparative Analysis, version 2.5 [computer programme]. Department of Sociology, University of Arizona, Tucson, AZ (2009)Google Scholar
  26. Ragin, C.C., Sonnett, J.: Between complexity and parsimony: limited diversity, counterfactual cases and comparative analysis. In: Kropp, S., Minkenberg, M. (eds.) Vergleichen in der Politikwissenschaft, pp. 180–197. VS Verlag für Sozialwissenschaften, Wiesbaden (2005)CrossRefGoogle Scholar
  27. Rihoux, B.: Qualitative Comparative Analysis (QCA) and related systematic comparative methods: recent advances and remaining challenges for social science research. Int. Sociol. 21(5), 679–706 (2006)CrossRefGoogle Scholar
  28. Rihoux, B., Álamos Concha, P.: From niche to mainstream method? A comprehensive mapping of QCA applications in journal articles from 1984 to 2011. Polit. Res. Quart. 66(1), 175–184 (2013)CrossRefGoogle Scholar
  29. Rohlfing, I.: Analyzing multilevel data with QCA: a straightforward procedure. Int. J. Soc. Res. Method. 15(6), 497–506 (2012)CrossRefGoogle Scholar
  30. Sager, F., Andereggen, C.: Dealing with complex causality in realist synthesis: the promise of Qualitative Comparative Analysis. Am. J. Eval. 33(1), 60–78 (2012)CrossRefGoogle Scholar
  31. Schneider, C.Q., Wagemann, C.: Set-theoretic Methods for the Social Sciences: A Guide to Qualitative Comparative Analysis (QCA). Cambridge University Press, Cambridge (2012)CrossRefGoogle Scholar
  32. Schneider, C.Q., Wagemann, C.: Doing justice to logical remainders in QCA: moving beyond the standard analysis. Polit. Res. Q. 66(1), 211–220 (2013)Google Scholar
  33. Smithson, M.: Fuzzy set inclusion: linking fuzzy set methods with mainstream techniques. Sociol. Methods Res. 33(4), 431–461 (2005)CrossRefGoogle Scholar
  34. Smithson, M., Verkuilen, J.: Fuzzy Set Theory: Applications in the Social Sciences. SAGE, London (2006)Google Scholar
  35. Thiem, A.: Clearly crisp, and not fuzzy: a reassessment of the (putative) pitfalls of multi-value QCA. Field Methods 25(2), 197–207 (2013a)CrossRefGoogle Scholar
  36. Thiem, A.: Unifying configurational comparative methods: Generalized-set Qualitative Comparative Analysis. Sociol. Methods Res. (2013b). doi: 10.1177/0049124113500,481
  37. Thiem, A., Duşa, A.: Boolean minimization in social science research: a review of current software for Qualitative Comparative Analysis (QCA). Soc. Sci. Comput. Rev. 31(4), 505–521 (2013a)CrossRefGoogle Scholar
  38. Thiem, A., Duşa, A.: QCA: a package for Qualitative Comparative Analysis. R J. 5(1), 87–97 (2013b)Google Scholar
  39. Thiem, A., Duşa, A.: Qualitative Comparative Analysis with R: A User’s Guide. Springer, New York (2013c)CrossRefGoogle Scholar
  40. Thiem A, Duşa A.: When more than time is of the essence: Enhancing the minimization of Boolean output functions with eQMC. J. Math. Sociol. (forthcoming)Google Scholar
  41. Vink, M.P., van Vliet, O: Not quite crisp, not yet fuzzy? Assessing the potentials and pitfalls of multi-value QCA. Field Methods 21(3), 265–289 (2009)Google Scholar
  42. Vink, M.P., van Vliet, O: Potentials and pitfalls of multi-value QCA: response to Thiem. Field Methods 25(2), 208–213 (2013)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of GenevaGenevaSwitzerland

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