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Aligica, Paul, and Anthony Evans. 2009. "Thought Experiments, Counterfactuals and Comparative Analysis." Review of Austrian Economics 22 (3):225-39.

Abstract: This article discusses the problem of "thought experiments" in Austrian economics and takes as a starting point Lawrence Moss' argument on the divide between the older Austrian economists - for whom thought experiments were crucial - and the new generation that, in Moss' view, has "abandoned" such methods. The article is an attempt not only to bridge this alleged divide but also to contribute to the development of the Austrian methodology. It is argued that what may be perceived as "abandonment" bolsters rather than precludes the role of thought experiments in the Austrian paradigm. The article identifies an entire family of comparative and counterfactual analysis research strategies available to the Austrians, all enjoying a solid epistemological and methodological grounding. The "comparative-counterfactual analytics" pattern threads together the conjectural histories, spontaneous orders and empirical case studies of the contemporary Austrians, with the classic tradition of older works. Consequently, the recent evolution of Austrian scholarship should not be seen as an aberration or abandonment but as a deliberate, natural and commendable development.

Amenta, Edwin, and Jane D. Poulsen. 1994. "Where to Begin: A Survey of Five Approaches to Selecting Independent Variables for Qualitative Comparative Analysis." Sociological Methods & Research 23 (1):22-53.

Abstract: The problem of selecting independent variables for qualitiative comparative analysis (QCA) is addressed. This is a different problem for QCA than for inferential statistical methods, for both technical and epistemological reasons. Technically, QCA can manipulate only a few variables at one time. Epistemologically, QCA expects causation to work in a combinatorial fashion. The authors isolate and reject four ways of choosing independent variables for QCA and advocate a fifth method, the conjunctural theories approach, which is more compatible with the characteristics of QCA. Their decision is supported by way of discussion and an empirical analysis based on theories of the welfare state and U.S. social spending in the Great Depression.

Anckar, Carsten. 2008. "On the Applicability of the Most Similar Systems Design and the Most Different Systems Design in Comparative Research." International Journal of Social Research Methodology 11 (5):389-401.

Abstract: In comparative political research we distinguish between the 'Most Similar Systems Design' (MSSD) and the 'Most Different Systems Design' (MDSD). In the present work, I argue that the applicability of the two research strategies is determined by the features of the research task. Three essential distinctions are important when assessing the applicability of the MSSD and the MDSD: (1) whether or not variable interactions are studied at a systemic level or at a sub-systemic level; (2) whether we use a deductive or inductive research strategy and (3) whether or not we operate with a constant or varying dependent variable. The article argues that the combination of these dimensions is essential for how the MSSD and the MDSD can and should be used in comparative research.

Aus, Jonathan. 2009. "Conjunctural Causation in Comparative Case-Oriented Research." Quality & Quantity 43 (2):173-83.

Abstract: This article highlights one of the major benefits of qualitative comparative methodology as applied within a "small-N" research design, namely its potential use for specifying the scope conditions of (theoretically competing) causal mechanisms. It is argued that the identification of set-theoretic relationships, multiple paths, and analytic efforts in typological mapping can make valuable contributions to the elaboration and further development of middle-range theory.

Basurto, Xavier, and Johanna Speer. 2012. "Structuring the Calibration of Qualitative Data as Sets for Qualitative Comparative Analysis (QCA)." Field Methods 24 (2):155-74.

Abstract: Most studies that apply qualitative comparative analysis (QCA) rely on macro-level data, but an increasing number of studies focus on units of analysis at the micro or meso level (i.e., households, firms, protected areas, communities, or local governments). For such studies, qualitative interview data are often the primary source of information. Yet, so far no procedure is available describing how to calibrate qualitative data as fuzzy sets. The authors propose a technique to do so and illustrate it using examples from a study of Guatemalan local governments. By spelling out the details of this important analytic step, the authors aim at contributing to the growing literature on best practice in QCA.

Baumgartner, Michael. 2009. "Inferring Causal Complexity." Sociological Methods & Research 38 (1):71-101.

Abstract: In The Comparative Method, Ragin (1987) outlined a procedure of Boolean causal reasoning operating on pure coincidence data that has since become widely known as qualitative comparative analysis (QCA) among social scientists. QCA - including its recent forms as presented in Ragin (2000, 2008) - is designed to analyze causal structures featuring no more than one effect and a possibly complex configuration of mutually independent direct causes of that effect. This article presents a procedure of causal reasoning that operates on the same type of empirical data as QCA and that implements Boolean techniques related to the ones resorted to by QCA. Yet in contrast to QCA, the procedure introduced here successfully identifies structures involving both multiple effects and mutually dependent causes. In this sense, this article generalizes QCA.
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Baumgartner, Michael. 2013. "Detecting Causal Chains in Small-n Data." Field Methods 25 (1):3-24.

Abstract: The first part of this article shows that qualitative comparative analysis (QCA) - also in its most recent form as in Ragin (2008) - does not correctly analyze data generated by causal chains. The incorrect modeling of data originating from chains essentially stems from QCA's reliance on Quine-McCluskey optimization to eliminate redundancies from sufficient and necessary conditions. Baumgartner (2009a, 2009b) has introduced a Boolean methodology, termed coincidence analysis (CNA), which is related to QCA, yet, contrary to the latter, does not eliminate redundancies by means of Quine-McCluskey optimization. The second part of the article applies CNA to chain-generated data. It turns out that CNA successfully detects causal chains in small-n data.

Baumgartner, Michael. 2015. "Parsimony and Causality." Quality & Quantity 49 (2):839-56.

Abstract: This paper takes issue with the current tendency in the literature on Qualitative Comparative Analysis (QCA) to settle for so-called intermediate solution formulas, in which parsimony is not maximized. I showthat there is a tight conceptual connection between parsimony and causality: onlymaximally parsimonious solution formulas reflect causal structures. However, in order to maximize parsimony, QCA - due to its reliance on Quine-McCluskey optimization (Q-M) - is often forced to introduce untenable simplifying assumptions. The paper ends by demonstrating that there is an alternative Boolean method for causal data analysis, viz. Coincidence Analysis (CNA), that replaces Q-M by a different optimization algorithm and, thereby, succeeds in consistently maximizing parsimony without reliance on untenable assumptions.

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

Abstract: This article applies coincidence analysis (CNA), a Boolean method of causal analysis presented in Baumgartner (2009a), to configurational data on the Swiss minaret vote of 2009. CNA is related to qualitative comparative analysis (QCA) (Ragin 2008), but contrary to the latter does not minimize sufficient and necessary conditions by means of Quine-McCluskey optimization, but based on its own custom built optimization algorithm. The latter greatly facilitates the analysis of data featuring chain-like causal dependencies among the conditions of an ultimate outcome - as can be found in the data on the Swiss minaret vote. Apart from providing a model of the causal structure behind the Swiss minaret vote, we show that a CNA of that data is preferable over a QCA.
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Baumgartner, Michael, and Alrik Thiem. 2015. "Identifying Complex Causal Dependencies in Configurational Data with Coincidence Analysis." The R Journal 7 (1):176-84.

Abstract: We present cna, a package for performing Coincidence Analysis (CNA). CNA is a configurational comparative method for the identification of complex causal dependencies - in particular, causal chains and common cause structures - in configurational data. After a brief introduction to the method's theoretical background and main algorithmic ideas, we demonstrate the use of the package by means of an artificial and a real-life data set. Moreover, we outline planned enhancements of the package that will further increase its applicability.

Bennink, Margot, Guy Moors, and John Gelissen. 2013. "Exploring Response Differences between Face-to-Face and Web Surveys: A Qualitative Comparative Analysis of the Dutch European Values Survey 2008." Field Methods 25 (4):319-38.

Abstract: Can existing longitudinal surveys profit from the (financial) advantages of web surveying by switching survey mode from face-to-face interviews to web surveys? Before such a radical change in data collection procedure can be undertaken, it needs to be established that mode effects cannot confound the responses to the survey items. To this end, the responses of the Dutch European Values Study of 2008 were compared to the responses of a time parallel web survey. The responses on 163 of the 256 items differed significantly across modes. To explain these response differences between modes, an exploratory crisp set qualitative comparative analysis approach was used. Five sufficient conditions - combinations of survey mode characteristics - but no necessary conditions for response differences between survey modes were found. Two survey characteristics were neither necessary nor sufficient to produce the outcome. Results suggest that switching modes may affect comparability between waves in a longitudinal survey.

Berg-Schlosser, Dirk, Gisèle de Meur, Benoît Rihoux, and Charles C. Ragin. 2009. "Qualitative Comparative Analysis (QCA) as an Approach." In Configurational Comparative Methods: Qualitative Comparative Analysis (QCA) and Related Techniques, ed. B. Rihoux and C. C. Ragin. London: Sage Publications. pp. 1-18.

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Berg-Schlosser, Dirk, and Lasse Cronqvist. 2005. "Macro-Quantitative vs. Macro-Qualitative Methods in the Social Sciences - An Example from Empirical Democratic Theory Employing New Software." Historical Social Research 30 (4):154-75.

Abstract: There are some new attempts to bridge the divide between quantitative and qualitative methods in the social sciences (see also BERG-SCHLOSSER & QUENTER 1996). This paper explicitly illustrates and tests some of these methods like regression, cluster, or discriminant analysis, on the one hand, and more recent case- and diversity-oriented methods like QCA, Multi-Value QCA (MVQCA), and Fuzzy-Set QCA (fs/QCA) on the other. This is done by using data to test Lipset's theory of socio-economic "requisites" of democracy on the basis of 18 cases in Europe in the interwar period. In this way, the specific strengths and weaknesses of the respective methods are demonstrated.

Bojadziev, George, and Maria Bojadziev. 2007. Fuzzy Logic for Business, Finance, and Management. 2nd ed. New Jersey: World Scientific.

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Bol, Damien, and Francesca Luppi. 2013. "Confronting Theories Based on Necessary Relations: Making the Best of QCA Possibilities." Political Research Quarterly 66 (1):205-10.

Abstract: Current standard practices put sufficiency at the core of Qualitative Comparative Analysis (QCA), while the analysis of necessity is limited to the test for necessary conditions. Here, we argue that the possibilities of QCA in the latter domain are much greater. In particular, it can be used to empirically confront theories centered on necessary relations and that involved various conditions. A new operation, labeled the "systematic necessity assessment," is therefore introduced. To show its added value, a published QCA study that confronts theories centered on necessary relations but using the regular minimization is replicated.

Braumoeller, Bear F. 2015. "Guarding Against False Positives in Qualitative Comparative Analysis." Political Analysis 23 (4):471-87.

Abstract: The various methodological techniques that fall under the umbrella description of qualitative comparative analysis (QCA) are increasingly popular for modeling causal complexity and necessary or sufficient conditions in medium-N settings. Because QCA methods are not designed as statistical techniques, however, there is no way to assess the probability that the patterns they uncover are the result of chance. Moreover, the implications of the multiple hypothesis tests inherent in these techniques for the false positive rate of the results are not widely understood. This article fills both gaps by tailoring a simple permutation test to the needs of QCA users and adjusting the Type I error rate of the test to take into account the multiple hypothesis tests inherent in QCA. An empirical application - a reexamination of a study of protest-movement success in the Arab Spring - highlights the need for such a test by showing that even very strong QCA results may plausibly be the result of chance.

Braumoeller, Bear F., and Gary Goertz. 2000. "The Methodology of Necessary Conditions." American Journal of Political Science 44 (4):844-58.

Abstract: Necessary conditions provide an interesting example of a concept that everyone knows, that many people use, and yet for which no explicit methodology exists. The gap between theory and empirical testing in political science is rarely as wide as it is in the case of necessary conditions. Political science is rich in theories and hypotheses that imply necessity, but adequate empirical tests are lacking. As the concept of a necessary condition is a useful one for social scientists, methodological tools for the evaluation of necessary condition hypotheses must be developed. This constitutes our purpose. We describe appropriate procedures for the two key aspects of the empirical evaluation of necessary condition hypotheses: determining (1) whether X is a necessary condition for Y and, if so, (2) whether X is trivially necessary.

Breiger, Ronald L., Eric Schoon, David Melamed, Victor Asal, and R. Karl Rethemeyer. 2014. "Comparative Configurational Analysis as a Two-Mode Network Problem: A Study of Terrorist Group Engagement in the Drug Trade." Social Networks 36 (0):23-39.

Abstract: We generalize a form of two-mode network analysis to make it applicable to a cases-by-variables data format, and apply our approach for the study of terrorist group engagement in the drug trade, emphasizing the implications of our approach for policy in a study of 395 terrorist organizations. Based on the organizations' levels of resources, network connectivity to other groups, ideological emphasis, and participation in multiple illicit economies, we identify several distinctive configurations of factors that lead to multiple types of drug activity. We also demonstrate a technique for assessing sampling variability in configurational models.

Buche, Jonas, and Markus B. Siewert. 2015. "Qualitative Comparative Analysis (QCA) in der Soziologie - Perspektiven, Potentiale und Anwendungsbereiche." Zeitschrift für Soziologie 44 (6):386-406.

Abstract: Qualitative Comparative Analysis (QCA) wurde von dem Soziologen Charles C. Ragin als Verbindung von fallorientierten, konfigurativen Ansätzen und mengentheoretischem Denken präsentiert. Mittlerweile hat sich QCA - von Ragin und anderen weiterentwickelt - als mengentheoretischer Ansatz zur Untersuchung sozialer Phänomene im sozialwissenschaftlichen Methodenkanon etabliert. Der vorliegende Beitrag zielt darauf ab, Forschungsperspektiven und -potentiale von QCA als (relativ) junge Methode für soziologische Fragestellungen aufzuzeigen. Auf der Grundlage einer Rundschau von 77 publizierten, soziologischen Zeitschriftenartikeln wird einerseits ein breiter Überblick über Anwendungsbereiche, aktuelle Trends und Entwicklungen von QCA in der Soziologie gegeben. Andererseits werden am Beispiel der publizierten Studien die einzelnen Analyseschritte einer QCA besprochen und dabei gängige Fallstricke aufgezeigt, wobei sowohl practiced practices als auch best practices in ihrer Anwendung herausgearbeitet werden.

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

Abstract: As originally developed by Charles Ragin in The Comparative Method (1987), qualitative comparative analysis (QCA) has been used extensively by comparative and historical sociologists as an effective tool for analyzing data sets of medium-N populations. Like many other methods, however, QCA is atemporal and obscures the sequential nature of paths of causation. QCA ignores the order of events by treating combinations of attributes as though they occur simultaneously rather than as unfolding over time. While preserving the essential strengths of QCA, the authors present a modification that is capable of capturing the temporal nature of causal interactions. This modification involves a hybrid of Boolean algebra and sequence analysis to create a parsimonious set of solutions. This technique is referred to as temporal qualitative comparative analysis, or TQCA.

Cioffi-Revilla, Claudio A. 1981. "Fuzzy Sets and Models of International Relations." American Journal of Political Science 25 (1):129-59.

Abstract: Ambiguity and uncertainty are inherent in many historical alliances, decisions, and perceptions of International Relations (IR). Random factors, unreliable quantitative data, and inaccurate measurement do not cause all this qualitative fuzziness. Existing methods of statistical analysis and classical mathematical structures are ill equipped for modeling and analyzing this empirical real-world fuzziness. Zadeh's fuzzy sets theory provides a systematic framework for modeling qualitative fuzziness in foreign policy decision-making and international systems analysis. Basic fuzzy operations, linguistic variables, and fuzzy logic (viz., inference and algorithms) are explained informally with IR examples. Implications for theory building and computer simulation are discussed.

Clark, William Roberts, Michael J. Gilligan, and Matt Golder. 2006. "A Simple Multivariate Test for Asymmetric Hypotheses." Political Analysis 14 (3):311-31.

Abstract: In this paper, we argue that claims of necessity and sufficiency involve a type of asymmetric causal claim that is useful in many social scientific contexts. Contrary to some qualitative researchers, we maintain that there is nothing about such asymmetries that should lead scholars to depart from standard social science practice. We take as given that deterministic and monocausal tests are inappropriate in the social world and demonstrate that standard multiplicative interaction models are up to the task of handling asymmetric causal claims in a multivariate, probabilistic manner. We illustrate our argument with examples from the empirical literature linking electoral institutions and party system size.

Collier, David. 2014. "The Set-Theoretic Comparative Method: Critical Assessment and the Search for Alternatives." Qualitative & Multi-Method Research 14 (1):2-9.

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Cooper, Barry, and Judith Glaesser. 2010. "Contrasting Variable-Analytic and Case-Based Approaches to the Analysis of Survey Datasets: Exploring how Achievement Varies by Ability across Configurations of Social Class and Sex." Methodological Innovations Online 5 (1):4-23.

Abstract: The context for this paper is the ongoing debate concerning the relative merits, for the analysis of quantitative data, of, on the one hand, variable-analytic correlational methods, and, on the other, the case-based set theoretic methods developed by Charles Ragin. While correlational approaches, based in linear algebra, typically use regression to establish the net effects of several "independent" variables on an outcome, the set theoretic approach analyses, more holistically, the conjunctions of factors sufficient and/or necessary for an outcome to occur. Here, in order to bring out key differences between the approaches, we focus our attention on the basic building blocks of the two approaches: respectively, the concept of linear correlation and the concept of a sufficient and/or necessary condition. We initially use invented data (for ability, educational achievement, and social class) to simulate what is at stake in this methodological debate and we then employ data taken from the British National Child Development Study to explore the structuring of the relationship between respondents' early measured ability and later educational achievement across various configurations of parental and grandparental class origin and sex. The substantive idea informing the analysis, derived from Boudon's work, is that, for respondents from higher class origins, ability will tend to be sufficient but not necessary for later educational achievement while, for lower class respondents, ability will tend to be necessary but not sufficient. We compare correlational analyses, controlling for class and gender, with fuzzy set analyses to show that set theoretic indices can better capture these varying relationships than correlational measures. In conclusion, we briefly consider how our demonstration of some of the advantages of the set theoretic approach for modelling empirical relationships might be related to the debate concerning the relation between observed regularities and causal mechanisms.

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):8.

Abstract: Charles Ragin's crisp set and fuzzy set Qualitative Comparative Analysis (csQCA and fsQCA) are being used by increasing numbers of social scientists interested in combining analytic rigour with case-based approaches. As with all techniques that become available in easy-to-use software packages, there is a danger that QCA will come to be used in a routinised manner, with not enough attention being paid to its particular strengths and weaknesses. Users of fsQCA in particular need to be very aware of particular problems that can arise when fuzzy logic lies behind their analyses. This paper aims to increase its readers' understanding of some of these problems and of some means by which they might be alleviated. We use a critical discussion of a recent paper by Freitag and Schlicht addressing social inequality in education in Germany as our vehicle. After summarising the substantive claims of the paper, we explain some key features of QCA. We subsequently discuss two main issues, (i) limited diversity and the various ways of using counterfactual reasoning to address it, and (ii) the logical paradoxes that can arise when using fsQCA. Making different choices than Freitag and Schlicht do in respect of dealing with these two issues, we undertake some reanalysis of their data, showing that their conclusions must be treated with some caution. We end by drawing some general lessons for users of QCA.

Cooper, Barry, and Judith Glaesser. 2015. "Analysing Necessity and Sufficiency with Qualitative Comparative Analysis: How do Results Vary as Case Weights Change?" Quality & Quantity 50 (1):327-46.

Abstract: Ragin's Qualitative Comparative Analysis (QCA) and related set theoretic methods are increasingly popular. This is a welcome development, since it encourages systematic configurational analyses of social phenomena. One downside of this growth in popularity is a tendency for more researchers to use the approach in a formulaic manner - something made possible, and more likely, by the availability of free software. We wish to see QCA employed, as Ragin intended, in a self-critical manner. For this to happen, researchers need to understand more of what is going on behind the results generated by the available software packages. One important aspect of set theoretic analyses of sufficiency and necessity is the effect that the distribution of cases in a dataset can have on results. We explore this issue in a number of ways. We begin by exploring how both deterministic and nondeterministic data-generating processes are reflected in the analyses of populations differing in only the weights of types of cases. We show how and why weights matter in causal analyses that focus on necessity and also, where models are not fully specified, sufficiency. We then draw on this discussion to show that a recent textbook discussion of hidden necessary conditions is weakened as a result of its neglect of weighting issues. Finally, having shown that case weights raise a number of difficulties for set theoretic analyses, we offer suggestions, drawing on two imagined population datasets concerning health outcomes, for mitigating their effect.

Cooper, Barry, and Judith Glaesser. 2011. "Using Case-Based Approaches to Analyse Large Datasets: A Comparison of Ragin's fsQCA and Fuzzy Cluster Analysis." International Journal of Social Research Methodology 14 (1):31-48.

Abstract: The paper undertakes a comparison of Ragin's fuzzy set Qualitative Comparative Analysis with cluster analysis. After describing key features of both methods, it uses a simple invented example to illustrate an important algorithmic difference in the way in which these methods classify cases. It then examines the consequences of this difference via analyses of data previously calibrated as fuzzy sets. The data, taken from the National Child Development Study, concern educational achievement, social class, ability and gender. The classifications produced by fsQCA and fuzzy cluster analysis (FCA) are compared and the reasons for the observed differences between them are discussed. The predictive power of both methods is also compared, employing both correlational and set theoretic comparisons, using highest qualification achieved as the outcome. In the main, using the real data, the two methods are found to produce similar results. A final discussion considers the generalisability or otherwise of this finding.

Cronqvist, Lasse, and Dirk Berg-Schlosser. 2009. "Multi-Value QCA (mvQCA)." In Configurational Comparative Methods: Qualitative Comparative Analysis (QCA) and Related Techniques, eds. B. Rihoux and C. C. Ragin. London: Sage Publications. pp. 69-86.

1.Paragraph:Multi-value QCA, as the name suggests, is an extension of csQCA. It retains the main principles of csQCA, namely to perform a synthesis of a data set, with the result that cases with the same outcome value are "covered" by a parsimonious solution (the minimal formula). As in csQCA, the minimal formula contains one or more terms, each of which covers a number of cases with the outcome, while no cases with a different outcome are explained by any of the terms in the minimal formula. The key difference is that whereas csQCA allows only dichotomous variables, mvQCA also allows multi-value variables. In fact, mvQCA is a generalization of csQCA, because indeed a dichotomous variable is a specific subtype of multi-value variables - it is simply a multi-value variable with only two possible values. Therefore, data sets analyzed with csQCA also can be processed using mvQCA.

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

Abstract: This article presents a new methodology for multilevel analysis using a small number of cases, named Comparative Multilevel Analysis (CMA). A classic problem in comparative studies has been the presence of too many variables and too few cases. One traditional solution to this problem has been to study subsystems within a system. However, the approach has fundamental limitations: it cannot analyse subsystems from different contexts, nor can it determine how conditions on the system level influence subsystems. By proposing four additions to traditional methodology, this article offers a new method of comparing subsystems from different contexts in order to analyse the effect of context on subsystems. The author also illustrates how CMA can be combined with Qualitative Comparative Analysis and Fuzzy-set, thereby enabling these methods to be used in the study of subsystem and context effects.

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

Abstract: Contextual analyses are essential in comparative research, as they investigate the importance of contextual conditions for causal relationships. During the last decades, an increasing number of comparative studies have also focused on how contextual conditions affect causal relationships. At the same time, new comparative methods have been developed based on set-theoretical logics. Two of the most prominent methods are csQCA and fsQCA, which are used in comparative studies with increasing frequency. However, the conventional design for contextual analysis is still based on quantitative methods and the use of interaction factors. This article discusses why the use of interaction-factors is not suitable together with QCA-methods. Instead of the conventional design, the article presents an alternative design for contextual analyses with QCA-methods grounded on subgroup-design. Based on one recently-developed methodology comparative multilevel analysis (CMA), some guidelines for performing contextual analyses with two set-theoretical methods (csQCA and fsQCA) are presented. As illustrated with examples, the combination of CMA and QCA provides opportunities to use QCA for contextual analysis.

Dul, Jan, Tony Hak, Gary Goertz, and Chris Voss. 2010. "Necessary Condition Hypotheses in Operations Management." International Journal of Operations & Production Management 30 (11):1170-90.

Abstract: Purpose: The purpose of this paper is to show that necessary condition hypotheses are important in operations management (OM), and to present a consistent methodology for building and testing them. Necessary condition hypotheses ("X is necessary for Y") express conditions that must be present in order to have a desired outcome (e.g. "success"), and to prevent guaranteed failure. These hypotheses differ fundamentally from the common co-variational hypotheses ("more X results in more Y") and require another methodology for building and testing them. Design/methodology/approach: The paper reviews OM literature for versions of necessary condition hypotheses and combines previous theoretical and methodological work into a comprehensive and consistent methodology for building and testing such hypotheses. Findings: Necessary condition statements are common in OM, but current formulations are not precise, and methods used for building and testing them are not always adequate. The paper outlines the methodology of necessary condition analysis consisting of two stepwise methodological approaches, one for building and one for testing necessary conditions. Originality/value: Because necessary condition statements are common in OM, using methodologies that can build and test such hypotheses contributes to the advancement of OM research and theory.

Duşa, Adrian. 2010. "A Mathematical Approach to the Boolean Minimization Problem." Quality & Quantity 44 (1):99-113.

Abstract: Any minimization problem involves a computer algorithm. Many such algorithms have been developed for the boolean minimizations, in diverse areas from computer science to social sciences (with the famous QCA algorithm). For a small number of entries (causal conditions in the QCA) any such algorithm will find a minimal solution, especially with the aid of the modern computers. However, for a large number of conditions a quick and complete solution is not easy to find using an algorithmic approach, due to the extremely large space of possible combinations to search in. In this article I will demonstrate a simple alternative solution, a mathematical method to obtain all possible minimized prime implicants. This method is not only easier to understand than other complex algorithms, but it proves to be a faster method to obtain an exact and complete boolean solution.

Duşa, Adrian. 2007. "User Manual for the QCA(GUI) Package in R." Journal of Business Research 60 (5):576-86.

Abstract: Although performing all available function directly from R's command line is possible, many users have expressed their desire for a user-friendly version of the QCA package with menus. Instead of designing the user interface from scratch it was a lot easier to use existing code and Rcmdr is the best engineered interface available for R. The QCAGUI package (the companion of the standard QCA package) is based on the Rcmdr user interface. Other, more advanced software exists that perform QCA algorithms but none of them offers the kind of development R has in terms of code readability, code sharing and helpful advice from a wide community. An R package for QCA emerges and its development is just beginning as the level of interest in R increases constantly.

Duşa, Adrian, and Alrik Thiem. 2015. "Enhancing the Minimization of Boolean and Multivalue Output Functions With eQMC." Journal of Mathematical Sociology 39 (2):92-108.

Abstract: Configurational comparative methods have gained in popularity among sociologists and political scientists. In particular, Qualitative Comparative Analysis (QCA) has attracted considerable attention in recent years. The process of Boolean minimization by means of the Quine-McCluskey algorithm (QMC) is the central procedure in QCA, but QMC's exactitude renders it memory intensive and slow in processing complex output functions. In this article, we introduce the enhanced QMC algorithm (eQMC) to alleviate these problems. eQMC is equally exact but, unlike QMC, capable of processing multivalent condition and outcome factors. Instead of replacing QMC, however, eQMC acts as an optimizing complement in contexts of limited empirical diversity. We demonstrate its speed and computer memory performance through simulations.

Eliason, Scott R., and Robin Stryker. 2009. "Goodness-of-Fit Tests and Descriptive Measures in Fuzzy-Set Analysis." Sociological Methods & Research 38 (1):102-46.

Abstract: In this article the authors develop goodness-of-fit tests for fuzzy-set analyses to formally assess the fit between empirical information and various causal hypotheses while accounting for measurement error in membership scores. These goodness-of-fit tests, and the accompanying logic, provide a sound inferential foundation for fuzzy-set methodology. The authors also develop descriptive measures to complement these tests. Examples from Stryker and Eliason (2003) and Mahoney (2003) show how goodness-of-fit tests and descriptive measures may be used to assess individual causal factors as well as conjunctions of factors. The authors show how these tools provide more information in a fuzzy-set analysis than do tests currently in use. In providing this inferential foundation, the authors also show that fuzzy-set methods (a) are no less amenable to falsificationist methods of the Neyman-Pearson type than are standard statistical techniques and (b) may be usefully applied in either an exploratory/inductive or a confirmatory/deductive research design.

Emmenegger, Patrick. 2011. "How Good are your Counterfactuals? Assessing Quantitative Macro-Comparative Welfare State Research with Qualitative Criteria." Journal of European Social Policy 21 (4):365-80.

Abstract: All causal statements based on historical data - both in qualitative and quantitative social research - rely on counterfactuals. In quantitative research, scholars attempt to arrive at valid counterfactuals by emulating an experimental design. However, because of treatments that are impossible to manipulate and the non-random assignment of data to treatment and control groups, causal statements are often based on invalid counterfactuals. In qualitative research, scholars attempt to arrive at valid counterfactuals by probing the historical and logical consistency of counterfactuals and by acknowledging the interconnectedness of events. Criteria to evaluate counterfactuals have been developed that allow for a discussion of the quality of counterfactuals used in causal statements. In this article, we suggest using these qualitative criteria to evaluate counterfactuals in quantitative macro-comparative welfare state research. We argue that these criteria can help us identify erroneous causal inferences in quantitative research based on historical data.

Emmenegger, Patrick, Jon Kvist, and Svend-Erik Skaaning. 2013. "Making the Most of Configurational Comparative Analysis: An Assessment of QCA Applications in Comparative Welfare-State Research." Political Research Quarterly 66 (1):185-90.

Abstract: QCA's ability of addressing complex theoretical expectations and taking account of configurational relationships is rarely fully exploited. Assessing comparative welfare-state research, which has employed QCA, we find that only about half of the studies reviewed have expressed complex theoretical propositions in set-theoretical terms, revisited cases subsequent to the formal analysis, or subjected findings to robustness checks. We discuss the relevance of each of these three aspects and argue that carefully considering these will improve the quality of QCA applications.

Fischer, Manuel. 2011. "Social Network Analysis and Qualitative Comparative Analysis: Their Mutual Benefit for the Explanation of Policy Network Structures." Methodological Innovations Online 6 (2):27-51.

Abstract: By switching the level of analysis and aggregating data from the micro-level of individual cases to the macro-level, quantitative data can be analysed within a more case-based approach. This paper presents such an approach in two steps: In a first step, it discusses the combination of Social Network Analysis (SNA) and Qualitative Comparative Analysis (QCA) in a sequential mixed-methods research design. In such a design, quantitative social network data on individual cases and their relations at the micro-level are used to describe the structure of the network that these cases constitute at the macro-level. Different network structures can then be compared by QCA. This strategy allows adding an element of potential causal explanation to SNA, while SNA-indicators allow for a systematic description of the cases to be compared by QCA. Because mixing methods can be a promising, but also a risky endeavour, the methodological part also discusses the possibility that underlying assumptions of both methods could clash. In a second step, the research design presented beforehand is applied to an empirical study of policy network structures in Swiss politics. Through a comparison of 11 policy networks, causal paths that lead to a conflictual or consensual policy network structure are identified and discussed. The analysis reveals that different theoretical factors matter and that multiple conjunctural causation is at work. Based on both the methodological discussion and the empirical application, it appears that a combination of SNA and QCA can represent a helpful methodological design for social science research and a possibility of using quantitative data with a more case-based approach.

Fiss, Peer C., Dmitry Sharapov, and Lasse Cronqvist. 2013. "Opposites Attract? Opportunities and Challenges for Integrating Large-N QCA and Econometric Analysis." Political Research Quarterly 66 (1):191-8.

Abstract: Contrasting insights that can be gained from large-N QCA and econometric analysis, we outline two novel ways to integrate both modes of inquiry. The first introduces QCA solutions into a regression model, while the second draws on recent work in lattice theory to integrate a QCA approach with a regression framework. These approaches allow researchers to test QCA solutions for robustness, address concerns regarding possible omitted variables, establish effect sizes, and test whether causal conditions are complements or substitutes, suggesting that an important way forward for set-theoretic analysis lies in an increased dialogue that explores complementarities with existing econometric approaches.

Fritzsche, Erik. 2014. "Making Hermeneutics Explicit: How QCA Supports an Insightful Dialogue between Theory and Cases." International Journal of Social Research Methodology 17 (4):403-26.

Abstract: Typically, qualitative comparative analysis (QCA) is praised for its hermeneutic dialogue between theory and empirical cases. However, in reporting research with QCA, these hermeneutic processes will usually not be illustrated. This paper aims at showing clear how QCA induces this dialogue between theory and data. As an illustrative example, I use a research situation dealing with a genuine research question of Legislative Studies: the causes of party unity. Using the classical dichotomous and the MV-QCA approach, the paper mainly shows how to deal productively with contradictory theoretical statements and how stepping from simpler to more complex models adds explanation while still making clear further routes to improve insights into the substantive research topic: both theoretically and empirically. Finally, non-observed configuration ('logical remainders') will be used to simplify the resulting theory, and its theoretical and empirical plausibility will be evaluated. The whole paper makes explicit how the QCA approach forces researchers to reveal the dialogue between theory and cases - just as it was intended by the inventor of this analytical tool.

Gerrits, Lasse, and Stefan Verweij. 2013. Critical Realism as a Meta-Framework for Understanding the Relationships between Complexity and Qualitative Comparative Analysis. Journal of Critical Realism 12(2): 166-82.

Abstract: Many methods are used in research on complexity. One of these is qualitative comparative analysis (QCA). Although many authors allude to the relationships between complexity and QCA, these links are rarely made explicit. We propose that one way of doing so is by using critical realism as a meta-framework. This article discusses the viability of this approach by examining the extent to which QCA is a complexity-informed method. This question is answered in three steps. First, we discuss the nature of complexity and its epistemological implications. Second, we focus on Bhaskar's perspective on critical realism and show how it can be used as a framework for understanding social complexity. Third, we examine the ontological and epistemological assumptions underlying QCA and synthesize these with our critical realist approach to complexity. We argue that complex reality is non-decomposable, contingent, non-compressible and time-asymmetric. We conclude that, although QCA is inevitably reductive (i.e. it compresses reality) and partial (i.e. it decomposes reality), its core premises are built upon the notions of contingency and time-asymmetry. Therefore, it is not only a powerful method for doing complexity-informed research, but is also a complexity-informed method by itself.

Glaesser, Judith, and Barry Cooper. 2011. "Selecting Cases for In-Depth Study from a Survey Dataset: An Application of Ragin's Configurational Methods." Methodological Innovations Online 6 (2):52-70.

Abstract: While 'establishing the phenomena', to use Merton's phrase, is an important part of the sociological enterprise, in then accounting for such empirical regularities, theoretical models are required to understand causal processes. Both regression analysis and configurational methods applied to large datasets can establish patterns of relationships. Following a realist view, we assume that causal mechanisms have generated such patterns, and sound theoretical models are required to understand them. In-depth case studies can contribute to advancing such causal knowledge. We describe how, in the particular context of the configurational mode of analysis that characterises Ragin's Qualitative Comparative Analysis (QCA), we have selected individuals for in-depth study with the eventual purpose of advancing causal or explanatory understanding of conjunctural empirical regularities concerning educational careers. While forms of regression analysis seek to establish the net effects of 'independent' variables, QCA, employing Boolean algebra, analyses the conjunctions of conditions sufficient and/or necessary for an outcome to occur. QCA aims to preserve, holistically, the features of cases and is therefore well-suited to case selection. We use QCA both to undertake an initial large scale cross-case analysis and to subsequently select cases to develop theoretical understanding via within-case analysis. Using QCA's measures of consistency with relations of sufficiency and necessity, we can classify cases as typical and deviant, with these two types of cases playing different roles in testing and developing theory. Drawing on analyses of the German SOEP dataset undertaken as part of a larger study which is applying case-based configurational methods to English and German survey datasets while undertaking subsequent in-depth interviews with selected cases, we demonstrate how QCA can be used to select cases for interview in a systematic and theoretically informed manner.

Glaesser, Judith, and Barry Cooper. 2014. "Exploring the Consequences of a Recalibration of Causal Conditions when Assessing Sufficiency with Fuzzy Set QCA." International Journal of Social Research Methodology 17 (4):387-401.

Abstract: The use of Charles Ragin's Qualitative Comparative Analysis (QCA) is increasing in the social sciences. However, some of its characteristics, especially those of its fuzzy set variant, are still not well understood by users. QCA, a set theoretic method, aims to describe, in a Boolean form, the configurations of conditions that are necessary and/or sufficient for some outcome. The calibration of set memberships is a central feature. We discuss how two alternative calibrations of a condition affect the assessment of consistency with sufficiency. Using first an abstract example and then an empirical one from the sociology of education, we explain why 'stricter' calibration of conditions results in higher consistency with sufficiency. We demonstrate that conventional truth table analysis is not an ideal way to compare the analytic consequences of alternative calibrations and therefore employ an alternative which allows a more direct comparison of consistency indices while keeping comparative configurational contexts intact.

Goertz, Gary, Tony Hak, and Jan Dul. 2013. "Ceilings and Floors: Where Are There No Observations?" Sociological Methods & Research 42 (1):3-40.

Abstract: There are situations where the data or the theory suggest or require, respectively, that one estimate the boundary lines that separate regions of observations from regions of no observations. Of particular interest are ceiling or floor lines. For example, many theories use terms such as veto player, constraint, only if, and so on, which suggest ceilings. Ceiling hypotheses have a nonstandard form claiming the probability of Y&xnbsp;will be zero for all values of Y&xnbsp;greater than the ceiling value of Yc for a given value of X. Conversely, ceiling hypotheses make no specific prediction about the value of Y for a given value of X&xnbsp;except that it will be less than the ceiling value. Floors work by guaranteeing minimum levels. The article gives numerous examples of theories that imply ceiling or floor hypotheses and numerous examples of data that fit such hypotheses. The article proposes quantile regression as a means of estimating the boundaries of the no-data zone as well as criteria for evaluating the importance of the boundary variable. These techniques are illustrated for ceiling and floor hypotheses relating gross domestic product/capita and democracy.

Griffin, Larry, and Charles Ragin. 1994. "Some Observations on Formal Methods of Qualitative Analysis." Sociological Methods & Research 23 (1):4-21.

Abstract: -

Grofman, Bernard, and Carsten Q. Schneider. 2009. "An Introduction to Crisp Set QCA, with a Comparison to Binary Logistic Regression." Political Research Quarterly 62 (4):662-72.

Abstract: The authors focus on the dichotomous crisp set form of qualitative comparative analysis (QCA). The authors review basic set theoretic QCA methodology, including truth tables, solution formulas, and coverage and consistency measures and discuss how QCA (a) displays relations between variables, (b) highlights descriptive or complex causal accounts for specific (groups of) cases, and (c) expresses the degree of fit. To help readers determine when QCA's configurational approach might be appropriate, the authors compare and contrast QCA to mainstream statistical methodologies such as binary logistic regressions done on the same data set.

Hackett, Ursula. 2015. "But not Both: The Exclusive Disjunction in Qualitative Comparative Analysis (QCA)." Quality & Quantity 49 (1):75-92.

Abstract: The application of Boolean logic using qualitative comparative analysis (QCA) is becoming more frequent in political science but is still in its relative infancy. Boolean 'AND' and 'OR' are used to express and simplify combinations of necessary and sufficient conditions.This paper draws out a distinction overlooked by theQCA literature: the difference between inclusive- and exclusive-or (OR and XOR). It demonstrates that many scholars who have used the Boolean OR in fact mean XOR, discusses the implications of this confusion, and explains the applications of XOR to QCA. Although XOR can be expressed in terms of OR and AND, explicit use of XOR has several advantages: it mirrors natural language closely, extends our understanding of equifinality and deals with mutually exclusive clusters of sufficiency conditions. XOR deserves explicit treatment within QCA because it emphasizes precisely the values that make QCA attractive to political scientists: contextualization, confounding variables, and multiple and conjunctural causation.

Haesebrouck, Tim. 2015a. "The Added Value of Multi-Value Qualitative Comparative Analysis." Forum Qualitative Sozialforschung 17 (1).

Abstract: This article aims to qualify the skeptical view of many leading methodologists on multi-value Qualitative Comparative Analysis (mvQCA). More specifically, it draws attention to a distinctive strength of this QCA-variant. In contrast to the other QCA-variants, mvQCA is capable of straightforwardly capturing the specific causal role of every category of a multi-value condition. This provides it with an important advantage over both crisp set (csQCA) and fuzzy set QCA (fsQCA). fsQCA is not capable of capturing the causal effect of an intermediate category if, depending on the context, it can have a different impact than the full presence of the corresponding condition. csQCA, in turn, tends to attribute a causal role to the absence of condition values, which in the case of multi-value conditions often encompass very different cases. The article first discusses the comparative advantage of mvQCA with a constructed data set, after which it reanalyzes two published studies to demonstrate these advantages with empirical data.

Haesebrouck, Tim. 2015b. "Pitfalls in QCA's Consistency Measure." Journal of Comparative Politics 8 (2):65-80.

Abstract: Over the years, Qualitative Comparative Analysis developed into a widely-used analytical technique in political science. This article, however, reveals that the consistency measure, QCA's single most important parameter of fit, is significantly flawed. Contrary to the requirements that were set forth when this measure was introduced, inconsistent cases with small membership scores exert greater bearing on the consistency score than inconsistent cases with large membership scores. In consequence, the measure does not accurately express the degree to which empirical evidence supports statements of sufficiency and necessity. After revealing this flaw, the article introduces a new formula for calculating consistency, which more accurately assesses the evidence for sufficiency and/or necessity. Subsequently, it demonstrates how the standard consistency measures leads to the misinterpretation of empirical evidence by reanalysing two recent QCA-application.

Haynes, Philip. 2014. "Combining the Strengths of Qualitative Comparative Analysis with Cluster Analysis for Comparative Public Policy Research: With Reference to the Policy of Economic Convergence in the Euro Currency Area." International Journal of Public Administration 37 (9):581-90.

Abstract: Qualitative Comparative Analysis (QCA) is a well-established method for comparing national public policy similarities and differences. It is argued that Cluster Analysis can add additional benefits to such research when used concurrently with QCA. Cluster Analysis provides a better method for the initial exploration of multivariate data and examining how countries compare because it can work with the full range of available interval data while patterns are created and viewed. This provides the best first method for exploring patterns and likely groupings of countries. QCA then provides a more robust method for theorizing about the construction of such groupings and their relationship around similar variable scores. QCA makes such theorizing transparent. The research example used to illustrate the benefits of combining Cluster Analysis and QCA is an analysis of the evolving of macroeconomic policy for the countries sharing the Euro, comparing 2005 (precrisis) with 2010 (postcrisis).

Hellström, Johan. 2011. "Conditional Hypotheses in Comparative Social Science: Mixed-Method Approaches to Middle-Sized Data Analysis." Methodological Innovations Online 6 (2):71-102.

Abstract: This paper discusses under which circumstances and how configurational comparative methods (i.e. QCA) and statistical methods can be combined to provide tests for the 'quasi'-sufficiency of any given set of combination of causal conditions. When combined, QCA provides the ability to explore causal substitutability (i.e. multiple paths to a given outcome) and the ways in which many multiple causes interact with one another to produce effects, while the statistical elements can provide robust indications of the probable validity of postulated hypotheses. The potential utility of the mixed-method approach for analyzing political phenomena is demonstrated by applying it to cross-national data regarding party positions on European integration and party-based Euroscepticism in Western Europe. The findings show that oppositional stances to European integration are partly associated with non-governmental ideological fringe parties on both the left and right. The empirical example presented in this paper demonstrates that configurational methods can be successfully combined with statistical methods and supplement the QCA-framework by providing statistical tests of 'almost sufficient' claims. However, combining QCA with statistical methods can sometimes be problematic in middle-sized data analysis, especially as the latter usually cannot handle limited diversity (i.e. insufficient information) in the data and/or overtly complex relationships (i.e. having a large number of conjunctional conditions or interacting variables).

Herrmann, Andrea Monika, and Lasse Cronqvist. 2009. "When Dichotomisation becomes a Problem for the Analysis of Middle-Sized Datasets." International Journal of Social Research Methodology 12 (1):33-50.

Abstract: This article aims at illustrating the circumstances in which Qualitative Comparative Analysis (QCA) and its ramifications, fs/QCA and MVQCA, become particularly useful tools of analysis. To this end, we discuss the most pertinent problem which researchers encounter when using QCA: the problem of contradicting observations. In QCA analysis, contradictions arise from the sheer number of cases and the problem of dichotomisation. In order to handle contradictions, the method for analysing middle-sized-N situations should therefore be chosen according to two parameters: the size of a dataset, and the need to preserve raw-data information. While QCA is an apt tool for analysing comparatively small middle-sized datasets with a correspondingly reduced necessity to preserve cluster information, the opposite holds true for fs/QCA. MVQCA strikes a balance between these two methods as it is most suitable for analysing genuinely middle-sized case sets for which some cluster information needs to be preserved.

Hicks, Alexander. 1994. "Qualitative Comparative Analysis and Analytical Induction." Sociological Methods & Research 23 (1):86-113.

Abstract: This article bridges two research traditions, analytical induction (AI) and qualitative comparative analysis (QCA) in the context of a study of early welfare state formation. First, the article differentiates classical AI from neoanalytical induction (NAI), tracing the latter to the former and identifying some problems with NAI. Next, it outlines QCA and identifies some problems with it. Third, it sketches two bridges, along with solutions that they offer for some limitations of NAI and QCA. One bridge links NAI's method, in essence a logical implementation of the idea of the working hypothesis, to QCA's powerful Boolean technology. The second bridge joins AI's stress on the reformulation of hypotheses in the face of negative evidence to QCA's capacities for complex inductive and logical specifications of the relations of explanatory to dependent variables. Following that, the article summarizes portions of a study of early 20th-century welfare state formation and uses them to illustrate the bridges. It concludes with a discussion of the analytical promise of a variant of QCA that stresses theory building in the AI tradition.

Hisdal, Ellen. 1988. "Are Grades of Membership Probabilities?" Fuzzy Sets and Systems 25 (3):325-48.

Abstract: A small sample is given of the difficulties with present-day fuzzy set theory with respect to the requirements of a scientific theory; and a summary of some probabilistic interpretations of grades of membership to be found in the literature. The 'TEE model' for grades of membership is then suggested. Instead of starting out from mathematical postulates, such as the assumed max and min operations for or and and, the TEE model uses a semantic, physio-logical, psycho-logical starting point by investigating the possibilities which a person has for assigning linguistic labels and partial grades of membership in a meaningful way. The assignment of partial grades of membership is explained by the assumption that humans have the ability to take errors of observation and intersubject differences into consideration. A membership value [mu][lambda](uex) is identified with the subject's estimate of the probability that the label [lambda] (e.g. [lambda] = tall) would be assigned to an object of exact attribute value uex in a natural language situation. This situation being a 'labeling' or a 'yes-no' one in which at least one of three possible sources of uncertainty is present. Almost all the accepted formulas of fuzzy set theory, as well as the shapes of the grade of membership curves, are then derived instead of having to be postulated. However, the derived formulas for or and and reduce to the max and min operations only in a number of special cases. In another special case they reduce to the summation and the 'zero operation' respectively. The generally valid formulas are presented.

Hudson, John, and Stefan Kühner. 2013. "Qualitative Comparative Analysis and Applied Public Policy Analysis: New Applications of Innovative Methods." Policy and Society 32 (4):279-87.

Abstract: QCA based methods have grown in popularity in recent years. Standing between quantitative and qualitative research, in principle they help balance the breadth of analysis provided by quantitative data with the depth of case study knowledge provided by qualitative analysis. The challenge of mixing depth and breadth has always been a particularly acute one for policy based research. Proponents of QCA techniques suggest they are better placed to handle the diversity of policy provision found in different spatial entities than standard linear quantitative methods, while also able to allow for hypothesis testing based upon a fine grained analysis that is more systematic in approach than the techniques typically employed in standard qualitative analyses. The full potential of these methods for policy analysis has yet to be realised however. Partly this is because knowledge of these methods remains at the margins of the policy analysis community, particularly amongst practitioners undertaking applied policy analyses such as policy evaluations. In the introduction to this volume we first outline some of the key principles of QCA research before moving on to identify some of its key advantages. We round off by highlighting key themes explored by the papers included within the volume.

Hug, Simon. 2013. "Qualitative Comparative Analysis: How Inductive Use and Measurement Error Lead to Problematic Inference." Political Analysis 21 (2):252-65.

Abstract: An increasing number of analyses in various subfields of political science employ Boolean algebra as proposed by Ragin's qualitative comparative analysis (QCA). This type of analysis is perfectly justifiable if the goal is to test deterministic hypotheses under the assumption of error-free measures of the employed variables. My contention is, however, that only in a very few research areas are our theories sufficiently advanced to yield deterministic hypotheses. Also, given the nature of our objects of study, error-free measures are largely an illusion. Hence, it is unsurprising that many studies employ QCA inductively and gloss over possible measurement errors. In this article, I address these issues and demonstrate the consequences of these problems with simple empirical examples. In an analysis similar to Monte Carlo simulation, I show that using Boolean algebra in an exploratory fashion without considering possible measurement errors may lead to dramatically misleading inferences. I then suggest remedies that help researchers to circumvent some of these pitfalls.
Set

Klir, George J., Ute H. St. Clair, and Bo Yuan. 1997. Fuzzy Set Theory: Foundations and Applications. Upper Saddle River, NJ: Prentice Hall.

Abstract: Since the early 1990s, literature on fuzzy set theory and its various applications has been rapidly growing. Hundreds of books on this subject are now available on the market. Most of them are either edited collections of papers on various themes or monographs on special topics. Textbooks on fuzzy set theory are still rather rare, in spite ofthe growing need for such textbooks at all levels of higher education. This book, Fuzzy Set Theory: Foundations and Applications, is intended to fill a particular gap in the literature. Its aim is to serve as a textbook for a general course in undergraduate liberal arts and sciences programs. This aim is reflected in the content of the book and the style in which it is written. As the title of the book suggests, it is a simple introduction to basic elements of fuzzy set theory. However, it also contains an overview of the corresponding elements of classical set theory, including basic ideas of classical relations, as well as an overview of classical logic. The emphasis is on conceptual rather than theoretical presentation of the material.

Kosko, Bart. 1993. Fuzzy Thinking: The New Science of Fuzzy Logic. New York: Hyperion.

Abstract: Kosko, an engineering professor at the University of Southern California, makes a provocative new scientific paradigm intelligible to the general reader. Fuzzy logic posits a world in which absolutes, such as those implied in the words "true" and "false", are less important and interesting than the matters of degree between them. "Fuzziness is grayness" and "the truth lies in the middle" according to Kosko, one of the pioneers of fuzzy logic theory, which he persuasively presents as a world view rooted more in Buddhist and Taoist assumptions than in the dichotomous Aristotelian tradition. He proposes FATs (Fuzzy Approximation Theorems) for the existence (and non-existence, as fuzziness demands) of God and as models of the abortion debate. In consumer terms, fuzzy logic is behind such "smart" machines as air conditioners and microwave ovens that gauge their operation to the conditions and demands of a given moment's task. Writing with style and risk, Kosko challenges assumptions, not about the existence of scientific authority, but about its nature.

Krogslund, Chris, Donghyun Danny Choi, and Mathias Poertner. 2015. "Fuzzy Sets on Shaky Ground: Parameter Sensitivity and Confirmation Bias in fsQCA." Political Analysis 23 (1):21-41.

Abstract: Scholars have increasingly turned to fuzzy set Qualitative Comparative Analysis (fsQCA) to conduct small- and medium-N studies, arguing that it combines the most desired elements of variable-oriented and case-oriented research. This article demonstrates, however, that fsQCA is an extraordinarily sensitive method whose results are worryingly susceptible to minor parametric and model specification changes. We make two specific claims. First, the causal conditions identified by fsQCA as being sufficient for an outcome to occur are highly contingent upon the values of several key parameters selected by the user. Second, fsQCA results are subject to marked confirmation bias. Given its tendency toward finding complex connections between variables, the method is highly likely to identify as sufficient for an outcome causal combinations containing even randomly generated variables. To support these arguments, we replicate three articles utilizing fsQCA and conduct sensitivity analyses and Monte Carlo simulations to assess the impact of small changes in parameter values and the method's built-in confirmation bias on the overall conclusions about sufficient conditions.

Krogslund, Chris, and Katherine Michel. 2014. "A Larger-N, Fewer Variables Problem? The Counterintuitive Sensitivity of QCA." Qualitative & Multi-Method Research 14 (1):25-33.

1. Paragraph: Studies employing Qualitative Comparative Analysis (QCA) often analyze a relatively small number of cases to assess the impact of a substantial number of variables on a given outcome. As emphasized in the quotation above, in the tradition of writing on the comparative method and multi-method research, this ratio of cases-to-variables is viewed as an analytic problem. In this exploratory research note, we raise questions about the implications of this ratio for the stability of findings in QCA. One common method of assessing result stability is the "drop-one" sensitivity test, which repeatedly reruns a particular analysis, each time dropping a single case. We find that, for the number of cases (n) to which analysts most routinely apply QCA, this type of sensitivity analysis produces paradoxical results.

Krohwinkel, Anna. 2015. "A Configurational Approach to Project Delays: Evidence From a Sequential Mixed Methods Study." Journal of Mixed Methods Research 9 (4):335-61.

Abstract: While qualitative comparative analysis (QCA) has often been portrayed as an alternative to mainstream statistical methods, there is a growing debate on how the techniques can be combined. This article shows how, using a sequential design, the integration of a large-N survival analysis with a smaller-N QCA yielded new insights about the reasons for project delay in a multiproject organization. While the regression served to trace significant explanatory variables and their net effects, the QCA nuanced these findings by demonstrating how variables combine across distinct categories of cases. As a result, the differing logics underlying externally and internally generated delays were elucidated. Implications for our understanding of multiproject organizing and for mixed methods research are discussed.

Kvist, Jon. 2006. "Diversity, Ideal Types and Fuzzy Sets in Comparative Welfare State Research." In Innovative Comparative Methods for Policy Analysis, eds. B. Rihoux and H. Grimm. New York: Springer Science+Business Media. pp. 167-84.

1.Paragraph: In the last 15 years diversity and ideal types have taken centre stage in comparative welfare state research, a growing field of the social sciences characterized by a fruitful dialogue between qualitative and quantitative oriented researchers (Amenta 2003). With the influential Three Worlds of Welfare Capitalism, Gosta Esping-Andersen (1990) placed diversity firmly on the research agenda. The Liberal, Conservative, and Social Democratic welfare state regimes depict ideal types for different groups of real welfare states that have undergone distinct political-institutional trajectories, or paths, in their historical development. At the same time, the ideal types also encapsulate distinct political economies with regard to the role of the state vis-a-vis the market and the family (further elaborated in Esping-Andersen 1999). These ideal types have become starting points for most subsequent studies of the causes and consequences of welfare state diversity.

Kvist, Jon. 2007. "Fuzzy Set Ideal Type Analysis." Journal of Business Research 60 (5):474-81.

Abstract: This article advances a new method for studying cases, fuzzy set ideal type analysis, which is a framework that allows a precise operationalization of theoretical concepts, the configuration of concepts into ideal types, and the categorisation of cases. In a Weberian sense, ideal types are analytical constructs for use as yardsticks for measuring the similarity and difference between concrete phenomena. Ideal type analysis involves differentiation of both categories and degrees of membership in such categories. In social science jargon, this analysis involves the evaluation of qualitative and quantitative differences or, in brief, of diversity. Fuzzy set theory provides a calculus of compatibility. Fuzzy set theory can measure and compute theoretical concepts and analytical constructs in a manner that remains true to their formulation and meaning. This article sets out elements and principles of fuzzy set theory relevant for ideal type analysis and demonstrates their usefulness in an example drawn from comparative welfare state research on the conformity of changing unemployment policies to predefined ideal typical models.

Lee, Sophia Seung-Yoon. 2013. "Fuzzy-Set Method in Comparative Social Policy: A Critical Introduction and Review of the Applications of the Fuzzy-Set Method." Quality & Quantity 47 (4):1905-22.

Abstract: This article critiques the Fuzzy-set Qualitative Analysis (fs/QCA) methodology by examining its applicability in three studies in the field of comparative social policy. In each of these three test cases, I focus on the validity of fuzzy-set's claimed function - its ability to combine theoretic discourse and evidence analysis. All three studies investigate welfare state reform in the late twentieth century and apply fs/QCA: (1) "Welfare Reform in the Nordic Countries in the 1990s: Using Fuzzy-set Theory to Assess Conformity to Ideal Types," (2) "States of Welfare or States of Workfare? Welfare State Restructuring in 16 Capitalist Democracies, 1985-2002," and (3) "The Diversity and Causality of Welfare State Reforms Explored with Fuzzy-sets." This article begins by discussing the ontology and epistemology of comparative social policy. The fuzzy set logic and set theoretic nature of social science theory is then discussed to align the ontology with fuzzy set methodology. Next, a more detailed introduction of fuzzy-set method (fs/QCA) is followed. This study suggests that fs/QCA is a unique and useful method for comparative social policy. It advances quantitative analysis by exploring cases configurationally and also advances the qualitative analysis by applying the fuzzy set logic and the principle of calibration.

Lieberson, Stanley. 1991. "Small N's and Big Conclusions: An Examination of the Reasoning in Comparative Studies Based on a Small Number of Cases." Social Forces 70 (2):307-20.

Abstract: An increasing number of studies, particularly in the area of comparative and historical research, are using the method of agreement and method of difference proposed by Mill (1872) to infer causality based on a small number of cases. This article examines the logic of the assumptions implicit in such studies. For example, the research must assume: (1) a deterministic approach rather than a probabilistic one, (2) no errors in measurement, (3) the existence of only one cause, and (4) the absence of interaction effects. These assumptions are normally inappropriate, since they contradict a realistic appraisal of most social processes, but are mandatory if we follow Mill's causal analyses based on small N's. Research should not attempt employment of such methods in small- N cases without a more rigorous justification of heroic assumptions and a guard against possible distortions.

Lieberson, Stanley. 1994. "More on the Uneasy Case for Using Mill-Type Methods in Small-N Comparative Studies." Social Forces 72 (4):1225-37.

Abstract: The methods of agreement and difference are outdated and inappropriate procedures for comparative or historical analysis based on a small number of cases. The methods cannot employ a probabilistic perspective, deal with data errors, use multivariate analyses, or take into account interaction effects. All of these are critical features in contemporary ways of thinking about social processes. Although Savolainen (1994) accepts the importance of having a method that can cope with these matters, he argues that Mill's methods permit such steps. However, he provides neither specific examples of where these methods actually address these issues nor does he present a formal set of rules whereby the methods of difference or agreement can estimate them. This is not surprising since Mill himself recognized that these methods were inappropriate for the kinds of problems addressed in most social research.

Longest, Kyle C., and Stephen Vaisey. 2008. "fuzzy: A program for Performing Qualitative Comparative Analyses (QCA) in Stata." Stata Journal 8 (1):79-104.

Abstract: Qualitative comparative analysis (QCA) is an increasingly popular analytic strategy, with applications to numerous empirical fields. This article briefly discusses the substantive motivation and technical details of QCA, as well as fuzzy-set QCA, followed by an in-depth discussion of how the new program fuzzy performs these techniques in Stata. An empirical example is presented that demonstrates the full suite of tools contained within fuzzy, including creating configurations, performing a series of statistical tests of the configurations, and reducing the identified configurations.

Lucas, Samuel R., and Alisa Szatrowski. 2014. "Qualitative Comparative Analysis in Critical Perspective." Sociological Methodology 44 (1):1-79.

Abstract: Qualitative comparative analysis (QCA) appears to offer a systematic means for case-oriented analysis. The method not only offers to provide a standardized procedure for qualitative research but also serves, to some, as an instantiation of deterministic methods. Others, however, contest QCA because of its deterministic lineage. Multiple other issues surrounding QCA, such as its response to measurement error and its ability to ascertain asymmetric causality, are also matters of interest. Existing research has demonstrated the use of QCA on real data, but such data do not allow one to establish the method's efficacy, because the true causes of real social phenomena are always contestable. In response, the authors analyze several simulated data sets for which true causal processes are known. They find that QCA finds the correct causal story only 3 times across 70 different solutions, and even these rare successes, on closer examination, actually reveal additional fundamental problems with the method. Further epistemological analyses of the results find key problems with QCA's stated epistemology, and results indicate that QCA fails even when its stated epistemological claims are ontologically accurate. Thus, the authors conclude that analysts should reject both QCA and its epistemological justifications in favor of existing effective methods and epistemologies for qualitative research.
Raw Set (T1)

Maggetti, Martino, and David Levi-Faur. 2013. "Dealing with Errors in QCA." Political Research Quarterly 66 (1):198-204.

Abstract: This paper discusses five strategies to deal with five types of errors in Qualitative Comparative Analysis (QCA): condition errors, systematic errors, random errors, calibration errors, and deviant case errors. These strategies are the comparative inspection of complex, intermediary, and parsimonious solutions; the use of an adjustment factor, the use of probabilistic criteria, the test of the robustness of calibration parameters, and the use of a frequency threshold for observed combinations of conditions. The strategies are systematically reviewed, assessed, and evaluated as regards their applicability, advantages, limitations, and complementarities.

Mahoney, James. 2001. "Beyond Correlational Analysis: Recent Innovations in Theory and Method." Sociological Forum 16 (3):575-93.

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Mahoney, James, and Gary Goertz. 2006. "A Tale of Two Cultures: Contrasting Quantitative and Qualitative Research." Political Analysis 14 (3):227-49.

Abstract: The quantitative and qualitative research traditions can be thought of as distinct cultures marked by different values, beliefs, and norms. In this essay, we adopt this metaphor toward the end of contrasting these research traditions across 10 areas: (1) approaches to explanation, (2) conceptions of causation, (3) multivariate explanations, (4) equifinality, (5) scope and causal generalization, (6) case selection, (7) weighting observations, (8) substantively important cases, (9) lack of fit, and (10) concepts and measurement. We suggest that an appreciation of the alternative assumptions and goals of the traditions can help scholars avoid misunderstandings and contribute to more productive "cross-cultural" communication in political science.

Mahoney, James, Erin Kimball, and Kendra L. Koivu. 2009. "The Logic of Historical Explanation in the Social Sciences." Comparative Political Studies 42 (1):114-46.

Abstract: Historical explanations seek to identify the causes of outcomes in particular cases. Although social scientists commonly develop historical explanations, they lack criteria for distinguishing different types of causes and for evaluating the relative importance of alternative causes of the same outcome. This article first provides an inventory of the five types of causes that are normally used in historical explanations: (1) necessary but not sufficient, (2) sufficient but not necessary, (3) necessary and sufficient, (4) INUS, and (5) SUIN causes. It then introduces a new method - sequence elaboration - for evaluating the relative importance of causes. Sequence elaboration assesses the importance of causes through consideration of their position within a sequence and through consideration of the types of causes that make up the sequence as a whole. Throughout the article, methodological points are illustrated with substantive examples from the field of international and comparative studies.

Markoff, John. 1990. "A Comparative Method: Reflections on Charles Ragin's Innovations in Comparative Analysis." Historical Methods 23 (4):177-81.

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Marx, Axel. 2010. "Crisp-Set Qualitative Comparative Analysis (csQCA) and Model Specification: Benchmarks for Future csQCA Applications." International Journal of Multiple Research Approaches 4 (2):138-58.

Abstract: AbstractCrisp-set qualitative comparative analysis (csQCA), a research approach developed by Charles Ragin in the 1980s, aims to combine qualitative and quantitative research strategies. Applications of the method have appeared in numerous journals. Recently, csQCA has been criticized concerning the validity of the models it generates as a result of the fact that it is unable to distinguish real from random data. It is argued that csQCA always identifies an explanatory model, even on the basis of random data. The paper addresses this hypothesis via a simulation. It uses randomly created datamatrices to show that csQCA can make a distinction between real and random data when model specification parameters are taken into account. First of all, the proportion of explanatory conditions on cases should be below a certain threshold, which differs as a function of the combination of conditions on cases. Secondly, there is an upper-limit to the number of explanatory conditions which can be used in a csQCA-analysis. The importance of the design parameters are the result of the problem of uniqueness which is a consequence of the use of Boolean algebra. Five implications for comparative case research-design and csQCA are discussed.

Marx, Axel, and Adrian Dusa. 2011. "Crisp-Set Qualitative Comparative Analysis (csQCA), Contradictions and Consistency Benchmarks for Model Specification." Methodological Innovations Online 6 (2):103-48.

Abstract: The purpose of this paper is to address and test two assumptions on which csQCA is based, namely that csQCA will generate contradictions and low consistency scores if models are ill-specified. The first part of the paper introduces csQCA in general and as a stepwise approach. In a second part a real-life example is introduced with the purpose of illustrating how csQCA operates and as an input for a simulation in the subsequent part. The third part introduces contradictions, consistency, their interrelatedness and the assumptions which are made with regard to contradictions and consistency. Subsequently the assumptions are tested via a simulation on the basis of a csQCA analysis of over 5 million random datasets. The paper argues that researchers cannot always assume that csQCA will generate contradictions or low consistency scores when models are ill-specified. Such an assumption is only justified when csQCA applications take limitations with regard to model specification (the number of conditions and the number of cases) into account. Benchmark tables for model specification purposes are developed. Since these tables are based on a probability value of 0.5 the paper also tests the results for contradictions and consistency for the probabilities which were present in a real-life example. This test shows that the 0.5 probability generates an appropriate measure for the occurrence of contradictions and consistency indicating that the benchmark tables can be used for different applications with different distributions of 0's and 1's in the conditions and outcomes. The paper ends with a conclusion.

Marx, Axel, Benoît Rihoux, and Charles Ragin. 2014. "The Origins, Development, and Application of Qualitative Comparative Analysis: The First 25 Years." European Political Science Review 6 (1):115-42.

Abstract: A quarter century ago, in 1987, Charles C. Ragin published The Comparative Method, introducing a new method to the social sciences called Qualitative Comparative Analysis (QCA). QCA is a comparative case-oriented research approach and collection of techniques based on set theory and Boolean algebra, which aims to combine some of the strengths of qualitative and quantitative research methods. Since its launch in 1987, QCA has been applied extensively in the social sciences. This review essay first sketches the origins of the ideas behind QCA. Next, the main features of the method, as presented in The Comparative Method, are introduced. A third part focuses on the early applications. A fourth part presents early criticisms and subsequent innovations. A fifth part then focuses on an era of further expansion in political science and presents some of the main applications in the discipline. In doing so, this paper seeks to provide insights and references into the origin and development of QCA, a non-technical introduction to its main features, the path travelled so far, and the diversification of applications.

Mendel, Jerry M., and Mohammad M. Korjani. 2013. "Theoretical Aspects of Fuzzy Set Qualitative Comparative Analysis (fsQCA)." Information Sciences 237 (0):137-61.

Abstract: Fuzzy set Qualitative Comparative Analysis (fsQCA) is a methodology for obtaining linguistic summarizations from data that are associated with cases. It has recently been described as a collection of 13 steps [7]. In this paper we focus on how to greatly speed up some of the computationally intensive steps of fsQCA and show how to use the speed-up equations to obtain some interesting and important properties of fsQCA. These properties not only provide additional understanding about fsQCA, but also lead to different ways to implement fsQCA. One of the properties is so important (Section 8) that unless its results are adopted, when a variable is described by more than one term (e.g., Low and High), fsQCA will provide incorrect results.

Mendel, Jerry M., and Mohammad M. Korjani. 2012. "Charles Ragin's Fuzzy Set Qualitative Comparative Analysis (fsQCA) used for Linguistic Summarizations." Information Sciences 202 (0):1-23.

Abstract: Fuzzy Set Qualitative Comparative Analysis (fsQCA) is a methodology for obtaining linguistic summarizations from data that are associated with cases. It was developed by the eminent social scientist Prof. Charles C. Ragin, but has, as of this date, not been applied by engineers or computer scientists. Unlike more quantitative methods that are based on correlation, fsQCA seeks to establish logical connections between combinations of causal conditions and an outcome, the result being rules that summarize the sufficiency between subsets of all of the possible combinations of the causal conditions (or their complements) and the outcome. The rules are connected by the word OR to the output. Each rule is a possible path from the causal conditions to the outcome. This paper, for the first time, explains fsQCA in a very quantitative way, something that is needed if engineers and computer scientists are to use fsQCA.

Meur, Gisèle de, Benoît Rihoux, and Sakura Yamasaki. 2009. "Addressing the Critiques of QCA." In Configurational Comparative Methods: Qualitative Comparative Analysis (QCA) and Related Techniques, eds. B. Rihoux and C. C. Ragin. London: Sage Publications. pp. 147-65.

1.Paragraph: As csQCA was launched earlier and has so far been used more extensively than the other QCA techniques, it has been the focus of more critiques than mvQCA and fsQCA. 1 In this chapter, we shall thus mostly concentrate on these critiques, some of which are specific to csQCA. Some critiques, however, can be expanded to the other QCA techniques. Most critiques of QCA concentrate on csQCA as a technique and less on QCA as an approach (as presented in Chapter 1). Building on a first attempt to review the critiques (De Meur, Rihoux, & Yamasaki, 2002), we draw a distinction between two very different sorts of critiques. On the one hand, there are those that we consider to be relevant, in the sense that they identify real limitations of csQCA.

Nurmi, Hannu, and Janusz Kacprzyk. 2007. "Fuzzy Sets in Political Science: An Overview." New Mathematics and Natural Computation 3 (3):281-99.

Abstract: The fuzzy set applications in political science cover decision making, games, collective choice, representation and comparative politics. The earliest applications were largely theoretical and suggestive rather than empirically anchored and testable models. We discuss a representative sample of applications and suggest some problems in making the fuzzy sets more generally applicable in political science.

Paul, Christopher, Colin P. Clarke, Beth Grill, and Terrance Savitsky. 2013. "Between Large-N and Small-N Analyses: Historical Comparison of Thirty Insurgency Case Studies." Historical Methods 46 (4):220-39.

Abstract: The authors study the 30 insurgencies occurring between 1978 and 2008 using four methods crossing the qualitative/quantitative divide. The four approaches are narrative, bivariate comparison, comparative qualitative analysis, and K-medoids clustering. The quantification of qualitative data allows the authors to compare more cases than they could "hold in their heads" under a traditional small-n qualitative approach, improving the quality of the overall narrative and helping to ensure that the quantitative analyses respected the nuance of the detailed case histories. Structured data-mining reduces the dimensionality of possible explanatory factors relative to the available observations to expose patterns in the data in ways more common in large-n studies. The four analytic approaches produced similar and mutually supporting findings, leading to robust conclusions.

Ragin, Charles C. 1987. The Comparative Method: Moving beyond Qualitative and Quantitative Strategies. Berkeley: University of California Press.

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Ragin, Charles C. 1998. "The Logic of Qualitative Comparative Analysis." International Review of Social History 43 (Supplement S6):105-24.

Abstract: Social scientists often face a fundamental dilemma when they conduct social research. On the one hand, they may emphasize the complexity of social phenomena - a common strategy in ethnographic, historical and macro social research - and offer in-depth case studies sensitive to the specificity of the things they study. On the other hand, they may make broad, homogenizing assumptions about cases, and document generalities - patterns hold across many instances. Research strategies that focus on complexity are often labeled "qualitative", "case-oriented", "small-N", or "intensive". Those that focus on generality are often labeled "quantitative", "variable-oriented", "large-N", or "extensive". While the contrasts between these two types of social research are substantial, it is easy to exaggerate their differences and to caricature the two approaches, for example, portraying quantitative work on general patterns as scientific but sterile and oppressive, and qualitative research on small Ns as rich and emancipatory but journalistic. It is important to avoid these caricatures because the contrasts between these two general approaches provide important leads both for finding a middle path between them and for resolving basic methodological issues in social science. Social scientists who study cases in an in-depth manner often see empirical generalizations simply as a means to another end - the interpretive understanding of cases. In this view, a fundamental goal of social science is to interpret significant features of the social world and thereby advance our collective understanding of how existing social arrangements came about and why we live the way we do. The rough general patterns that social scientists may be able to identify simply aid the understanding of specific cases; they are not viewed as predictive. Besides, the task of interpreting and then representing socially significant phenomena (or the task of making selected social phenomena significant by representing them) is a much more immediate and tangible goal. In this view, empirical generalizations and social science theory are important - to the extent that they aid the goal interpretive understanding.

Ragin, Charles C. 2000. Fuzzy-Set Social Science. Chicago: University of Chicago Press.

Abstract: In this innovative approach to the practice of social science, Charles Ragin explores the use of fuzzy sets to bridge the divide between quantitative and qualitative methods. Paradoxically, the fuzzy set is a powerful tool because it replaces an unwieldy, "fuzzy" instrument-the variable, which establishes only the positions of cases relative to each other, with a precise one-degree of membership in a well-defined set.

Ragin, Charles C. 2006. "Set Relations in Social Research: Evaluating Their Consistency and Coverage." Political Analysis 14 (3):291-310.

Abstract: Because of its inherently asymmetric nature, set-theoretic analysis offers many interesting contrasts with analysis based on correlations. Until recently, however, social scientists have been slow to embrace set-theoretic approaches. The perception was that this type of analysis is restricted to primitive, binary variables and that it has little or no tolerance for error. With the advent of "fuzzy" sets and the recognition that even rough set-theoretic relations are relevant to theory, these old barriers have crumbled. This paper advances the set-theoretic approach by presenting simple descriptive measures that can be used to evaluate set-theoretic relationships, especially relations between fuzzy sets. The first measure, "consistency," assesses the degree to which a subset relation has been approximated, whereas the second measure, "coverage," assesses the empirical relevance of a consistent subset. This paper demonstrates further that set-theoretic coverage can be partitioned in a manner somewhat analogous to the partitioning of explained variation in multiple regression analysis.

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

Abstract: Redesigning Social Inquiry provides a substantive critique of the standard approach to social research-namely, assessing the relative importance of causal variables drawn from competing theories. Instead, Ragin proposes the use of set-theoretic methods to find a middle path between quantitative and qualitative research. Through a series of contrasts between fuzzy-set analysis and conventional quantitative research, Ragin demonstrates the capacity for set-theoretic methods to strengthen connections between qualitative researchers' deep knowledge of their cases and quantitative researchers' elaboration of cross-case patterns. Packed with useful examples, Redesigning Social Inquiry will be indispensable to experienced professionals and to budding scholars about to embark on their first project.

Ragin, Charles C. 2009. "Qualitative Comparative Analysis Using Fuzzy Sets (fsQCA)." In Configurational Comparative Methods: Qualitative Comparative Analysis (QCA) and Related Techniques, ed. B. Rihoux and C. C. Ragin. London: Sage Publications. pp. 87-121.

1.Paragraph: One apparent limitation of the truth table approach is that it is designed for conditions that are simple presence/absence dichotomies (i.e., Boolean or "crisp" sets-see Chapter 3) or multichotomies (mvQCA-see Chapter 4). Many of the conditions that interest social scientists, however, vary by level or degree. For example, while it is clear that some countries are democracies and some are not, there is a broad range of in-between cases.

Ragin, Charles. 2013. "New Directions in the Logic of Social Inquiry." Political Research Quarterly 66 (1):171-4.

Abstract: This essay contrasts the conventional template for conducting social inquiry and the alternate template provided by configurational, case-oriented analytic methods, first formalized in The Comparative Method. The essential contrasts address the fundamental building blocks of social research, ranging from the definition of relevant cases to the understanding of social causation. The alternate template described in this essay provides a much stronger basis for the articulation of within-case and cross-case analysis than is offered by the conventional template.

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

Abstract: Caren and Panofsky (2005) seek to advance qualitative comparative analysis (QCA) by demonstrating that it can be used to study causal conditions that occur in sequences and introduce a technique they call TQCA (temporal QCA). In their formulation, the causal conjuncture is a sequence of conditions or events. The authors applaud their effort and agree that it is important to address this aspect of causation. This comment clarifies and corrects aspects of their analysis and present methods for assessing temporality that are more amenable to truth table analysis and the use of existing software, fsQCA. The methods presented utilize codings that indicate event order in addition to codings that indicate whether specific events occurred. They also demonstrate how to use "don't care" codings to bypass consideration of event sequences when they are not relevant (e.g., as when only a single event occurs).

Rihoux, Benoît. 2013. "Qualitative Comparative Analysis (QCA), Anno 2013: Reframing The Comparative Method's Seminal Statements." Swiss Political Science Review 19 (2):233-45.

Abstract: This review article examines the ways in which QCA is being (re)framed by some main authors in the field, in a context of expansion and diversification of this approach and set of techniques. Charles Ragin's seminal The Comparative Method (1987) is first synthetized in the form of eight statements which are then confronted to eight recent book-length publications: three QCA textbooks and five methodological volumes also touching upon QCA. On the whole, it appears that most statements have been considerably refined, both conceptually and technically, whereas only one statement is not taken on board anymore. In addition, QCA is being reframed and extended in different ways beyond Charles Ragin's initial statements.

Rihoux, Benoît. 2006. "Qualitative Comparative Analysis (QCA) and Related Systematic Comparative Methods: Recent Advances and Remaining Challenges for Social Science Research." International Sociology 21 (5):679-706.

Abstract: During the past two decades, a set of systematic comparative case analysis techniques has been developing at a steady pace. During the last few years especially, the main initial technique, qualitative comparative analysis (QCA), has been complemented by other related methods and techniques. The purpose of this article is to critically assess some main recent developments in this field. QCA and connected methods can be considered at two levels: as a research strategy and as a set of concrete techniques. The author first argues that such a strategy displays some decisive advantages in social science research, especially in small-and intermediate-N research designs. Second, QCA as well as three other related techniques, namely multi-value QCA (MVQCA), fuzzy sets and MSDO/MDSO, are presented in brief, and some current debates with regard to these techniques are also summarized. In the third section, the article surveys recent contributions and ongoing efforts that have provided some advances in the application of these techniques, around five key issues: case selection and model specification; measurement, dichotomization and linkage with theory; contradictions and non-observed cases; the time and process dimension; and the confrontation or combination with other methods. Finally, the article discuss the potential for further development of these methods in social science research broadly defined.

Rihoux, Benoît, Priscilla Álamos-Concha, Damien Bol, Axel Marx, and Ilona Rezsöhazy. 2013. "From Niche to Mainstream Method? A Comprehensive Mapping of QCA Applications in Journal Articles from 1984 to 2011." Political Research Quarterly 66 (1):175-84.

Abstract: This article provides a first systematic mapping of QCA applications, building upon a database of 313 peer-reviewed journal articles. We find out that the number of QCA applications has dramatically increased during the past few years. The mapping also reveals that csQCA remains the most frequently used technique, that political science, sociology, and management are the core disciplines of application, that macrolevel analyses, medium-N designs, and a monomethod use of QCA remain predominant. A particular focus is also laid on the ratio between the number of cases and number of conditions and the compliance to benchmarks in this respect.

Rihoux, Benoît, and Gisèle De Meur. 2009. "Crisp-Set Qualitative Comparative Analysis (csQCA)." In Configurational Comparative Methods: Qualitative Comparative Analysis (QCA) and Related Techniques, eds. C. C. Ragin and B. Rihoux. London: SAGE. pp. 33-68.

1.Paragraph: csQCA was the first QCA technique developed, in the late 1980s, by Charles Ragin and programmer Kriss Drass. Ragin's research in the field of historical sociology led him to search for tools for the treatment of complex sets of binary data that did not exist in the mainstream statistics literature. He adapted for his own research, with the help of Drass, Boolean algorithms that had been developed in the 1950s by electrical engineers to simplify switching circuits, most notably Quine (1952) and McCluskey (1966). In these so-called minimization algorithms (see Box 3.2), he had found an instrument for identifying patterns of multiple conjunctural causation and a tool to "simplify complex data structures in a logica1 and holistic manner" (Ragin, 1987, p. viii). csQCA is the most widely used QCA technique so far. In this chapter, a few basic operations of Boolean algebra will first be explicated, so the reader can grasp the nuts and bolts of csQCA. Then, using a few variables from the interwar project (see Chapter 2), the successive steps, arbitrations, and "good practices" of a standard application of csQCA will be presented.

Rihoux, Benoît, and Axel Marx. 2013. "Qualitative Comparative Analysis at 25: State of Play and Agenda." Political Research Quarterly 66 (1):167-71.

Abstract: This paper introduces the mini-symposium on Qualitative Comparative Analysis (QCA) and set-theoretic methods, both crisp sets and fuzzy sets, and situates the different contributions in a wider methodological debate concerning cross-case analysis. The paper argues that QCA is not just a set of techniques, but a distinctive research approach, with its own goals and set of assumptions. Concerning the wide methodological debate, special attention is paid to the added value of QCA and specific innovations introduced in the mini-symposium.

Rihoux, Benoît, Ilona Rezsöhazy, and Damien Bol. 2011. "Qualitative Comparative Analysis (QCA) in Public Policy Analysis: an Extensive Review." German Policy Studies 7 (3):9-82.

Abstract: This article provides a first systematic review of the connection between public policy analysis and QCA (Qualitative Comparative Analysis) techniques, with an emphasis on the state-of-the-art in QCA empirical applications. QCA is first presented both as an approach and as a set of techniques (crisp-set, multi-value and fuzzy-set QCA), both of which feature specific characteristics. In a second section, it is argued that there is a preferential connection between QCA and public policy analysis: in terms of research design and also in terms of the actual goals and needs of policy-oriented research. Further, the bulk of the article contains an exhaustive survey of empirical applications published so far. To do so, a typology of applications is developed along two dimensions: the stages in the policy process (from agenda-setting and policy initiation to policy evaluation) and the level at which the 'cases' or units of analysis are empirically defined (from micro to macro). A total of 143 applications are surveyed, gathered in 16 clusters according to the two dimensions in the typology. For all these applications, the focus is laid on the concrete ways in which QCA has been exploited, with short indications on the research questions and research results. In conclusion, the achievements reached so far, as well as some remaining limitations, are discussed. Some of the most promising avenues for further research are also sketched, in terms of 'mixed' methods designs, causal mechanisms, 'casing strategies', and unexploited 'niches' both in terms of levels of analysis and stages of policy processes.

Rohlfing, Ingo. 2012. "Analyzing Multilevel Data with QCA: A Straightforward Procedure." International Journal of Social Research Methodology 15 (6):497-506.

Abstract: The social sciences are witnessing a growing body of multilevel theories and debates about the proper methodological tools for the analysis of multilevel data. In a recent contribution to this journal, multilevel Qualitative Comparative Analysis (QCA) was proposed as a new methodological tool for discerning set-relational patterns in multilevel data. I argue that the presentation of multilevel QCA is erroneous in two respects. First, multilevel QCA ignores the fact that equifinal solutions entail diversity and therefore leads one to overestimate the complexity of QCA solutions. Second, the ordinary minimization procedure of truth tables that contain multilevel data yields the same solutions as multilevel QCA, but is much easier to implement. I conclude that the established inventory of QCA does not need to be extended by a special multilevel approach.

Rohlfing, Ingo. 2015. "Mind the Gap: A Review of Simulation Designs for Qualitative Comparative Analysis." Research & Politics 2 (4). DOI: 10.1177/2053168015623562.

Abstract: In a simulation-based analysis of Qualitative Comparative Analysis (QCA), Krogslund et al. (2015) conclude that its performance is suboptimal in several settings. I review their simulation setups and discuss three errors that were made in their analysis. First, the simulations involving inclusion thresholds are overpowered based on a misunderstanding of their role in truth table analyses. Second, the fact that a truth table analysis could exhibit model ambiguity and yield more than one model is ignored. If multiple models are derived from a truth table and they are combined into one, one overestimates the complexity of the models and underestimates their number, making it impossible to retrieve the target model of the simulation. Third, the simulations on the consequences of including irrelevant conditions intermingle sensitivity to overfitting with sensitivity to varying the inclusion thresholds. A reconsideration of KCP's simulations correcting for the errors confirms some of their findings, but also reveals that some of those errors lead to an underestimation of QCA's robustness. On a broader level, the review underscores that simulations are useful for the evaluation of QCA, but that simulation designs need to match QCA's mechanics and principles to produce valid conclusions about its performance.

Rohlfing, Ingo, and Carsten Q. Schneider. 2013. "Improving Research On Necessary Conditions: Formalized Case Selection for Process Tracing after QCA." Political Research Quarterly 66 (1):220-30.

Abstract: This paper aims at strengthening causal inference in necessary condition research. We demonstrate how process tracing based on purposefully selected cases can complement findings on cross-case patterns identified with Qualitative Comparative Analysis (QCA). Using an empirical example, we discuss the meaning of typical and deviant cases in analyses of necessity, develop formulas for identifying the most typical and most deviant cases, and detail the implications of so-called SUIN conditions for meaningful case selection. In addition, we clarify various viable variants of comparative process tracing and formulas for identifying the best-matching pairs of cases.

Rohwer, Götz. 2011. "Qualitative Comparative Analysis: A Discussion of Interpretations." European Sociological Review 27 (6):728-40.

Abstract: The article discusses interpretations of 'Qualitative Comparative Analysis' (QCA) proposed by Charles Ragin. The first section argues that QCA can be understood alternatively as a method of data description or as a method for the construction of deterministic functional models. It is shown that thinking in terms of models is required for generalizations. The second section discusses causal interpretations of such models. It is argued that one can use deterministic models without supposing a deterministic metaphysics. The third section briefly introduces stochastic functional models and shows how they can be used for QCA applications. In addition to showing that QCA can be well understood as a specific method of model construction, the article argues that deterministic and stochastic functional models are quite similar and, depending on the application context and the available data, both kinds of models could be useful.

Rohwer, Götz. 2014. "Factual and Modal Notions in Social Research." Quality & Quantity 48 (1):547-61.

Abstract: The article discusses a distinction between factual and modal notions, and corresponding generalizations, in social research. The discussion starts from the suggestion, made by Charles Ragin, that theoretical statements in social research most often can be formulated as statements about sets of cases and relations between such sets. In contrast to this view, it is argued that theoretical statements in social research often require modal notions referring to possibilities and probabilities which cannot be formulated as statements about sets of cases. In order to show this, the article reformulates Ragin's set-theoretic approach in the conceptual framework of statistical variables. It is shown that this can be done for both crisp and fuzzy set versions of Ragin's approach. The article then goes on to argue that social research is often interested in modal generalizations (probabilistic and deterministic rules) which require a fundamentally different conceptual framework. The article shows how such a framework can be defined, and finally indicates its usage for causal interpretations.

Rubinson, Claude. 2013. "Contradictions in fsQCA." Quality & Quantity 47 (5):2847-67.

Abstract: The lack of support for contradictions in fsQCA limits the method's usefulness for conducting inductive research. In this paper, I describe how to extend fsQCA to accommodate contradictory conditions. I review kirq (Reichert and Rubinson 2011), a new software package for QCA that includes support for fuzzy-set contradictions. For researchers using software that does not support fuzzy-set contradictions, I describe how to identify them by hand.

Savolainen, Jukka. 1994. "The Rationality of Drawing Big Conclusions Based on Small Samples: In Defense of Mill's Methods." Social Forces 72 (4):1217-24.

Abstract: Skocpol endorses the application of Mill's methods of causal inference for comparative historical explanations. According to Lieberson (1991), in studies where the sample size is very small, Mill's methods are inappropriate because they: (1) do not allow for probabilistic theories; (2) cannot handle interaction effects; (3) cannot accommodate multiple causes; (4) require the absence of measurement errors. Each of these claims turn out to be incorrect due to confusion over the uses of Mill's methods, failure to appreciate the aims of case-oriented explanations, and a narrow conception of cause. Small sample size does not constitute an obstacle to the application of Mill's methods.

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.

Abstract: Comparative methods based on set theoretic relationships such as 'fuzzy set Qualitative Comparative Analysis' (fs/QCA) represent a useful tool for dealing with complex causal hypotheses in terms of necessary and sufficient conditions under the constraint of a medium-sized number of cases. However, real-world research situations might make the application of fs/QCA difficult in two respects - namely, the complexity of the results and the phenomenon of limited diversity. We suggest a two-step approach as one possibility to mitigate these problems. After introducing the difference between remote and proximate factors, the application of a two-step fs/QCA approach is demonstrated analyzing the causes of the consolidation of democracy. We find that different paths lead to consolidation, but all are characterized by a fit of the institutional mix chosen to the societal context in terms of power dispersion. Hence, we demonstrate that the application of fs/QCA in a two-step manner helps to formulate and test equifinal and conjunctural hypotheses in medium-size N comparative analyses, and thus to contribute to an enhanced understanding of social phenomena.

Schneider, Carsten Q., and Ingo Rohlfing. 2012. "Does Set-Relational Causation Fit into a Potential Outcome Framework? An Assessment of Gerring's Proposal." Qualitative & Multi-Method Research 10 (1):8-14.

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Schneider, Carsten Q., and Ingo Rohlfing. 2013. "Doing Justice to Logical Remainders in QCA: Moving Beyond the Standard Analysis." Political Research Quarterly 66 (1):211-20.

Abstract: Limited diversity is among the most understudied methodological challenges. QCA allows for a more conscious treatment of logical remainders than most other comparative methods. The current state of the art is the Standard Analysis (Ragin 2008; Ragin and Sonnett 2004). We discuss two of its pitfalls, both rooted in the primacy given to parsimony. First, the Standard Analysis is no safeguard against untenable assumptions. As a remedy, we propose the Enhanced Standard Analysis (ESA). Second, researchers should consider including theoretically sound counterfactual claims even if they do not contribute to parsimony. We label this Theory-Guided Enhanced Standard Analysis (TESA).

Schneider, Carsten Q., and Ingo Rohlfing. 2013. "Combining QCA and Process Tracing in Set-Theoretic Multi-Method Research." Sociological Methods & Research 42 (4):559-97.

Abstract: Set-theoretic methods and Qualitative Comparative Analysis (QCA) in particular are case-based methods. There are, however, only few guidelines on how to combine them with qualitative case studies. Contributing to the literature on multi-method research (MMR), we offer the first comprehensive elaboration of principles for the integration of QCA and case studies with a special focus on case selection. We show that QCA's reliance on set-relational causation in terms of necessity and sufficiency has important consequences for the choice of cases. Using real world data for both crisp-set and fuzzy-set QCA, we show what typical and deviant cases are in QCA-based MMR. In addition, we demonstrate how to select cases for comparative case studies aiming to discern causal mechanisms and address the puzzles behind deviant cases. Finally, we detail the implications of modifying the set-theoretic cross-case model in the light of case-study evidence. Following the principles developed in this article should increase the inferential leverage of set-theoretic MMR.

Seawright, Jason. 2005. "Qualitative Comparative Analysis vis-à-vis Regression." Studies in Comparative International Development 40 (1):3-26.

Abstract: Discussions of Charles C. Ragin's Qualitative Comparative Analysis (QCA) have not adequately considered the assumptions about causation on which this method depends. Yet in evaluating any method, it is important to ask the question: How many untestable, or hard-to-test, assumptions must be met for us to believe the findings it produces? Advocates of QCA claim that one of its major strengths is that it requires fewer restrictive assumptions than techniques such as regression analysis. Hence, close assessment of the assumptions that are entailed is particularly salient to evaluating QCA. This article addresses these issues by considering three of the most important kinds of assumptions discussed in the context of regression analysis: assumptions about the correct form of the relationship, missing variables, and inferring causation from association. For each assumption, the role of corresponding assumptions in QCA will be explored and illustrated through an analysis of left-party electoral fortunes in Latin America. Regarding the correct form of causal relationships, QCA in effect builds highly demanding assumptions into measurement procedures. Concerning missing variables, whereas earlier versions of QCA require a strong assumption of no causally relevant missing variables, more recent procedures allow some kinds of missing variables, but build in mutually contradictory statistical assumptions about those variables. Resolving these contradictions essentially converts QCA into an application of regression analysis. Regarding the process of inferring causation from association, QCA makes causal inference on the basis of patterns of association purely by assumption. That is, association is assumed to have a one-to-one relationship with causation. For all three groups of assumptions, QCA is found to require assumptions that are at least as restrictive as those employed in regression analysis.

Singpurwalla, Nozer D., Jane M. Booker, D. V. Lindley, Michael Laviolette, Lotfi A. Zadeh, and A. P. Dempster. 2004. "Membership Functions and Probability Measures of Fuzzy Sets." Journal of the American Statistical Association 99 (467):867-89.

Abstract: The notion of fuzzy sets has proven useful in the context of control theory, pattern recognition, and medical diagnosis. However, it has also spawned the view that classical probability theory is unable to deal with uncertainties in natural language and machine learning, so that alternatives to probability are needed. One such alternative is what is known as "possibility theory." Such alternatives have come into being because past attempts at making fuzzy set theory and probability theory work in concert have been unsuccessful. The purpose of this article is to develop a line of argument that demonstrates that probability theory has a sufficiently rich structure for incorporating fuzzy sets within its framework. Thus probabilities of fuzzy events can be logically induced. The philosophical underpinnings that make this happen are a subjectivistic interpretation of probability, an introduction of Laplace's famous genie, and the mathematics of encoding expert testimony. The benefit of making probability theory work in concert with fuzzy set theory is an ability to deal with different kinds of uncertainties that may arise within the same problem.

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

Abstract: Configurational comparative methods constitute promising methodological tools that narrow the gap between variable-oriented and case-oriented research. Their infancy, however, means that the limits and advantages of these techniques are not clear. Tests on the sensitivity of qualitative comparative analysis (QCA) results have been sparse in previous empirical studies, and so has the provision of guidelines for doing this. Therefore this article uses data from a textbook example to discuss and illustrate various robustness checks of results based on the employment of crisp-set QCA and fuzzy-set QCA. In doing so, it focuses on three issues: the calibration of raw data into set-membership values, the frequency of cases linked to the configurations, and the choice of consistency thresholds. The study emphasizes that robustness tests, using systematic procedures, should be regarded as an important, and maybe even indispensable, analytical step in configurational comparative analysis.

Smithson, Michael. 1987. Fuzzy Set Analysis for Behavioral and Social Sciences. New York: Springer.

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Smithson, Michael. 2005. "Fuzzy Set Inclusion: Linking Fuzzy Set Methods With Mainstream Techniques." Sociological Methods & Research 33 (4):431-61.

Abstract: The concept of set inclusion has remained insufficiently developed in the fuzzy set literature to be of much use to social scientists. However, a fully fledged concept of fuzzy set inclusion, along with appropriate statistical methods for evaluating it, could be very useful in the social sciences. This article combines fuzzy set and statistical methods, in the form of a cumulative distribution-based approach to evaluating fuzzy set inclusion without making strong assumptions about measurement levels. It establishes criteria for distinguishing an "inclusion relation" from independence plus skew as well as from other kinds of relationships. A measure of inclusion is developed that is sensitive to the degree to which individual cases violate a strict inclusion rule. A technique for modeling localized inclusion relations in contingency tables and scatter plots is also presented. Finally, the connections between the fuzzy set approach to set inclusion and mainstream statistical techniques are briefly adumbrated.

Smithson, Michael, and Jay Verkuilen. 2006. Fuzzy Set Theory: Applications in the Social Sciences. London: SAGE.

Abstract: Fuzzy set theory deals with sets or categories whose boundaries are blurry or, in other words, 'fuzzy'. This book presents an accessible introduction to fuzzy set theory, focusing on its applicability to the social sciences. Unlike most books on this topic, "Fuzzy Set Theory" provides a systematic, yet practical guide for researchers wishing to combine fuzzy set theory with standard statistical techniques and model-testing.

Soda, Giuseppe, and Santi Furnari. 2012. "Exploring the Topology of the Plausible: Fs/QCA Counterfactual Analysis and the Plausible Fit of Unobserved Organizational Configurations." Strategic Organization 10 (3):285-96.

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Stockemer, Daniel. 2013. "Fuzzy Set or Fuzzy Logic? Comparing the Value of Qualitative Comparative Analysis (fsQCA) versus Regression Analysis for the Study of Women's Legislative Representation." European Political Science 12 (1):86-101.

Abstract: In this article I compare the results of Qualitative Comparative Analysis (fsQCA) applied to a medium-sized data set on women's legislative representation in Asian and Latin American countries to those of regression analysis based on the same data set. I find that both methods are suboptimal. Explaining the outcome of high women's representation, fsQCA suggests complex configurations of conditions with low empirical coverage and high sensitivity to coding. While, not without shortcomings, OLS regression analysis performs somewhat better than fsQCA. On the one hand, this method identifies two statistically significant and substantively relevant variables (i.e. quota rules and communist regimes), which strongly increase the percentage of women deputies. On the other hand, the model's interpretation is not completely clear cut, as scholars may disagree over the relevance of the one marginally statistically and substantively significant variable, the longevity of democracy.

Tanner, Sean. 2014. "QCA is of Questionable Value for Policy Research." Policy and Society 33 (3):287-98.

Abstract: Qualitative Comparative Analysis (QCA) has been championed as a valuable tool for public policy research. Focusing on the field of policy evaluation, this research note assesses QCA by comparing research that uses this method to studies based on standard practices for quantitative policy analysis. While attention is centrally focused on causal inference, questions of measurement are also addressed. The analysis suggests that QCA adds little value to current methods of policy scholarship, and its contribution in fact falls far short, compared with present-day standard practices. For example, a properly defined "net effects" framework - which is pointedly rejected by QCA - provides valuable insights regarding the causal effects that are a central concern of policy evaluation. By contrast, as an approach to policy analysis, QCA suffers from severe limitations in both its framework and its findings.

Thiem, Alrik. 2013. "Clearly Crisp, and Not Fuzzy: A Reassessment of the (Putative) Pitfalls of Multi-value QCA." Field Methods 25 (2):197-207.

Abstract: In a recent contribution to this journal, Vink and van Vliet seek to raise researchers' awareness of the potentials and pitfalls of multi-value Qualitative Comparative Analysis (MvQCA). The authors are unconvinced by the technique's distinctness from the more established crisp-set QCA (csQCA) and fuzzy-set QCA (fsQCA) variants and question its added value to configurational comparative methodology on five points. This article demonstrates why none of them challenges mvQCA. Two points do not relate to the method, two are based on incorrect reasoning, and one results from a misunderstanding of notational systems. This comment seeks to prove the suspicion against mvQCA that has prevailed thus far in the literature unjustified. It argues that this variant is as useful a contribution to the toolbox of comparative social science methodology as csQCA and fsQCA.

Thiem, Alrik. 2014. "Unifying Configurational Comparative Methods: Generalized-Set Qualitative Comparative Analysis." Sociological Methods & Research 43 (2):313-37.

Abstract: Crisp-set Qualitative Comparative Analysis, fuzzy-set Qualitative Comparative Analysis (fsQCA), and multi-value Qualitative Comparative Analysis (mvQCA) have emerged as distinct variants of QCA, with the latter still being regarded as a technique of doubtful set-theoretic status. Textbooks on configurational comparative methods have emphasized differences rather than commonalities between these variants. This article has two consecutive objectives, both of which focus on commonalities. First, but secondary in importance, it demonstrates that all set types associated with each variant can be combined within the same analysis by introducing a standardized notational system. By implication, any doubts about the set-theoretic status of mvQCA vis-à-vis its two sister variants are removed. Second, but primary in importance and dependent on the first objective, this article introduces the concept of the multivalent fuzzy set variable. This variable type forms the basis of generalized-set Qualitative Comparative Analysis (gsQCA), an approach that integrates the features peculiar to mvQCA and fsQCA into a single framework while retaining routine truth table construction and minimization procedures. Under the concept of the multivalent fuzzy set variable, all existing QCA variants become special cases of gsQCA.

Thiem, Alrik. 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.

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Thiem, Alrik. 2014. "Membership Function Sensitivity of Descriptive Statistics in Fuzzy-Set Relations." International Journal of Social Research Methodology 17 (6):625-42.

Abstract: Fuzzy-set theory has provided researchers with a new perspective on many social-scientific problems. In particular, the method of fuzzy-set Qualitative Comparative Analysis (fsQCA) has gained in popularity across various disciplines. However, while the methodological development of fsQCA has progressed on a number of fronts, sensitivity diagnostics have only recently been put on the agenda. This article analyses how coverage as an important descriptive statistic in fsQCA is influenced by the interaction between membership function form and crossover threshold choice. Depending on the relative location of the latter, changes in the former influence coverage in either a negative or a positive direction, and to different magnitudes. This influence is not uniform but varies in relation to cases' distance from unique peak points. Although the orientation of this article is theoretical, its results have implications for empirical research. Most importantly, the influence of membership functions should become part of routine sensitivity checks.

Thiem, Alrik. 2014. "Navigating the Complexities of Qualitative Comparative Analysis: Case Numbers, Necessity Relations, and Model Ambiguities." Evaluation Review 38 (6):487-513.

Abstract: Background: In recent years, the method of Qualitative Comparative Analysis (QCA) has been enjoying increasing levels of popularity in evaluation and directly neighboring fields. Its holistic approach to causal data analysis resonates with researchers whose theories posit complex conjunctions of conditions and events. However, due to QCA's relative immaturity, some of its technicalities and objectives have not yet been well understood. Objectives: In this article, I seek to raise awareness of six pitfalls of employing QCA with regard to the following three central aspects: case numbers, necessity relations, and model ambiguities. Most importantly, I argue that case numbers are irrelevant to the methodological choice of QCA or any of its variants, that necessity is not as simple a concept as it has been suggested by many methodologists, and that doubt must be cast on the determinacy of virtually all results presented in past QCA research. Method: By means of empirical examples from published articles, I explain the background of these pitfalls and introduce appropriate procedures, partly with reference to current software, that help avoid them. Conclusion: QCA carries great potential for scholars in evaluation and directly neighboring areas interested in the analysis of complex dependencies in configurational data. If users beware of the pitfalls introduced in this article, and if they avoid mechanistic adherence to doubtful "standards of good practice" at this stage of development, then research with QCA will gain in quality, as a result of which a more solid foundation for cumulative knowledge generation and well-informed policy decisions will also be created.

Thiem, Alrik. 2015. "Parameters of Fit and Intermediate Solutions in Multi-Value Qualitative Comparative Analysis." Quality & Quantity 49 (2):657-74.

Abstract: 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.

Thiem, Alrik. 2015. "Using Qualitative Comparative Analysis for Identifying Causal Chains in Configurational Data: A Methodological Commentary on Baumgartner and Epple (2014)." Sociological Methods & Research 44 (4):723-36.

Abstract: In a recent contribution to Sociological Methods & Research, Baumgartner and Epple (B&E) employ Coincidence Analysis (CNA) to explain the outcome of the vote on the Swiss minaret initiative of 2009. Although the authors also present a substantive argument, their principal objective is to prove the superiority of CNA over Qualitative Comparative Analysis (QCA) due to the former's capability of identifying causal chains in configurational data without resort to Quine-McCluskey (QMC) optimization, whereby logical contradictions are allegedly introduced into the latter's minimization process that trivialize the results. In this methodological commentary, I demonstrate that CNA does not challenge QCA per se but merely seeks to find fault with QMC. However, the link between QCA and QMC has never been inextricable, and alternative algorithms not beset by the one-difference restriction B&E consider problematic have long been in use. Hence, it follows that CNA introduces a new algorithm but does not perforce offer a superior method. To support this argument, I showcase the untapped potential of QCA for identifying causal chains in data that even incorporate multivalent factors. In employing the eQMC algorithm, whose general approach to Boolean minimization resembles that of CNA in decisive parts, I extend the authors' original analysis in several directions, without generating logical contradictions along the way. I conclude that future research should continue to explore the methodological implications of the issues which CNA's introduction has raised for QCA. Ultimately, however, the integration of their individual strengths represents one of the most promising avenues for the further development of configurational comparative methods.

Thiem, Alrik. 2016. "Analyzing Multilevel Data with QCA: Yet Another Straightforward Procedure." Quality & Quantity 50 (1):121-8.

Abstract: A significant body of social-scientific literature has developed contextual theories. In a recent contribution to Quality & Quantity, Denk and Lehtinen (Qual Quant 48(6):3475-3487, 2014) present Comparative Multilevel Analysis (CMA) as an innovative method whereby the effects of contexts on outcomes of interest can be studied configurationally if combined with Qualitative Comparative Analysis (QCA). In contradistinction, I argue that CMA is neither innovative in nor necessary for ascertaining the influence of context in a configurational-comparative manner. QCA is appreciably more powerful than the authors acknowledge and provides all required functionality. In repetition of Rohlfing's (Int J Soc Res Methodol 15(6):497-506, 2012) verdict on Denk's (Int J Soc Res Methodol 13(1):29-39, 2010) earlier version of CMA, I conclude that QCA need not be extended in the direction proposed by Denk and Lehtinen. Researchers interested in the contextual analysis of configurational data are well-served by the existing toolbox of QCA.

Thiem, Alrik, and Adrian Duşa. 2012. "Introducing the QCA Package: A Market Analysis and Software Review." Qualitative & Multi-Method Research 10 (2):45-9.

Abstract: The increasing popularity of Qualitative Comparative Analysis (QCA) as a tool for social-scientific inquiry has also led to a proliferation of tailored software. Users now have the choice between three graphical interface (GUI) and three command line interface (CLI) solutions. In this article, we first present a short analysis of the QCA software market, following which we introduce the QCA package for the R environment - a highly versatile CLI - by drawing operational parallels to fs/QCA, the most common GUI software.

Thiem, Alrik, and Adrian Duşa. 2013. Qualitative Comparative Analysis with R: A User's Guide. New York: Springer.

Abstract: Social science theory often builds on sets and their relations. Correlation-based methods of scientific enquiry, however, use linear algebra and are unsuited to analyzing set relations. The development of Qualitative Comparative Analysis (QCA) by Charles Ragin has given social scientists a formal tool for identifying set-theoretic connections based on Boolean algebra. As a result, interest in this method has markedly risen among social scientists in recent years. This book offers the first complete introduction on how to perform QCA in the R software environment for statistical computing and graphics with the QCA package. Developed as a comprehensive solution, QCA provides an unprecedented scope of functionality for analyzing crisp, multi-value and fuzzy sets. The reader is not required to have knowledge of R, but the book assumes an understanding of the fundamentals of QCA. Using examples from published work, the authors demonstrate how to make the most of QCA's wide-ranging capabilities for the reader's own purposes. Although mainly written for political scientists, this book is also of interest to scholars from other disciplines in the social sciences such as sociology, business, management, organization, anthropology, education and health.

Thiem, Alrik, and Adrian Duşa. 2013. "QCA: A Package for Qualitative Comparative Analysis." The R Journal 5 (1):87-97.

Abstract: We present QCA, a package for performing Qualitative Comparative Analysis (QCA). QCA is becoming increasingly popular with social scientists, but none of the existing software alternatives covers the full range of core procedures. This gap is now filled by QCA. After a mapping of the method's diffusion, we introduce some of the package's main capabilities, including the calibration of crisp and fuzzy sets, the analysis of necessity relations, the construction of truth tables and the derivation of complex, parsimonious and intermediate solutions.

Thiem, Alrik, and Adrian Duşa. 2013. "Boolean Minimization in Social Science Research: A Review of Current Software for Qualitative Comparative Analysis (QCA)." Social Science Computer Review 31 (4):505-21.

Abstract: Besides an increase in the number of empirical applications, the widening landscape of tailored computer programs attests to the success of qualitative comparative analysis (QCA) as a social research method. Users now have the choice between three graphical user interface (GUI) and three command line interface (CLI) solutions. In addition to different functional foci, each program possesses several technical particularities, some of which the vast majority of end users remain unaware of. Since these particularities may influence results and in turn substantive conclusions, this review is a timely undertaking. More specifically, we compare the two most common GUIs fs/QCA and Tosmana as well as the CLI QCA. By reanalyzing data from a sociological study on rural grassroots associations in Norway, major differences and similarities with respect to truth table construction, minimization algorithms, and prime implicant chart management are illustrated.

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

Abstract: Sensitivity diagnostics has recently been put high on the agenda of methodological research into Qualitative Comparative Analysis (QCA). Existing studies in this area rely on the technique of exhaustive enumeration, and the majority of works examine the reactivity of QCA either only to alterations in discretionary parameter values or only to data quality. In this article, we introduce the technique of combinatorial computation for evaluating the interaction effects between two problems afflicting data quality and two discretionary parameters on the stability of QCA reference solutions. In this connection, we challenge a hitherto unstated assumption intrinsic to exhaustive enumeration, show that combinatorial computation permits the formulation of general laws of sensitivity in QCA, and demonstrate that our technique is most efficient.

Thomson, Stephanie L. 2011. "The Problem of Limited Diversity in Qualitative Comparative Analysis: A Discussion of Two Proposed Solutions." International Journal of Multiple Research Approaches 5 (2):254-68.

Abstract: I use data from the 1980 survey of the British 1970 Birth Cohort Study (BCS70; N = 1,890) and the case-based, set theoretic method qualitative comparative analysis (QCA) to assess to what extent maternal interest in education is sufficient for high attainment in mathematics for 1890 cases. Specifically, I examine whether maternal interest is sufficient only for children of certain social classes and a particular sex. I use QCA because it assumes that ?multiple conjunctural causation? is at work rather than an average effect of one variable across all cases (Ragin, 2000, p. 104). This allows us to explore which combinations of factors - or configurations - consistently achieve the outcome and, hence, account for factors whose effects are a function of other factors in the configuration (Cooper & Glaesser, 2008). During the analysis, I encounter limited diversity in the data and explore two approaches that claim to allow the analysis to continue even when limited diversity is present. In the first of these analyses, the counterfactual method, the researcher uses existing theory to check the plausibility of results where there is limited empirical support. In the second approach, the two-stage method, a preliminary analysis is performed and, based on those results, factors are removed from the model and, hence, the complexity of the model is reduced. I argue, here, that the counterfactual method is preferable to the two-stage method because the two-stage method might distort findings and make them overly simplistic. I then demonstrate the difference in results when the two approaches are applied to these same data.

Vanderborght, Yannick, and Sakura Yamasaki. 2004. "Des Cas Logiques... Contradictoires? Un Piège de l'AQQC Déjoué à travers l'étude de la Faisabilité Politique de l'Allocation Universelle." Revue Internationale de Politique Comparée 11 (1):51-66.

Abstract: L'objectif de cet article est double. D'une part, il vise à analyser les facteurs susceptibles d'influencer la faisabilité politique d'une Allocation Universelle. Nous observons, de façon surprenante, que sa visibilité publique est négativement associée à sa présence sur l'agenda politique. D'autre part, nous mettons en évidence un piège méthodologique de l'AQQC, très rarement traité bien qu'à l'origine de résultats incorrects: le problème des hypothèses simplificatrices contradictoires. Différentes manières de résoudre ce problème sont suggérées, et nous concluons en insistant sur l'importance d'un dialogue entre cas et théorie.

Verkuilen, Jay. 2005. "Assigning Membership in a Fuzzy Set Analysis." Sociological Methods & Research 33 (4):462-96.

Abstract: This article provides a largely nontechnical discussion of the acquisition of membership values in fuzzy set analyses. First the basic properties of a membership are discussed. Then the three common strategies of membership assignment - direct subjective assignment, indirect subjective assignment, and transformation - are critically examined in turn. Examples are used to illustrate the techniques. The connection with existing psychometric and statistical methods is particularly emphasized, focusing on the notion of a membership value as a random variable as a means to assess uncertainty in assignment.

Viertl, Reinhard, and Dietmar Hareter. 2006. Beschreibung und Analyse unscharfer Information: Statistische Methoden für unscharfe Daten. Wien: Springer.

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Vink, Maarten P., and Olaf van Vliet. 2013. "Potentials and Pitfalls of Multi-value QCA: Response to Thiem." Field Methods 25 (2):208-13.

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Vink, Maarten P., and Olaf van Vliet. 2009. "Not Quite Crisp, Not Yet Fuzzy? Assessing the Potentials and Pitfalls of Multi-value QCA." Field Methods 21 (3):265-89.

Abstract: This article assesses the strengths and shortcomings multi-value qualitative comparative analysis (mvQCA), a comparative technique for small- to medium-sized data sets that has been integrated in the TOSMANA software developed by Lasse Cronqvist. The main difference with "crisp-set" QCA is that in mvQCA, the conditions can have more values than just the Boolean values 0 and 1, whereas the main difference with "fuzzy-set" QCA is that mvQCA conditions remain discrete. The major advantage of nondichotomous categorization, according to its proponents, is that it reduces the likelihood of contradictory configurations because of a more homogeneous grouping of cases. We give an overview of existing mvQCA applications, with a detailed discussion of two recent publications, and argue that crisp-set and fuzzy-set alternatives should be less easily discarded. as the mvQCA solution conies with substantial set-theoretical costs.

Vis, Barbara. 2012. "The Comparative Advantages of fsQCA and Regression Analysis for Moderately Large-N Analyses." Sociological Methods & Research 41 (1):168-98.

Abstract: This article contributes to the literature on comparative methods in the social sciences by assessing the strengths and weaknesses of regression analysis and fuzzy-set qualitative comparative analysis (fsQCA) for studies with a moderately large-n (between approximately 50 and 100). Moderately large-n studies are interesting in this respect since they allow for regression analysis as well as fsQCA analysis. These two approaches have a different epistemological foundation and thereby answer different, yet related, research questions. To illustrate the comparison of fsQCA and regression analysis empirically, I use a recent data set (n = 53) that includes data on the conditions under which governments in Western democracies increase their spending on active labor market policies (ALMPs). This comparison demonstrates that while each approach has merits and demerits, fsQCA leads to a fuller understanding of the conditions under which the outcome occurs.

Wagemann, Claudius, and Carsten Q. Schneider. 2010. "Qualitative Comparative Analysis (QCA) and Fuzzy-Sets: Agenda for a Research Approach and a Data Analysis Technique." Comparative Sociology 9 (3):376-96.

Abstract: "Qualitative Comparative Analysis" (QCA) is an increasingly applied methodological tool in comparative social sciences. It is well suited for the analysis of causally complex claims framed in terms of necessity and sufficiency. This article presents the epistemology of QCA and discusses its applicability to social science research questions. It also illustrates some of the features that have recently been added to this set of methodological tools. This article is best read in close conjunction with Schneider and Wagemann's "Standards of Good QCA Practice," the next paper in this journal issue.

Wagemann, Claudius, and Carsten Q. Schneider. 2015. "Transparency Standards in Qualitative Comparative Analysis." Qualitative & Multi-Method Research 13 (1):38-42.

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Yamasaki, Sakura, and Benoît Rihoux. 2009. "A Commented Review of Applications." In Configurational Comparative Methods: Qualitative Comparative Analysis (QCA) and Related Techniques, ed. B. Rihoux and C. C. Ragin. London: Sage Publications. pp. 123-45.

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Yamasaki, Sakura, and Astrid Spreitzer. 2006. "Beyond Methodological Tenets: The Worlds of QCA and SNA and their Benefits to Policy Analysis." In Innovative Comparative Methods for Policy Analysis: Beyond the Quantitative-Qualitative Divide, eds. B. Rihoux and H. Grimm. New York: Springer Science+Business Media. pp. 96-120.

1.Paragraph: The aim of this study is to present combinations of Social Network Analysis (SNA) and Qualitative Comparative Analysis (QCA) and their benefit to Policy Analysis. We think that QCA and SNA are particularly suited to explain complex meso- or macro-social phenomena, just like policies. SNA gives access to a set of actors (individuals, groups, organizations, etc.) and allows to quantitatively measure and to visualize the relationships between these actors. The main goal is to model these relationships in order to study action and structure in their mutual dependence (Wasserman and Faust 1997). QCA on the other hand helps to uncover regularities across cases while maintaining within-case complexity; its strength lies on its ability to reduce complexity without loosing the analytical insights, a feature complemented by formalized "multiple conjunctural explanations" (Ragin 1987, 2003a). We first expose our understanding of Policy Analysis followed by the main challenges that research on the topic faces. We then explain why we think that SNA and QCA can answer these issues. As such, we shed some light on the main principles of the methods, and the main points for which they appear as supplementing to each other. Finally, we illustrate our arguments through two combinations of SNA and QCA applied to the field of Policy Analysis. We conclude on the main benefits as well as limitations of a combinatorial approach of the two methods vis-a-vis Policy Analysis.

Zadeh, Lofti A. 1965. "Fuzzy Sets." Information and Control 8 (3):338-53.

Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.

Zadeh, Lofti A. 1978. "Fuzzy Sets as a Basis for a Theory of Possibility." Fuzzy Sets and Systems 1 (1):3-28.

Abstract: The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable. More specifically, if F is a fuzzy subset of a universe of discourse U = {u} which is characterized by its membership function [mu]F, then a proposition of the form "X is F", where X is a variable taking values in U, induces a possibility distribution which equates the possibility of X taking the value u to [mu]F(u)--the compatibility of u with F. In this way, X becomes a fuzzy variable which is associated with the possibility distribution in much the same way as a random variable is associated with a probability distribution. In general, a variable may be associated both with a possibility distribution and a probability distribution, with the weak connection between the two expressed as the possibility/probability consistency principle. A thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is, in the main, possibilistic rather than probabilistic in nature. Thus, by employing the concept of a possibility distribution, a proposition, p, in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p. Several types of conditional translation rules are discussed and, in particular, a translation rule for propositions of the form "X is F is [alpha]-possible", where [alpha] is a number in the interval [0,1], is formulated and illustrated by examples.


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