Combinational regularity analysis (CORA): An introduction for psychologists.

BackgroundModern configurational comparative methods (CCMs) of causal inference, such as Qualitative Comparative Analysis (QCA) and Coincidence Analysis (CNA), have started to make inroads into medical and health research over the last decade. At the same time, these methods remain unable to process data on multi-morbidity, a situation in which at least two chronic conditions are simultaneously present. Such data require the capability to analyze complex effects. Against a background of fast-growing numbers of patients with multi-morbid diagnoses, we present a new member of the family of CCMs with which multiple conditions and their complex conjunctions can be analyzed: Combinational Regularity Analysis (CORA).MethodsThe technical heart of CORA consists of algorithms that have originally been developed in electrical engineering for the analysis of multi-output switching circuits. We have adapted these algorithms for purposes of configurational data analysis. To demonstrate CORA, we provide several example applications, both with simulated and empirical data, by means of the eponymous software package CORA. Also included in CORA is the possibility to mine configurational data and to visualize results via logic diagrams.ResultsFor simple single-condition analyses, CORA’s solution is identical with that of QCA or CNA. However, analyses of multiple conditions with CORA differ in important respects from analyses with QCA or CNA. Most importantly, CORA is presently the only configurational method able to simultaneously explain individual conditions as well as complex conjunctions of conditions.ConclusionsThrough CORA, problems of multi-morbidity in particular, and configurational analyses of complex effects in general, come into the analytical reach of CCMs. Future research aims to further broaden and enhance CORA’s capabilities for refining such analyses.

This study assesses the extent to which the two main Configurational Comparative Methods (CCMs), i.e. Qualitative Comparative Analysis (QCA) and Coincidence Analysis (CNA), produce different models. It further explains how this non-identity is due to the different algorithms upon which both methods are based, namely QCA’s Quine–McCluskey algorithm and the CNA algorithm. I offer an overview of the fundamental differences between QCA and CNA and demonstrate both underlying algorithms on three data sets of ascending proximity to real-world data. Subsequent simulation studies in scenarios of varying sample sizes and degrees of noise in the data show high overall ratios of non-identity between the QCA parsimonious solution and the CNA atomic solution for varying analytical choices, i.e. different consistency and coverage threshold values and ways to derive QCA’s parsimonious solution. Clarity on the contrasts between the two methods is supposed to enable scholars to make more informed decisions on their methodological approaches, enhance their understanding of what is happening behind the results generated by the software packages, and better navigate the interpretation of results. Clarity on the non-identity between the underlying algorithms and their consequences for the results is supposed to provide a basis for a methodological discussion about which method and which variants thereof are more successful in deriving which search target.

The ongoing debate within Configurational Comparative Methods (CCMs) primarily revolves around how different solution types are derived and interpreted. While Qualitative Comparative Analysis (QCA) generates three types of solutions (conservative, parsimonious, and intermediate), Coincidence Analysis (CNA) produces only one. This difference has fueled discussions regarding their respective methodological strengths and limitations. This paper aims to clarify fundamental misconceptions surrounding QCA, particularly in relation to CNA. It critically examines the role of sufficiency, necessity, and the implications of different minimization approaches. By addressing key misinterpretations (such as the assumption-free nature of certain solutions and the role of counterfactuals) this paper provides a structured comparison of QCA and CNA. Additionally, it highlights the methodological trade-offs involved in prioritizing either robust sufficiency or redundancy-free models. The paper concludes with recommendations for researchers in CCMs, aiming to foster a more precise understanding of these methods and their appropriate applications.

This special issue addresses questions of causality and validity of different solution types in configurational comparative methods (CCMs). First, what main parameters characterize the debate about correct causal interpretation of solution types? Second, to what extent has this debate been linked to a theory of causation? The special issue contribution by Mahoney and Acosta bases qualitative comparative analysis (QCA) within a regularity theory of causation integrating type-level inferences and counterfactual cases. Swiatczak clarifies how the different algorithms underlying QCA and Coincidence Analysis (CNA) produce non-identical models. Baumgartner defines and benchmarks QCA solution types against the search target of minimal robust sufficiency. Alamos-Concha et al. identify the conservative solution as most appropriate for a multimethod design combining a counterfactual causal understanding at the cross-case level with an in-depth mechanistic explanation at the within-case level. Finally, Mahoney and Owen develop a general set-theoretic framework for the study of necessity and sufficiency in quantitative research using a counterfactual understanding of causality. Our introduction reviews the state of the art, identifies current limitations and open questions regarding the theoretical basis for causal interpretation of QCA solutions.

The one-day workshop[b] [/b]provides a comprehensive overview of the current landscape of all three modern Configurational Comparative Methods (CCMs): Qualitative Comparative Analysis (QCA), Coincidence Analysis (CNA) and Combinational Regularity Analysis (CORA). The workshop will enhance participants' understanding of the commonalities and differences between these three CCMs and equip them with the knowledge to make an informed decision on which method to employ for their research, and the basic skills required to apply QCA, CNA and CORA. An official Instats certificate of completion and 1 ECTS Equivalent point are provided at the seminar's conclusion.

The one-day workshop[b] [/b]provides a comprehensive overview of the current landscape of all three modern Configurational Comparative Methods (CCMs): Qualitative Comparative Analysis (QCA), Coincidence Analysis (CNA) and Combinational Regularity Analysis (CORA). The workshop will enhance participants' understanding of the commonalities and differences between these three CCMs and equip them with the knowledge to make an informed decision on which method to employ for their research, and the basic skills required to apply QCA, CNA and CORA. An official Instats certificate of completion and 1 ECTS Equivalent point are provided at the seminar's conclusion.

Qualitative Comparative Analysis (QCA) is a configurational comparative method that is still hotly debated among scholars. Nonetheless, the method has made major inroads into the field of International Relations. The present chapter has three main goals. First, it argues that QCA can add significantly to our accumulation of knowledge about cause-effect relations. Second, using an existing study on contributions to military missions of the European Union, it demonstrates the functionality and workings of QCA in order to give applied researchers concrete technical guidance on how to employ the method correctly. Third and last, the chapter briefly introduces Coincidence Analysis (CNA) and Combinational Regularity Analysis (CORA) – two more recent configurational methods that have solved many of the methodological and technical problems QCA still remains affected by.

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.

Qualitative Comparative Analysis (QCA) was launched in the late 1980s by Charles Ragin, as a research approach bridging case-oriented and variable-oriented perspectives. It conceives cases as complex combinations of attributes (i.e. configurations), is designed to process multiple cases, and enables one to identify, through minimization algorithms, the core equifinal combinations of conditions leading to an outcome of interest. It systematizes the analysis in terms of necessity and sufficiency, models social reality in terms of set-theoretic relations, and provides powerful logical tools for complexity reduction. It initially came along with one technique, crisp-set QCA (csQCA), requiring dichotomized coding of data. As it has expanded, the QCA field has been enriched by new techniques such as multi-value QCA (mvQCA) and especially fuzzy-set QCA (fsQCA), both of which enable finer-grained calibration. It has also developed further with diverse extensions and more advanced designs, including mixed- and multimethod designs in which QCA is sequenced with focused case studies or with statistical analyses. QCA’s emphasis on causal complexity makes it very fit to address various types of objects and research questions touching upon political decision making—and indeed QCA has been applied in multiple related social scientific fields. While QCA can be exploited in different ways, it is most frequently used for theory evaluation purposes, with a streamlined protocol including a sequence of core operations and good practices. Several reliable software options are also available to implement the core of the QCA procedure. However, given QCA’s case-based foundation, much researcher input is still required at different stages. As it has further developed, QCA has been subject to fierce criticism, especially from a mainstream statistical perspective. This has stimulated further innovations and refinements, in particular in terms of parameters of fit and robustness tests which also correspond to the growth of QCA applications in larger-n designs. Altogether the field has diversified and broadened, and different users may exploit QCA in various ways, from smaller-n case-oriented uses to larger-n more analytic uses, and following different epistemological positions regarding causal claims. This broader field can therefore be labeled as that of both “Configurational Comparative Methods” (CCMs) and “Set-Theoretic Methods” (STMs).

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.

To date, hundreds of researchers have employed the method of Qualitative Comparative Analysis (QCA) for the purpose of causal inference. In a recent series of simulation studies, however, several authors have questioned the correctness of QCA in this connection. Some prominent representatives of the method have replied in turn that simulations with artificial data are unsuited for assessing QCA. We take issue with either position in this impasse. On the one hand, we argue that data-driven evaluations of the correctness of a procedure of causal inference require artificial data. On the other hand, we prove all previous attempts in this direction to have been defective. For the first time in the literature on configurational comparative methods, we lay out a set of formal criteria for an adequate evaluation of QCA before implementing a battery of inverse-search trials to test how this method performs in different recovery contexts according to these criteria. While our results indicate that QCA is correct when generating the parsimonious solution type, they also demonstrate that the method is incorrect when generating the conservative and intermediate solution type. In consequence, researchers using QCA for causal inference, particularly in human-sensitive areas such as public health and medicine, should immediately discontinue employing the method’s conservative and intermediate search strategies.

Configurational Comparative Methods: Qualitative Comparative Analysis (QCA) and Related Techniques, Benoit Rihoux and Charles Ragin, eds., Thousand Oaks CA: Sage Publications, 2009, pp. xxv, 209. - Volume 44 Issue 3

Modern Configurational Comparative Methods (CCMs), such as Qualitative Comparative Analysis (QCA) and Coincidence Analysis (CNA), have gained in popularity among social scientists over the last thirty years. A new CCM called Combinational Regularity Analysis (CORA) has recently joined this family of methods. In this article, we provide a software tutorial for the open-source package CORA, which implements the eponymous method. In particular, we demonstrate how to use CORA to discover shared causes of complex effects and how to interpret corresponding solutions correctly, how to mine configurational data to identify minimum-size tuples of solution-generating inputs, and how to visualize solutions by means of logic diagrams.

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.

Configurational Comparative Methods (CCMs), also called ‘set-theoretic’ methods, is a broad and encompassing label that embraces crisp-set and fuzzy-set Qualitative Comparative Analysis (QCA) as well as some alternative techniques. All CCM-related techniques conceive cases as configurations of attributes and are geared towards systematic cross-case analysis. QCA represents both a distinctive research approach, with its own aims and set of assumptions, and an umbrella term for specific techniques such as fuzzy-set QCA (fsQCA), which will be the focus of this chapter (Ragin, 2000, 2008a; Rihoux and Ragin, 2009; Schneider and Wagemann, 2012; Thiem and Dusa, 2013). In Ragin’s seminal book (1987), the CCM approach was launched by the development of a new technique in which investigation was based on grouping dichotomous cases, crisp-set QCA (csQCA). It was later developed into fsQCA and other related techniques. The comparative essence of QCA stems from the fact that it was initially geared towards the analysis of multiple cases in a small- and intermediate-N research design (Marx et al., 2013). Ragin’s motivation (1987, 1997) was to develop a ‘synthetic strategy’ as a middle way between the case-oriented (or ‘qualitative’) and the variable-oriented (or ‘quantitative’) approaches. According to Ragin, this middle way would ‘integrate the best features of the case-oriented approach with the best features of the variable-oriented approach’ (Ragin, 1987: p. 84).KeywordsTruth TableQualitative Comparative AnalysisCausal PathPermissive RegulationMembership ScoreThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.