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CORA (Combinational Regularity Analysis) is a significant advancement over QCA (Thiem 2022). First and most importantly, CORA can analyze multiple outcomes as well as the conjunctions of these outcomes simultaneously (Thiem et al. 2022), even with multi-value variables (Mkrtchyan et al. 2023). To this end, CORA generalizes the INUS Theory from the level of single outcomes to entire systems of outcomes. In this way, not only can the causes of individual effects be found, but also the causes of all possible combinations of these effects (e.g., x, y, z, xy, xz, yz, xyz), some of which may be shared. A classical example where such analytical capabilities are needed is the problem of multi-morbidity in medicine and psychology (Suls and Green 2019). But in every other situation in which it is expected that the cause of a complex effect is not simply the sum of the causes of each isolated effect does CORA provide a suitable method if the goal is to analyze the data from a configurational perspective.

A second difference to QCA is that CORA can explicitly address the problem of model ambiguity by a data-mining approach that progresses through tuple-selections of exogenous factors. The idea behind this approach is that any explanatory model that is found with any number of exogenous factors will, ceteris paribus, also always be found in an analysis with only those factors involved in this model. More precisely, if CORA cannot identify a fitting model with some set of combinations of factors, it adds one more factor to this set. From this perspective, the approach represents a type of Occam’s Razor, which says that explanations that involve fewer variables are, ceteris paribus, to be preferred over explanations that are more complex.

Third, CORA is the only configurational method to date that offers a consistent and effective way of visualizing solutions. To do so, it draws on logic diagrams (Thiem et al. 2023). Logic diagrams are well-established tools in electrical engineering for representing switching circuits, and for many prominent researchers in the area of causal inference, they “capture … the very essence of causation” (Pearl 2009: 415). The standardized form of logic diagrams offered by CORA are referred to as logigrams. All the above-mentioned features of CORA are available in the open source Python software duo of CORA and LOGIGRAM (Sebechlebská et al. 2023) Overall, CORA's advantages over QCA are numerous:

  • CORA has a clearly defined search target (generalized INUS structures)
  • CORA is solidly anchored in Boolean/Post algebra and logic
  • CORA can analyze shared causes of complex effects as well as individual causes simultaneously
  • CORA offers a data-mining approach to variable selection
  • CORA includes an in-built visualization module for logic diagrams
  • CORA is not affected by any of QCA's problems relating to logical remainders
  • CORA offers multiple optimization algorithms for different data situations
  • CORA is available via a fully open-source software package hosted and maintained on GitHub 

CORA can be launched from its GitHub site. Just click on the "Open in Colab" button under the heading "Google Colab". A dedicated series of software video tutorials will be released soon.



  • Mkrtchyan, Lusine, Alrik Thiem, and Zuzana Sebechlebská. 2023. "Re-Establishing a Lost Connection: Multi-Value Logic in Causal Data Analysis in Social Science Disciplines." IEEE Access 11:10471-82. Link
  • Pearl, Judea. 2009. Causality: Models, Reasoning, and Inference. 2nd ed. Cambridge: Cambridge University Press.
  • Sebechlebská, Zuzana, Lusine Mkrtchyan, and Alrik Thiem. 2023. CORA and LOGIGRAM: A Duo of Python Packages for Combinational Regularity Analysis (CORA). JOSS: The Journal of Open Source Software 8 (85):5019. Link 
  • Suls, Jerry, and Paige A. Green. 2019. "Multimorbidity in health psychology and behavioral medicine." Health Psychology 38 (9):769-71.
  • Thiem, Alrik. 2022. "Qualitative Comparative Analysis (QCA)." In Handbook of Research Methods in International Relations, ed. R. J. Huddleston, T. Jamieson and P. James. Cheltenham: Edward Elgar. Link
  • Thiem, Alrik, Lusine Mkrtchyan, and Zuzana Sebechlebská. 2022. "Combinational Regularity Analysis (CORA) — a new method for uncovering complex causation in medical and health research." BMC Medical Research Methodology 22 (1):333Link
  • Thiem, Alrik, Zuzana Sebechlebská, and Lusine Mkrtchyan. 2023. "Logic diagrams: A visual tool with untapped potential." Nature Reviews Methods Primers 3 (1):21Link

Screenshots of CORA





QCApro is my successor package to the QCA package (Dusa & Thiem 2014; Thiem & Dusa 2012; 2013a; 2013b; 2013c). Just like QCAQCApro implements the method of Qualitative Comparative Analysis (QCA)—a family of techniques for analyzing configurational data in accordance with the INUS theory of causation (Baumgartner 2008; Graßhoff & May 2001; Mackie 1965; 1974), but it has fixed various technical and methodological problems of the QCA package, it includes many new features and enhancements for applying QCA, and it provides several purpose-built functions for testing general methodological properties of QCA and for evaluating several procedures suggested in the QCA literature such as Schneider and Wagemann's (2013) Enhanced Standard Analysis or Lucas and Szatrowski's (2014) test for confirmation bias. Here are some of the most important advantages of QCApro:

  • full functionality for csQCA, mvQCA and fsQCA
  • only software for QCA that standardly implements an objective function suitable for causal data analysis
  • fast minimization algorithm with many possibilities for discretionary parameter-setting
  • sophisticated calibration procedures for fuzzy sets (e.g., linear, quadratic, logistic)
  • extensive set of functions for methodological evaluations, robustness diagnostics and sensitivity tests
  • includes a comprehensive glossary for Configurational Comparative Methods
  • includes several data sets from various research areas for easier familiarization
  • many working examples provided in documentation

If you make use of the QCApro package in your work, please acknowledge it in the interest of good scientific practice and transparency. The appropriate citation displays on loading the package or by using the command citation(package = "QCApro") after having loaded the package. The aforesaid command also provides a suitable BibTeX entry for LaTeX users. To browse the latest news about QCApro (bug fixes, enhancements, etc.), enter news(package = "QCApro").

You can either download the package you need from this website and install it from a local folder or you can install the package directly from with R or your R editor via the Comprehensive R Archive Network (see also the CRAN website of QCApro). 

Happy QCAing!


Important note: QCApro and QCA are two entirely different packages, but both have been developed on the basis of QCA 1.1-4 (because QCA 1.1-4 has been removed from CRAN, I have provided the source file below). Between versions 2.0 and 2.4, the QCA package had been demoted by its maintainer Adrian Duşa from a stand-alone package to a gateway package for another package called QCAGUI, to which all material from QCA 1.1-4 was transferred, so that users who updated or installed the QCA package in fact installed QCAGUI through the back door. As of version 2.5, all material was moved back again from QCAGUI to the QCA package, and the QCAGUI package has now been made obsolete.

When loading QCA or an old version of QCAGUI into an R session, and you also have QCApro installed, you are asked by QCA to uninstall QCApro from your computer in order to avoid conflicts. Of course, you need not uninstall QCApro, but you should not have loaded QCA/QCAGUI and QCApro in one and the same R session as this may cause problems.

Note also that QCA3 by Ronggui Huang is yet another R package for QCA that is unrelated to QCA, QCApro or QCAGUI. In March 2017, QCA3 was removed from the CRAN repository since it is no longer updated.


Downloads for Microsoft Windows users (binary zip files)

Downloads for Mac OS users (binary tgz files)

Sources (tar.gz files)



  • Baumgartner, Michael. 2008. "Regularity theories reassessed." Philosophia 36 (3):327-54. Link.
  • Dusa, Adrian, and Alrik Thiem. 2014. QCA: A package for Qualitative Comparative Analysis. R package version 1.1-4. URL: http://www.alrik-thiem.net/software/.
  • Graßhoff, Gerd, and Michael May. 2001. "Causal Regularities." In Current Issues in Causation, eds. Wolfgang Spohn, Marion Ledwig and Michael Esfeld. Münster: Mentis, pp.85-113.
  • Lucas, Samuel R., and Alisa Szatrowski. 2014. "Qualitative Comparative Analysis in critical perspective." Sociological Methodology 44 (1):1-79. Link.
  • Mackie, John L. 1965. “Causes and conditions.” American Philosophical Quarterly 2 (4):245-64. Link.
  • Mackie, John L. 1974. The cement of the universe: A study of causation. Oxford: Oxford University Press.
  • Schneider, Carsten Q., and Claudius Wagemann. 2013. "Doing justice to logical remainders in QCA: Moving beyond the standard analysis." Political Research Quarterly 66 (1):211-20. Link.
  • Thiem, Alrik, and Adrian Dusa. 2012. "Introducing the QCA package: A market analysis and software review.” Qualitative & Multi-Method Research 10 (2):45-9. Link.
  • Thiem, Alrik, and Adrian Dusa. 2013a. “Boolean minimization in social science research: A review of current software for Qualitative Comparative Analysis (QCA).” Social Science Computer Review 31 (4):505-21. Link.
  • Thiem, Alrik, and Adrian Dusa. 2013b. “QCA: A package for Qualitative Comparative Analysis.” The R Journal 5 (1):87-97. Link.
  • Thiem, Alrik, and Adrian Dusa. 2013c. Qualitative Comparative Analysis with R: A user's guide. New York: Springer. Link.


Screenshots of QCApro