Coincidence Analysis (CNA) is a configurational comparative method of causal data analysis that was first introduced for crisp-set (i.e. binary) data in Baumgartner (2009a, 2009b, 2013) and generalized for multi-value and fuzzy-set data in Baumgartner and Ambuehl (2020). The cna package implements the method's latest stage of development.
CNA infers causal structures as defined by modern variants of the so-called INUS-theory (Mackie 1974; Grasshoff and May 2001; Baumgartner and Falk 2019) from empirical data. The INUS-theory is a type-level difference-making theory that spells out causation in terms of redundancy-free Boolean dependency structures. It is optimally suited for the anaylsis of causal structures with the following features: conjunctivity—causes are arranged in complex bundles that only become operative when all of their components are properly co-instantiated, each of which in isolation is ineffective or leads to different outcomes—and disjunctivity—effects can be brought about along alternative causal routes such that, when suppressing one route, the effect may still be produced via another one.
Causal structures featuring conjunctivity and disjunctivity pose severe challenges for
methods of causal data analysis. As many theories of causation (other than the INUS-theory) entail that it is necessary (though not sufficient) for X to be a cause of Y that there be some kind of dependence (e.g. probabilistic or counterfactual) between X and Y, standard methods (e.g. Spirtes et al. 2000) infer that X is not a cause of Y if X and Y are not pairwise dependent.
Howeover, there often are no dependencies between an individual component X of a conjunctive cause and the corresponding effect Y (for concrete examples see the package vignette (accessed from R by typing
vignette("cna")). In the absence of pairwise dependencies, X can only be identified as a cause of Y if it is embedded in a complex Boolean structure over many factors and that structure is fitted to the data as a whole. But the space of Boolean functions over even a handful of factors is vast. So, a method for INUS-discovery must find ways to efficiently navigate in that vast space of possibilities. That is the purpose of CNA.
CNA is not the only method for the discovery of INUS structures. Other methods that can be used for that purpose are Logic Regression (Ruczinski et al. 2003, Kooperberg and Ruczinski 2005), which is implemented in the R package LogicReg, and Qualitative Comparative Analysis (Ragin 1987; 2008; Cronqvist and Berg-Schlosser 2009), whose most powerful implementations are provided by the R packages QCApro and QCA. But CNA is the only method of its kind that can process data generated by causal structures with more than one outcome and, hence, can analyze common-cause and causal chain structures as well as causal cycles and feedbacks. Moreover, unlike the models produced by Logic Regression or Qualitative Comparative Analysis, CNA's models are guaranteed to be redundancy-free, which makes them directly causally interpretable in terms of the INUS-theory; and CNA is more successful than any other method at exhaustively uncovering all INUS models that fit the data equally well. For comparisons of CNA with Qualitative Comparative Analysis and Logic Regression see (Baumgartner and Ambuehl 2020) and (Baumgartner and Falk 2021), respectively.
There exist two additional R packages for data analysis with CNA: cnaOpt, which systematizes the search for optimally fitting CNA models, and frscore, which automatizes robustness scoring of CNA models.
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Department of Philosophy
University of Bergen
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Baumgartner, Michael. 2009b. “Uncovering Deterministic Causal Structures: A Boolean Approach.” Synthese 170(1):71-96.
Baumgartner, Michael. 2013. “Detecting Causal Chains in Small-n Data.” Field Methods 25 (1):3-24.
Baumgartner, Michael and Mathias Ambuehl. 2020. “Causal Modeling with Multi-Value and Fuzzy-Set Coincidence Analysis.” Political Science Research and Methods. 8:526-542.
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Ragin, Charles C. 1987. The Comparative Method. Berkeley: University of California Press.
Ragin, Charles C. 2008. Redesigning Social Inquiry: Fuzzy Sets and Beyond. Chicago: University of Chicago Press.
Ruczinski, Ingo, Charles Kooperberg, and Michael LeBlanc. 2003. “Logic Regression”. Journal of Computational and Graphical Statistics 12:475-511.
Spirtes Peter, Clark Glymour, and Richard Scheines. 2000. “Causation, Prediction, and Search.” 2 edition. MIT Press, Cambridge.
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