Description Details Author(s) References

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—most notably Bayesian network methods (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 manuscript), respectively.

The main changes in versions 3.1 and 3.2 of the cna package concern improved processing of high-dimensional data and automatic detection of the data type. The exhaustive analysis of data with more than 20 factors has been improved by avoiding the construction of complete configuration tables whenever possible. To illustrate the resulting performance increase, a high-dimensional data example `d.highdim`

has been added to the package.
Moreover, all relevant functions now automatically detect whether the processed data are of type crisp-set, multi-value or fuzzy-set. Also, the causal `ordering`

can newly be specified as a character string in `cna()`

, an argument `outcome`

has been added to `cna()`

, and a new argument `maxVarNum`

to `randomAsf()`

and `randomCsf()`

.
The package vignette (`vignette("cna")`

), which presents the theoretical background of CNA and introduces to causal modeling with cna, has been updated accordingly.

Package: | cna |

Type: | Package |

Version: | 3.2.0 |

Date: | 2021-06-14 |

License: | GPL (>= 2) |

**Authors**:

Mathias Ambuehl

mathias.ambuehl@consultag.ch

Michael Baumgartner

Department of Philosophy

University of Bergen

michael.baumgartner@uib.no

**Maintainer**:

Mathias Ambuehl

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

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.

doi:10.1017/psrm.2018.45.

Baumgartner, Michael and Christoph Falk. 2019. “Boolean Difference-Making: A Modern Regularity Theory of Causation”. *The British Journal for the Philosophy of Science*.

doi:10.1093/bjps/axz047.

Baumgartner Michael and Christoph Falk. manuscript. “Configurational causal modeling and logic regression.” https://people.uib.no/mba110/docs/CNA_LR.pdf

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

Grasshoff, Gerd and Michael May. 2001. “Causal Regularities”. In W. Spohn, M. Ledwig, and
M. Esfeld (Eds.). *Current Issues in Causation*, pp. 85-114. Paderborn: Mentis.

Mackie, John L. 1974. *The Cement of the Universe: A Study of Causation*. Oxford: Oxford University Press.

Kooperberg, Charles and Ingo Ruczinski. 2005. “Identifying Interacting SNPs Using Monte Carlo Logic Regression.” Genetic Epidemiology, 28(2):157-170. doi:10.1002/gepi.20042.

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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