Abstract
This section explains how to perform QCA using fuzzy sets, commonly referred to as fsQCA. Since the publication of Ragin (2000), fsQCA has become increasingly popular because continuous base variables need not be dichotomized. After a short theoretical introduction to the concept of fuzzy-set calibration, we introduce the two most popular calibration methods: direct assignment and transformational assignment. While the former is quickly dealt with, more time will be spent on the latter as its mechanisms and implications have so far received little attention. In the remainder of the chapter, the results from the study by Emmenegger (2011) on job-security regulations in Western democracies are replicated.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
There can be some interval on the base variable \([x_{i}, x_{j}]\) over which set membership scores remain equal, but it is generally assumed that they vary over some interval along the domain, usually between the threshold for set exclusion and that for set inclusion.
- 2.
More precisely, the Freedom House index measures freedom rather than democracy, but its two dimensions include political rights and civil liberties. For more details about the data and documentation, see http://www.freedomhouse.org.
- 3.
The Herfindahl–Hirschman index measures the size of firms in relation to their industry and thus indicates the degree of competition between them. Different versions of this index exist.
- 4.
Another example of a set based on a mid-point concept is the set of “moderately developed countries”. The example given in Table 5.3, Ragin (2008, p. 93), claims to demonstrate the calibration of the set of “moderately developed countries”, whereas in fact it describes the calibration of the set of “at least moderately developed countries” as written in the text. The former is a mid-point concept and must be calibrated by a different function from that applied to calibrate the latter.
- 5.
Square brackets mean “inclusive of,” round brackets “exclusive of”.
- 6.
Only the piecewise logistic function is available in fs/QCA through the “calibrate” command and in the QCA3 package through the directCalibration() command. Both functions differ slightly from each other.
- 7.
By “form of the membership function,” we mean both the choice of the calibration thresholds and the membership function.
- 8.
It is possible to combine \(p > 1\) and \(0 < q < 1\), \(0 < p < 1\) and \(q > 1\) respectively, to get double-concentrated or double-dilated membership functions.
- 9.
A value of 0.95 requires \(\phi = \log (19)\), 0.975 \(\phi = \log (39)\), 0.98 \(\phi = \log (49)\), 0.99 \(\phi = \log (99)\), and so on.
- 10.
The arbitrariness of membership functions has been one of the main criticisms in fuzzy-set theory (Arfi 2010, pp. 5f.).
- 11.
After having loaded the dataset, further information on it can be obtained with the usual help call ?Emme.
- 12.
Notice that \(\mathbf {S} \) and \(\mathbf {C} \) are both subsets of \(\mathbf {S} +\mathbf {C} \). When \(\mathbf {S} \) and/or \(\mathbf {C} \) are/is individually necessary, the combination \(\mathbf {S} +\mathbf {C} \) must also be necessary.
- 13.
By default, the QCA package also computes PRI scores for binary and multi-value crisp-set data, but in csQCA and mvQCA, PRI always equals inclusion.
- 14.
Labeling all cases, as in Fig. 1, Emmenegger (2011, p. 347) is usually not necessary.
- 15.
1, 2, 3, and 4 stand for below, to the left, above, and to the right.
- 16.
As the identify() function will only label each pair of coordinates once, check whether some cases have exactly the same values and overlap each other on a single point, for example with a cross-tabulation of fuzzy-set membership scores.
- 17.
For more options such as label offsets and identification tolerance, enter ?identify.
- 18.
The eqmcc() function can also directly process datasets with fuzzy-set membership scores. However, it is recommended that the function only be used after having created and evaluated the truth table.
- 19.
This argument has been suggested by Michael Baumgartner.
- 20.
Unique coverage scores do not apply to minimal sums.
- 21.
It may happen that there are multiple inessential PIs, none of which dominates the other.
- 22.
It is important to use double quotes around the number 27 because row names are of data type character. Alternatively, truth table rows can also be accessed in the solution object. The same output would have been generated by EmmeSP$tt$tt["27", 1:6].
- 23.
If a truth table object is passed to eqmcc(), the neg.out argument has no effect.
- 24.
Loops are a more advanced programming technique. Alternatively, individual plots can be produced as shown in Sect. 4.2.3.
- 25.
See also split.screen() and layout() for similar functionality.
- 26.
The analogous argument for multiple column figures is mfcol.
- 27.
If you want to add line segments to a plot, use the segments() function for single lines and the lines() function for joined segments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 The Author(s)
About this chapter
Cite this chapter
Thiem, A., Duşa, A. (2013). Fuzzy-Set QCA. In: Qualitative Comparative Analysis with R. SpringerBriefs in Political Science, vol 5. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4584-5_4
Download citation
DOI: https://doi.org/10.1007/978-1-4614-4584-5_4
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-4583-8
Online ISBN: 978-1-4614-4584-5
eBook Packages: Humanities, Social Sciences and LawPolitical Science and International Studies (R0)