| Title: | Advanced Functionality for Performing and Evaluating Qualitative Comparative Analysis |
|---|---|
| Description: | Provides advanced functionality for performing configurational comparative research with Qualitative Comparative Analysis (QCA), including crisp-set, multi-value, and fuzzy-set QCA. It also offers advanced tools for sensitivity diagnostics and methodological evaluations of QCA. |
| Authors: | Alrik Thiem [aut, cre, cph], Michael Baumgartner [ctb], Adrian Dusa [ctb], Reto Spoehel [ctb] |
| Maintainer: | Alrik Thiem <[email protected]> |
| License: | GPL-3 |
| Version: | 1.1-2 |
| Built: | 2024-10-31 06:52:55 UTC |
| Source: | CRAN |
QCApro is a successor package to the QCA package, with QCA 1.1-4 as its original basis (Dusa and Thiem 2014; Thiem and Dusa 2012; 2013a; 2013b; 2013c). Just like its predecessor, QCApro implements the method of Qualitative Comparative Analysis (QCA)—a family of techniques for analyzing configurational data in accordance with the INUS theory of causation (Mackie 1965; 1974), but it has fixed various technical and methodological problems of the QCA package and includes many new features and enhancements for applying QCA.
Moreover, QCApro is currently the only QCA software that provides many purpose-built functions for testing methodological properties of QCA and QCA-related procedures. For example, the effects of changing discretionary parameters such as the inclusion cut-off on the degree of ambiguity affecting a QCA solution can be analyzed (Baumgartner and Thiem 2017a), the consequences of increasing limited empirical diversity on the probability of QCA not committing causal fallacies can be computed (Baumgartner and Thiem 2017b), and the relation between correlational and implicational independence can be examined (Thiem and Baumgartner 2016).
Three variants can currently be processed by QCApro: crisp-set QCA (csQCA; Ragin 1987), multi-value QCA (mvQCA; Cronqvist and Berg-Schlosser 2009; Thiem 2013; 2014) and fuzzy-set QCA (fsQCA; Ragin 2000; 2008). A subvariant of csQCA called temporal QCA (tQCA) is also available (Caren and Panofsky 2005; Ragin and Strand 2008).
Several datasets from various areas are integrated in QCApro so as to facilitate familiarization with the package's functionality. Currently covered are business, management and organization (d.stakeholder), education (d.education), environmental sciences (d.biodiversity), evaluation (d.transport), legal studies (d.napoleon), political science (d.jobsecurity, d.partybans, d.represent), public health (d.health, d.tumorscreen), urban affairs (d.urban), and sociology (d.homeless, d.socialsecurity). For more details, see the datasets' documentation files.
As an additional resource, QCApro includes a comprehensive glossary for Configurational Comparative Methods. The glossary is directly accessible via the link 'User guides, package vignettes and other documentation' in the package's help index or the 'doc' folder of the package's installation folder.
If you make use of the QCApro package in your work, please acknowledge it in the interest of good scientific practice and transparency. The package citation displays on loading the package or by using the command citation(package = "QCApro") after loading. The aforesaid command also provides a suitable BibTeX entry. To browse the latest news about the QCApro package (bug fixes, enhancements, etc.), enter news(package = "QCApro").
Happy QCAing!
| Package: | QCApro |
| Type: | Package |
| Version: | 1.1-2 |
| Date: | 2018-01-10 |
| License: | GPL-3 |
Author:
Alrik Thiem
Department of Political Science
University of Lucerne, Switzerland
E-Mail
Personal Website
ResearchGate Website
Maintainer:
Alrik Thiem
Department of Political Science
University of Lucerne, Switzerland
E-Mail
Personal Website
ResearchGate Website
Baumgartner, Michael, and Alrik Thiem. 2017a. “Model Ambiguities in Configurational Comparative Research.” Sociological Methods & Research 46 (4):954-87. DOI: 10.1177/0049124115610351.
Baumgartner, Michael, and Alrik Thiem. 2017b. “Often Trusted but Never (Properly) Tested: Evaluating Qualitative Comparative Analysis.” Sociological Methods & Research. Advance online publication. DOI: 10.1177/0049124117701487.
Caren, Neal, and Aaron Panofsky. 2005. “TQCA: A Technique for Adding Temporality to Qualitative Comparative Analysis.” Sociological Methods & Research 34 (2):147-72. DOI: 10.1177/0049124105277197.
Cronqvist, Lasse, and Dirk Berg-Schlosser. 2009. “Multi-Value QCA (mvQCA).” In Configurational Comparative Methods: Qualitative Comparative Analysis (QCA) and Related Techniques, eds. B. Rihoux and C. C. Ragin. London: Sage Publications, pp. 69-86.
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/.
Mackie, John L. 1965. “Causes and Conditions.” American Philosophical Quarterly 2 (4):245-64. URL: http://www.jstor.org/stable/20009173.
Mackie, John L. 1974. The Cement of the Universe: A Study of Causation. Oxford: Oxford University Press.
Ragin, Charles C. 1987. The Comparative Method: Moving beyond Qualitative and Quantitative Strategies. Berkeley: University of California Press.
Ragin, Charles C. 2000. Fuzzy-Set Social Science. Chicago: University of Chicago Press.
Ragin, Charles C. 2008. Redesigning Social Inquiry: Fuzzy Sets and Beyond. Chicago: University of Chicago Press.
Ragin, Charles C., and Sarah Ilene Strand. 2008. “Using Qualitative Comparative Analysis to Study Causal Order: Comment on Caren and Panofsky (2005).” Sociological Methods & Research 36 (4):431-41. DOI: 10.1177/0049124107313903.
Thiem, Alrik. 2013. “Clearly Crisp, and Not Fuzzy: A Reassessment of the (Putative) Pitfalls of Multi-Value QCA.” Field Methods 25 (2):197-207. DOI: 10.1177/1525822x13478135.
Thiem, Alrik. 2014. “Parameters of Fit and Intermediate Solutions in Multi-Value Qualitative Comparative Analysis.” Quality & Quantity 49 (2):657-74. DOI: 10.1007/s11135-014-0015-x.
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. DOI: 10.1177/0894439313478999.
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.
Thiem, Alrik, and Michael Baumgartner. 2016. “Modeling Causal Irrelevance in Evaluations of Configurational Comparative Methods.” Sociological Methodology 46 (1):345-57. DOI: 10.1177/0081175016654736.
This evaluation function computes the degree of ambiguity across variations of a reference research design. It has initially been programmed for Baumgartner and Thiem (2017).
ambiguity(data, outcome = c(""), neg.out = c(FALSE), exo.facs = c(""), tuples = c(), incl.cut1 = c(1), incl.cut0 = c(1), sol.type = c("ps"), row.dom = c(FALSE), min.dis = c(FALSE))ambiguity(data, outcome = c(""), neg.out = c(FALSE), exo.facs = c(""), tuples = c(), incl.cut1 = c(1), incl.cut0 = c(1), sol.type = c("ps"), row.dom = c(FALSE), min.dis = c(FALSE))
data |
A set of configurational data as processable by the
|
outcome |
A character vector of outcomes. |
neg.out |
A logical vector specifying whether to negate outcomes. |
exo.facs |
A character vector with the names of the exogenous factors. |
tuples |
A numeric vector of tuples of exogenous factors to be created
from |
incl.cut1 |
The minimum sufficiency inclusion score for an output function value of "1". |
incl.cut0 |
The maximum sufficiency inclusion score for an output function value of "0". |
sol.type |
A character vector specifying the solution types to be generated. |
row.dom |
A logical vector imposing row dominance as a constraint on the solution to eliminate dominated inessential prime implicants. |
min.dis |
A logical vector imposing minimal disjunctivity as a constraint on the solution to eliminate models with more prime implicants than the model(s) with the fewest prime implicants. |
This evaluation function computes the degree of ambiguity across variations of a reference design by recording the number of models for each design solution. It has initially been programmed for Baumgartner and Thiem (2015).
The argument data requires a set of configurational data as processable by
the eQMC function.
The argument outcome is a character vector, specifying the outcome(s) to be analyzed, either in curly-bracket notation (e.g., O{value}) if the outcome is from a multivalent (or a bivalent) factor, or in upper-case notation if the outcome is from a bivalent factor (e.g., O as a short-cut for O{1}). Outcomes from multivalent crisp-set factors always require curly-bracket notation. Outcomes can be single levels of factors not simultaneously passed to exo.facs. At least one outcome has to be specified.
The argument neg.out requires a logical vector of length one or two, whose values, which must not be duplicated, specify whether to negate the outcomes determined by outcome. If an element in outcome is a level from a multivalent factor, neg.out = TRUE makes the disjunction of all remaining levels the outcome. Possible values for neg.out include FALSE, TRUE, FALSE, TRUE and TRUE, FALSE.
The argument exo.facs is a character vector with the names of the exogenous factors. If omitted, all factors in data are used except that/those of the outcome/s given in outcome. and tuples specifies a numeric vector of tuples of exogenous factors to be created from exo.facs.
Minterms with an inclusion score of at least incl.cut1 are coded positive (OUT = "1"), minterms with an inclusion score below incl.cut1 but with at least incl.cut0 are coded as a contradiction (OUT = "C"), and minterms with an inclusion score below incl.cut0 are coded negative (OUT = "0"). If inc .cut0 is not explicitly changed, it is set equal to incl.cut1.
The argument sol.type requires a character vector specifying the solution types to be generated. For example, c("ps", "cs") means parsimonious and conservative solution type.
The argument row.dom requires a logical vector, and controls whether the principle of row dominance is imposed as a constraint on the solution. An inessential prime implicant dominates another if all configurations covered by are also covered by , but they are not interchangeable (cf. McCluskey 1956, 1425; McCluskey 1965, 164-152). If row dominance is operative, models that contain dominated prime implicants will not be returned.
The argument min.dis requires a logical vector, and controls whether the principle of minimal disjunctivity is imposed as a constraint on the solution (McCluskey 1965, 12 -126). If minimal disjunctivity is operative, models that contain more than the number of prime implicants of the model(s) with the fewest prime implicants will not be returned.
A list with the following two main components:
tuples |
A list of all tuples of exogenous factors of the respective size
taken from all factors given in |
n.models |
A list of matrices giving the number of models in each solution
for each design. The coding of labels has the following structure:
|
| Thiem, Alrik | : development, documentation, programming, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Baumgartner, Michael, and Alrik Thiem. 2017. “Model Ambiguities in Configurational Comparative Research.” Sociological Methods & Research 46 (4):954-87. DOI: 10.1177/0049124115610351.
McCluskey, Edward J. 1956. “Minimization of Boolean Functions.” Bell Systems Technical Journal 35 (6):1417-44. DOI: 10.1002/j.1538-7305.1956.tb03835.x.
McCluskey, Edward J. 1965. Introduction to the Theory of Switching Circuits. Princeton: Princeton University Press.
## Not run: # load dataset data(d.tumorscreen) # designs: outcomes HPF and LPF; all 3 to 5-tuples of exogenous factors designs <- ambiguity(d.tumorscreen, outcome = c("HPF", "LPF"), neg.out = c(FALSE, TRUE), tuples = 3:5) # share of solutions with ambiguities mapply(function (x) round(colSums((x > 1)) / nrow(x), 2), designs$n.models) ## End(Not run)## Not run: # load dataset data(d.tumorscreen) # designs: outcomes HPF and LPF; all 3 to 5-tuples of exogenous factors designs <- ambiguity(d.tumorscreen, outcome = c("HPF", "LPF"), neg.out = c(FALSE, TRUE), tuples = 3:5) # share of solutions with ambiguities mapply(function (x) round(colSums((x > 1)) / nrow(x), 2), designs$n.models) ## End(Not run)
This function generates configurational data from raw data (base variables) and some specified threshold(s). The calibration of bivalent fuzzy-set factors is possible for positive and negative end-point and mid-point concepts, using the method of transformational assignment.
calibrate(x, type = "crisp", thresholds = NA, include = TRUE, logistic = FALSE, idm = 0.95, ecdf = FALSE, p = 1, q = 1)calibrate(x, type = "crisp", thresholds = NA, include = TRUE, logistic = FALSE, idm = 0.95, ecdf = FALSE, p = 1, q = 1)
x |
An interval or ratio-scaled base variable. |
type |
The calibration type, either "crisp" or "fuzzy". |
thresholds |
A vector of thresholds. |
include |
Logical, include threshold(s) ( |
logistic |
Calibrate to fuzzy-set variable using the logistic function. |
idm |
The set inclusion degree of membership for the logistic function. |
ecdf |
Calibrate to fuzzy-set variable using the empirical cumulative distribution function of the base variable. |
p |
Parameter: if |
q |
Parameter: if |
Calibration is the process by which configurational data is produced, that is, by which set membership scores are assigned to cases. With interval and ratio-scaled base variables, calibration can be based on transformational assignments using (piecewise-defined) membership functions.
For type = "crisp", one threshold produces a factor with two levels: 0 and
1. More thresholds produce factors with multiple levels. For example, two thresholds
produce three levels: 0, 1 and 2.
For type = "fuzzy", this function can generate bivalent fuzzy-set variables
by linear, s-shaped, inverted s-shaped and logistic transformation for end-point
concepts. It can generate bivalent fuzzy-set variables by trapezoidal, triangular
and bell-shaped transformation for mid-point concepts (Bojadziev and Bojadziev
2007; Clark et al. 2008; Thiem 2014; Thiem and Dusa 2013).
For calibrating bivalent fuzzy-set variables based on end-point concepts,
thresholds should be specified as a numeric vector c(thEX, thCR, thIN),
where thEX is the threshold for full exclusion, thCR the threshold
for the crossover, and thIN the threshold for full inclusion.
If thEX thCR thIN, then the membership
function is increasing from thEX to thIN. If thIN
thCR thEX, then the membership function is decreasing from
thIN to thEX.
For calibrating bivalent fuzzy-set variables based on mid-point concepts,
thresholds should be specified as a numeric vector
c(thEX1, thCR1, thIN1, thIN2, thCR2, thEX2), where thEX1 is the first
(left) threshold for full exclusion, thCR1 the first (left) threshold for
the crossover, thIN1 the first (left) threshold for full inclusion,
thIN2 the second (right) threshold for full inclusion, thCR2 the
second (right) threshold for crossover, and thEX2 the second (right) threshold
for full exclusion.
If thEX1 thCR1 thIN1 thIN2
thCR2 thEX2, then the membership function is first
increasing from thEX1 to thIN1, then flat between thIN1 and
thIN2, and finally decreasing from thIN2 to thEX2. In contrast,
if thIN1 thCR1 thEX1 thEX2
thCR2 thIN2, then the membership function is first
decreasing from thIN1 to thEX1, then flat between thEX1 and
thEX2, and finally increasing from thEX2 to thIN2.
The parameters p and q control the degree of concentration and
dilation. They should be left at their default values unless good reasons for
changing them exist.
If logistic = TRUE, the argument idm specifies the inclusion degree
of membership.
If ecdf = TRUE, calibration is based on the empirical cumulative distribution
function of x.
A numeric vector of set membership scores between 0 and 1 for bivalent crisp-set factors and bivalent fuzzy-set variables, or a numeric vector of levels for multivalent crisp-set factors (beginning with 0 at increments of 1).
| Dusa, Adrian | : programming |
| Thiem, Alrik | : development, documentation, programming, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Bojadziev, George, and Maria Bojadziev. 2007. Fuzzy Logic for Business, Finance, and Management. 2nd ed. Hackensack, NJ: World Scientific. Link.
Clark, Terry D., Jennifer M. Larson, John N. Mordeson, Joshua D. Potter, and Mark J. Wierman. 2008. Applying Fuzzy Mathematics to Formal Models in Comparative Politics. Berlin: Springer. Link.
Thiem, Alrik. 2014. “Membership Function Sensitivity of Descriptive Statistics in Fuzzy-Set Relations.” International Journal of Social Research Methodology 17 (6):625-42. DOI: 10.1080/13645579.2013.806118.
Thiem, Alrik, and Adrian Dusa. 2013. Qualitative Comparative Analysis with R: A User's Guide. New York: Springer. Link.
# base variable; random draw from standard normal distribution set.seed(30) x <- rnorm(30) # calibration thresholds th <- quantile(x, seq(from = 0.05, to = 0.95, length = 6)) # calibration of bivalent crisp-set factor calibrate(x, thresholds = th[3]) # calibration of trivalent crisp-set factor calibrate(x, thresholds = c(th[2], th[4])) # fuzzy-set calibration # 1. positive end-point concept, linear # 2. positive and corresponding negative end-point concept, logistic # 3. positive end-point concept, ECDF # 4. negative end-point concept, s-shaped (quadratic) # 5. negative end-point concept, inverted s-shaped (root) # 6. positive mid-point concept, triangular # 7. positive mid-point concept, trapezoidal # 8. negative mid-point concept, bell-shaped yl <- "Set Membership" xl <- "Base Variable Value" par(mfrow = c(2,4), cex.main = 1) plot(x, calibrate(x, type = "fuzzy", thresholds = c(th[1], (th[3]+th[4])/2, th[6])), xlab = xl, ylab = yl, main = "1. positive end-point concept,\nlinear") plot(x, calibrate(x, type = "fuzzy", thresholds = c(th[1], (th[3]+th[4])/2, th[6]), logistic = TRUE, idm = 0.99), xlab = xl, ylab = yl, main = "2. positive and corresponding negative\nend-point concept, logistic") points(x, calibrate(x, type = "fuzzy", thresholds = c(th[6], (th[3]+th[4])/2, th[1]), logistic = TRUE, idm = 0.99)) plot(x, calibrate(x, type = "fuzzy", thresholds = c(th[1], (th[3]+th[4])/2, th[6]), ecdf = TRUE), xlab = xl, ylab = yl, main = "3. positive end-point concept,\nECDF") plot(x, calibrate(x, type = "fuzzy", thresholds = c(th[6], (th[3]+th[4])/2, th[1]), p = 2, q = 2), xlab = xl, ylab = yl, main = "4. negative end-point concept,\ns-shaped (quadratic)") plot(x, calibrate(x, type = "fuzzy", thresholds = c(th[6], (th[3]+th[4])/2, th[1]), p = 0.5, q = 0.5), xlab = xl, ylab = yl, main = "5. negative end-point concept,\ninverted s-shaped (root)") plot(x, calibrate(x, type = "fuzzy", thresholds = th[c(1,2,3,3,4,5)]), xlab = xl, ylab = yl, main = "6. positive mid-point concept,\ntriangular") plot(x, calibrate(x, type = "fuzzy", thresholds = th[c(1,2,3,4,5,6)]), xlab = xl, ylab = yl, main = "7. positive mid-point concept,\ntrapezoidal") plot(x, calibrate(x, type = "fuzzy", thresholds = th[c(3,2,1,5,4,3)], p = 3, q = 3), xlab = xl, ylab = yl, main = "8. negative mid-point concept,\nbell-shaped")# base variable; random draw from standard normal distribution set.seed(30) x <- rnorm(30) # calibration thresholds th <- quantile(x, seq(from = 0.05, to = 0.95, length = 6)) # calibration of bivalent crisp-set factor calibrate(x, thresholds = th[3]) # calibration of trivalent crisp-set factor calibrate(x, thresholds = c(th[2], th[4])) # fuzzy-set calibration # 1. positive end-point concept, linear # 2. positive and corresponding negative end-point concept, logistic # 3. positive end-point concept, ECDF # 4. negative end-point concept, s-shaped (quadratic) # 5. negative end-point concept, inverted s-shaped (root) # 6. positive mid-point concept, triangular # 7. positive mid-point concept, trapezoidal # 8. negative mid-point concept, bell-shaped yl <- "Set Membership" xl <- "Base Variable Value" par(mfrow = c(2,4), cex.main = 1) plot(x, calibrate(x, type = "fuzzy", thresholds = c(th[1], (th[3]+th[4])/2, th[6])), xlab = xl, ylab = yl, main = "1. positive end-point concept,\nlinear") plot(x, calibrate(x, type = "fuzzy", thresholds = c(th[1], (th[3]+th[4])/2, th[6]), logistic = TRUE, idm = 0.99), xlab = xl, ylab = yl, main = "2. positive and corresponding negative\nend-point concept, logistic") points(x, calibrate(x, type = "fuzzy", thresholds = c(th[6], (th[3]+th[4])/2, th[1]), logistic = TRUE, idm = 0.99)) plot(x, calibrate(x, type = "fuzzy", thresholds = c(th[1], (th[3]+th[4])/2, th[6]), ecdf = TRUE), xlab = xl, ylab = yl, main = "3. positive end-point concept,\nECDF") plot(x, calibrate(x, type = "fuzzy", thresholds = c(th[6], (th[3]+th[4])/2, th[1]), p = 2, q = 2), xlab = xl, ylab = yl, main = "4. negative end-point concept,\ns-shaped (quadratic)") plot(x, calibrate(x, type = "fuzzy", thresholds = c(th[6], (th[3]+th[4])/2, th[1]), p = 0.5, q = 0.5), xlab = xl, ylab = yl, main = "5. negative end-point concept,\ninverted s-shaped (root)") plot(x, calibrate(x, type = "fuzzy", thresholds = th[c(1,2,3,3,4,5)]), xlab = xl, ylab = yl, main = "6. positive mid-point concept,\ntriangular") plot(x, calibrate(x, type = "fuzzy", thresholds = th[c(1,2,3,4,5,6)]), xlab = xl, ylab = yl, main = "7. positive mid-point concept,\ntrapezoidal") plot(x, calibrate(x, type = "fuzzy", thresholds = th[c(3,2,1,5,4,3)], p = 3, q = 3), xlab = xl, ylab = yl, main = "8. negative mid-point concept,\nbell-shaped")
This dataset is from Basurto (2013), who analyzes the determinants of the emergence and endurance of autonomy among local institutions for biodiversity conservation in Costa Rica using fsQCA.
data(d.biodiversity)data(d.biodiversity)
This data frame contains 30 rows (cases) and the following 9 columns (factors):
| [ , 1] | AU | endogenous factor: | local autonomy |
| ("1" always, "0" never) | |||
| [ , 2] | EM | exogenous factor: | local communal involvement through direct employment |
| ("1" 100 percent, "0" 0 percent) | |||
| [ , 3] | SP | exogenous factor: | local direct spending |
| ("1" always, "0" never) | |||
| [ , 4] | CO | exogenous factor: | co-management with local or regional stakeholders |
| ("1" present, "0" absent) | |||
| [ , 5] | CI | exogenous factor: | degree of influence of national civil service policies |
| ("1" 100 percent civil service employees, "0" 0 percent) | |||
| [ , 6] | PO | exogenous factor: | national participation in policy-making |
| ("1" perceived programme influence, "0" no perceived influence) | |||
| [ , 7] | RE | exogenous factor: | research-oriented partnerships |
| ("1" many, "0" few) | |||
| [ , 8] | CN | exogenous factor: | conservation-oriented partnerships |
| ("1" many, "0" few) | |||
| [ , 9] | DE | exogenous factor: | direct support by development organizations |
| ("1" always, "0" never) |
| Thiem, Alrik: collection, documentation |
Alrik Thiem (Personal Website; ResearchGate Website)
Basurto, Xavier. 2013. “Linking Multi-Level Governance to Local Common-Pool Resource Theory using Fuzzy-Set Qualitative Comparative Analysis: Insights from Twenty Years of Biodiversity Conservation in Costa Rica.” Global Environmental Change 23 (3):573-87. DOI: 10.1016/j.gloenvcha.2013.02.011.
This dataset is from Schneider and Sadowski (2010), who analyze the determinants of PhD placement success for 14 economics departments using csQCA.
data(d.education)data(d.education)
This data frame contains 14 rows (cases) and the following 7 columns (factors):
| [ , 1] | NPM1 | exogenous factor | : | local competition | ("1" used, "0" not used) |
| [ , 2] | NPM2 | exogenous factor | : | national competition | ("1" used, "0" not used) |
| [ , 3] | NPM3 | exogenous factor | : | transparency | ("1" used, "0" not used) |
| [ , 4] | NPM4 | exogenous factor | : | university regulations | ("1" used, "0" not used) |
| [ , 5] | NPM5 | exogenous factor | : | target agreements | ("1" used, "0" not used) |
| [ , 6] | NPM6 | exogenous factor | : | state regulations | ("1" used, "0" not used) |
| [ , 7] | O | endogenous factor | : | placement success | ("1" yes, "0" no) |
| Thiem, Alrik: collection, documentation |
Alrik Thiem (Personal Website; ResearchGate Website)
Schneider, Peter, and Dieter Sadowski. 2010. “The Impact of New Public Management Instruments on PhD Education.” Higher Education 59 (5):543-65. DOI: 10.1007/s10734-009-9264-3.
This dataset is originally from Caren and Panofsky (2005), who analyze the determinants of unionization attempts by graduate student workers at research universities using tQCA. Their study has been replicated and corrected by Ragin and Strand (2008).
data(d.graduate)data(d.graduate)
This data frame contains 17 rows (cases) and the following 6 columns (factors):
| [ , 1] | P | exogenous factor | : | public university | ("1" yes, "0" no) |
| [ , 2] | E | exogenous factor | : | support of elite allies | ("1" yes, "0" no) |
| [ , 3] | A | exogenous factor | : | national union affiliation | ("1" yes, "0" no) |
| [ , 4] | S | exogenous factor | : | a strike or strike threat | ("1" yes, "0" no) |
| [ , 5] | EBA | exogenous factor | : | E present before A | ("1" yes, "0" no, "-" don't care) |
| [ , 6] | REC | endogenous factor | : | union recognition | ("1" yes, "0" no) |
| Thiem, Alrik: collection, documentation |
Alrik Thiem (Personal Website; ResearchGate Website)
Caren, Neal, and Aaron Panofsky. 2005. “TQCA: A Technique for Adding Temporality to Qualitative Comparative Analysis.” Sociological Methods & Research 34 (2):147-72. DOI: 10.1177/0049124105277197.
Ragin, Charles C., and Sarah Ilene Strand. 2008. “Using Qualitative Comparative Analysis to Study Causal Order: Comment on Caren and Panofsky (2005).” Sociological Methods & Research 36 (4):431-41. DOI: 10.1177/0049124107313903.
This dataset is from Blackman, Wistow and Byrne (2011), who analyze the determinants of varying progress with tackling health inequalities with respect to cancers and cardiovascular disease among a group of 27 local authority areas in England.
data(d.health)data(d.health)
This data frame contains 27 rows (cases) and the following 18 columns (factors):
| [ , 1] | CAN | endogenous factor: | area gap for deaths before age 75 from cancers |
| ("1" narrowing, "0" not narrowing) | |||
| [ , 2] | BC | exogenous factor: | assessments of commissioning |
| ("1" basic, "0" not basic) | |||
| [ , 3] | SP | exogenous factor: | assessments of strategic partnership working |
| ("1" less than good, "0" at least good) | |||
| [ , 4] | PH | exogenous factor: | assessments of public health workforce planning |
| ("1" less than good, "0" at least good) | |||
| [ , 5] | PR | exogenous factor: | frequency of progress reviews |
| ("1" less frequent, "0" more frequent) | |||
| [ , 6] | CH | exogenous factor: | working culture of individual commitment and champions |
| ("1" yes, "0" no) | |||
| [ , 7] | AS | exogenous factor: | organisational culture |
| ("1" aspirational, "0" comfortable or complacent) | |||
| [ , 8] | LI | exogenous factor: | index of multiple deprivation |
| ("1" lower, "0" higher) | |||
| [ , 9] | HS | exogenous factor: | spend per head on cancer programmes |
| ("1" higher, "0" lower) | |||
| [ , 10] | LC | exogenous factor: | crime rate |
| ("1" lower, "0" higher) | |||
| [ , 11] | TS | exogenous factor: | primary care trust performance rating |
| ("1" higher, "0" lower) | |||
| [ , 12] | CVD | endogenous factor: | area gap for deaths before age 75 from cardiovascular disease |
| ("1" narrowing, "0" not narrowing) | |||
| [ , 13] | SC | exogenous factor: | smoking cessation services |
| ("1" better than basic, "0" basic) | |||
| [ , 14] | PC | exogenous factor: | primary care services |
| ("1" better than basic, "0" basic) | |||
| [ , 15] | MP | exogenous factor: | a few major programmes |
| ("1" yes, "0" no) | |||
| [ , 16] | GL | exogenous factor: | leadership |
| ("1" good or excellent, "0" less than good) | |||
| [ , 17] | BA | exogenous factor: | budget allocation relative to target |
| ("1" higher, "0" lower) | |||
| [ , 18] | IM | exogenous factor: | internal migration |
| ("1" lower, "0" higher) |
| Thiem, Alrik: collection, documentation |
Alrik Thiem (Personal Website; ResearchGate Website)
Blackman, Tim, Jonathan Wistow, and David Byrne. 2011. “A Qualitative Comparative Analysis of Factors Associated with Trends in Narrowing Health Inequalities in England.” Social Science & Medicine 72 (12):1965-74. DOI: 10.1016/j.socscimed.2011.04.003.
This dataset is from Cress and Snow (2000), who analyze the determinants of the outcomes attained by homeless social movement organizations using csQCA.
data(d.homeless)data(d.homeless)
This data frame contains 15 rows (cases) and the following 10 columns (factors):
| [ , 1] | VI | exogenous factor | : | viability | ("1" present, "0" absent) |
| [ , 2] | DT | exogenous factor | : | disruptive tactics | ("1" present, "0" absent) |
| [ , 3] | SA | exogenous factor | : | sympathetic allies | ("1" present, "0" absent) |
| [ , 4] | CS | exogenous factor | : | city support | ("1" present, "0" absent) |
| [ , 5] | DF | exogenous factor | : | diagnostic frame | ("1" present, "0" absent) |
| [ , 6] | PF | exogenous factor | : | prognostic frame | ("1" present, "0" absent) |
| [ , 7] | REP | endogenous factor | : | representation | ("1" present, "0" absent) |
| [ , 8] | RES | endogenous factor | : | resources | ("1" present, "0" absent) |
| [ , 9] | RIG | endogenous factor | : | rights | ("1" present, "0" absent) |
| [ , 10] | REL | endogenous factor | : | relief | ("1" present, "0" absent) |
| Thiem, Alrik: collection, documentation |
Alrik Thiem (Personal Website; ResearchGate Website)
Cress, Daniel M., and David A. Snow. 2000. “The Outcomes of Homeless Mobilization: The Influence of Organization, Disruption, Political Mediation, and Framing.” American Journal of Sociology 105 (4):1063-104. Link.
This dataset is from Emmenegger (2011), who analyzes the determinants of high job security regulations in Western democracies using fsQCA.
data(d.jobsecurity)data(d.jobsecurity)
This data frame contains 19 rows (cases) and the following 7 columns (factors):
| [ , 1] | S | exogenous factor | : | level of statism | ("1" high, "0" not high) |
| [ , 2] | C | exogenous factor | : | level of non-market coordination | ("1" high, "0" not high) |
| [ , 3] | L | exogenous factor | : | level of labour movement strength | ("1" high, "0" not high) |
| [ , 4] | R | exogenous factor | : | level of Catholicism | ("1" high, "0" not high) |
| [ , 5] | P | exogenous factor | : | level of religious party strength | ("1" high, "0" not high) |
| [ , 6] | V | exogenous factor | : | institutional veto points | ("1" many, "0" not many) |
| [ , 7] | JSR | endogenous factor | : | level of job security regulations | ("1" high, "0" not high) |
| Thiem, Alrik: collection, documentation |
The row names are the official International Organization for Standardization (ISO) country code elements as specified in ISO 3166-1-alpha-2.
Alrik Thiem (Personal Website; ResearchGate Website)
Emmenegger, Patrick. 2011. “Job Security Regulations in Western Democracies: A Fuzzy Set Analysis.” European Journal of Political Research 50 (3):336-64. DOI: 10.1111/j.1475-6765.2010.01933.x.
This dataset is from Arvind and Stirton (2010), who analyze the reception of the Code Napoleon in Germany using fsQCA.
data(d.napoleon)data(d.napoleon)
This data frame contains 14 rows (cases) and the following 8 columns (factors):
| [ , 1] | D | exogenous factor | : | legal system | ("1" heterogenous, "0" homogenous) |
| [ , 2] | C | exogenous factor | : | territory | ("1" ruled by France, "0" ruled by enemy) |
| [ , 3] | I | exogenous factor | : | state institutions | ("1" strong, "0" none) |
| [ , 4] | F | exogenous factor | : | economy | ("1" seigneural-feudal, "0" proto-industrial) |
| [ , 5] | L | exogenous factor | : | ideology of state ruler | ("1" liberal, "0" conservative) |
| [ , 6] | N | exogenous factor | : | nativist tendencies | ("1" yes, "0" no) |
| [ , 7] | A | exogenous factor | : | sentiments towards France | ("1" very negative, "0" very positive) |
| [ , 8] | O | endogenous factor | : | adoption of Code Napoleon | ("1" yes, "0" no) |
| Thiem, Alrik: collection, documentation |
Alrik Thiem (Personal Website; ResearchGate Website)
Arvind, Thiruvallore T., and Lindsay Stirton. 2010. “Explaining the Reception of the Code Napoleon in Germany: A Fuzzy-Set Qualitative Comparative Analysis.” Legal Studies 30 (1):1-29. DOI: 10.1111/j.1748-121X.2009.00150.x.
This dataset is from Hartmann and Kemmerzell (2010), who analyze the determinants of the introduction of party ban provisions and their actual implementation in sub-Saharan Africa using mvQCA.
data(d.partybans)data(d.partybans)
This data frame contains 48 rows (cases) and the following 7 columns (factors):
| [ , 1] | C | exogenous factor: | colonial tradition |
| ("2" British, "1" French, "0" other) | |||
| [ , 2] | F | exogenous factor: | former regime type competition |
| ("2" no, "1" limited, "0" multi-party) | |||
| [ , 3] | T | exogenous factor: | mode of transition |
| ("2" managed, "1" pacted, "0" democracy before 1990) | |||
| [ , 4] | R | exogenous factor: | regime type |
| ("2" authoritarian, "1" liberalizing, "0" democratic) | |||
| [ , 5] | V | exogenous factor: | ethnic violence |
| ("1" yes, "0" no) | |||
| [ , 6] | PB | endogenous factor: | party ban provisions introduced |
| ("1" yes, "0" no) | |||
| [ , 7] | PBI | endogenous factor: | party bans implemented |
| ("1" yes, "0" no) |
| Thiem, Alrik: collection, documentation |
The row names are the official International Organization for Standardization (ISO) country code elements as specified in ISO 3166-1-alpha-2.
Alrik Thiem (Personal Website; ResearchGate Website)
Hartmann, Christof, and Joerg Kemmerzell. 2010. “Understanding Variations in Party Bans in Africa.” Democratization 17 (4):642-65. DOI: 10.1080/13510347.2010.491189.
This dataset is from Krook (2010), who analyzes the determinants of high women's representation in Western-democratic parliaments using csQCA.
data(d.represent)data(d.represent)
This data frame contains 22 rows (cases) and the following 6 columns (factors):
| [ , 1] | ES | exogenous factor: | PR electoral system |
| ("1" yes, "0" no) | |||
| [ , 2] | QU | exogenous factor: | quota for women |
| ("1" yes, "0" no) | |||
| [ , 3] | WS | exogenous factor: | social-democratic welfare system |
| ("1" yes, "0" no) | |||
| [ , 4] | WM | exogenous factor: | autonomous women's movement |
| ("1" yes, "0" no) | |||
| [ , 5] | LP | exogenous factor: | seats held by left-libertarian parties |
| ("1" at least 7 percent, "0" less than 7 percent) | |||
| [ , 6] | WNP | endogenous factor: | women in single/lower house of parliament |
| ("1" at least 30 percent, "0" less than 30 percent) |
| Thiem, Alrik: collection, documentation |
The row names are the official International Organization for Standardization (ISO) country code elements as specified in ISO 3166-1-alpha-2.
Alrik Thiem (Personal Website; ResearchGate Website)
Krook, Mona Lena. 2010. “Women's Representation in Parliament: A Qualitative Comparative Analysis.” Political Studies 58 (5):886-908. DOI: 10.1111/j.1467-9248.2010.00833.x.
This dataset is from Hicks, Misra and Ng (1995), who analyze the emergence of social security programs in 15 industrializing countries during the period 1880-1930 using csQCA.
data(d.socialsecurity)data(d.socialsecurity)
This data frame contains 30 rows (cases) and the following 6 columns (factors):
| [ , 1] | LG | exogenous factor | : | liberal government | ("1" present, "0" absent) |
| [ , 2] | CG | exogenous factor | : | Catholic government | ("1" present, "0" absent) |
| [ , 3] | PS | exogenous factor | : | patriarchal state | ("1" present, "0" absent) |
| [ , 4] | UD | exogenous factor | : | unitary democracy | ("1" present, "0" absent) |
| [ , 5] | WM | exogenous factor | : | working-class mobilization | ("1" present, "0" absent) |
| [ , 6] | CO | endogenous factor | : | consolidation | ("1" present, "0" absent) |
| Thiem, Alrik: collection, documentation |
Alrik Thiem (Personal Website; ResearchGate Website)
Hicks, Alexander, Joya Misra, and Tang N. Ng. 1995. “The Programmatic Emergence of the Social Security State.” American Sociological Review 60 (3):329-49. Link.
This dataset is from Crilly, Zollo and Hansen (2012), who analyze the determinants of firms' responses to institutional pressures using fsQCA.
data(d.stakeholder)data(d.stakeholder)
This data frame contains 17 rows (cases) and the following 5 columns (factors):
| [ , 1] | PA | exogenous factor | : | potential for asymmetry | ("1" high, "0" low) |
| [ , 2] | SC | exogenous factor | : | stakeholder consensus | ("1" high, "0" low) |
| [ , 3] | OI | exogenous factor | : | organizational interest | ("1" high, "0" low) |
| [ , 4] | MC | exogenous factor | : | managerial consensus | ("1" high, "0" low) |
| [ , 5] | SA | endogenous factor | : | substantive action | ("1" high, "0" low) |
| Thiem, Alrik: collection, documentation |
Alrik Thiem (Personal Website; ResearchGate Website)
Crilly, Donal, Maurizio Zollo, and Morten T. Hansen. 2012. “Faking It or Muddling Through? Understanding Decoupling in Response to Stakeholder Pressures.” Academy of Management Journal 55 (6):1429-48. DOI: 10.5465/amj.2010.0697.
This dataset is from Sager and Andereggen (2012), who analyze the determinants of high transport project acceptance in Switzerland using mvQCA.
data(d.transport)data(d.transport)
This data frame contains 21 rows (cases) and the following 10 columns (factors):
| [ , 1] | FED | exogenous factor: | federal level |
| ("2" federal, "1" cantonal, "0" municipal) | |||
| [ , 2] | FIN | exogenous factor: | financial situation |
| ("1" positive, "0" negative) | |||
| [ , 3] | URB | exogenous factor: | sociostructural project location |
| ("1" urban, "0" rural) | |||
| [ , 4] | GER | exogenous factor: | cultural project location |
| ("1" German-speaking, "0" French-speaking) | |||
| [ , 5] | HIS | exogenous factor: | prior history |
| ("1" yes, "0" no) | |||
| [ , 6] | COO | exogenous factor: | planning coordination |
| ("1" strong, "0" not strong) | |||
| [ , 7] | PRO | exogenous factor: | administrative professionalization |
| ("1" high, "0" not high) | |||
| [ , 8] | DIS | exogenous factor: | administration's discretion |
| ("1" broad, "0" not broad) | |||
| [ , 9] | EXP | exogenous factor: | influence of external experts |
| ("1" great, "0" not great) | |||
| [ , 10] | ACC | endogenous factor: | project acceptance |
| ("1" high, "0" not high) |
| Thiem, Alrik: collection, documentation |
Alrik Thiem (Personal Website; ResearchGate Website)
Sager, Fritz, and Celine Andereggen. 2012. “Dealing With Complex Causality in Realist Synthesis: The Promise of Qualitative Comparative Analysis.” American Journal of Evaluation 33 (1):60-78. DOI: 10.1177/1098214011411574.
This dataset is from Cragun et al. (2014), who analyze the association between different universal tumor screening procedures and certain levels of patient follow-through with germ-line testing for Lynch Syndrome after a screen-positive result using csQCA.
data(d.tumorscreen)data(d.tumorscreen)
This data frame contains 15 rows (cases) and the following 8 columns (factors):
| [ , 1] | HPF | endogenous factor | : | high patient follow-through | ("1" yes, "0" no) |
| [ , 2] | LPF | endogenous factor | : | low patient follow-through | ("1" yes, "0" no) |
| [ , 3] | CA | exogenous factor | : | challenges to adoption at least as high as facilitators | ("1" yes, "0" no) |
| [ , 4] | AR | exogenous factor | : | automatic reflex test of screen-positive tumors | ("1" yes, "0" no) |
| [ , 5] | RR | exogenous factor | : | genetic counselor receives positive screen results | ("1" yes, "0" no) |
| [ , 6] | DR | exogenous factor | : | genetic counselor discloses screening result to patient | ("1" yes, "0" no) |
| [ , 7] | DC | exogenous factor | : | difficulty in contacting patients | ("1" yes, "0" no) |
| [ , 8] | PR | exogenous factor | : | need for physician referral is a barrier | ("1" yes, "0" no) |
| Thiem, Alrik: collection, documentation |
Alrik Thiem (Personal Website; ResearchGate Website)
Cragun, Deborah, Rita D. DeBate, Susan T. Vadaparampil, Julie Baldwin, Heather Hampel, and Tuya Pal. 2014. “Comparing Universal Lynch Syndrome Tumor-Screening Programs to Evaluate Associations between Implementation Strategies and Patient Follow-Through.” Genetics in Medicine 16 (10):773-82. DOI: 10.1038/gim.2014.31.
This dataset is from Kilburn (2004), who analyzes the influence of city context on urban regimes across 14 cities in the United States using csQCA.
data(d.urban)data(d.urban)
This data frame contains 14 rows (cases) and the following 6 columns (factors):
| [ , 1] | MLC | exogenous factor | : | mobility of local capital | ("1" high, "0" not high) |
| [ , 2] | FRB | exogenous factor | : | fiscal resource base | ("1" large, "0" not large) |
| [ , 3] | CP | exogenous factor | : | civic participation | ("1" high, "0" not high) |
| [ , 4] | WSR | exogenous factor | : | ward-style representation | ("1" high, "0" not high) |
| [ , 5] | CS | exogenous factor | : | city size | ("1" large, "0" not large) |
| [ , 6] | RT | endogenous factor | : | regime type | ("1" progressive, "0" developmental/caretaker) |
| Thiem, Alrik: collection, documentation |
Alrik Thiem (Personal Website; ResearchGate Website)
Kilburn, H. Whitt. 2004. “Explaining U.S. Urban Regimes.” Urban Affairs Review 39 (5):633-51. DOI: 10.1177/1078087403262861.
This function negates simple or complex Boolean expressions using the two De Morgan Laws.
DeMorgan(expression, and.split = "", use.tilde = FALSE) is.DeMorgan(x)DeMorgan(expression, and.split = "", use.tilde = FALSE) is.DeMorgan(x)
expression |
A string representing a Boolean expression or a solution object of class 'qca'. |
and.split |
The AND-operator (if any). |
use.tilde |
Logical, use '~' for negation with bivalent variables. |
x |
An object of class 'DeMorgan'. |
The two De Morgan laws posit that the negation of a disjunction is the conjunction of its separate negations, and the negation of a conjunction is the disjunction of its separate negations (Hohn 1966, p.80).
The argument expression can be any complex string representing a
Boolean expression of disjunctions and conjunctions, or a solution object of
class 'qca' (objects returned by the 'eQMC' function).
A list of solutions with their negations as components if expression
is an object of class 'qca', or simply a list with the following components
if expression is a string:
initial |
The initial expression. |
negated |
The negation of the initial expression. |
| Dusa, Adrian | : development, programming, testing |
| Thiem, Alrik | : development, documentation, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Hohn, Franz E. 1966. Applied Boolean Algebra: An Elementary Introduction. 2nd ed. New York: Macmillan.
Ragin, Charles C. 1987. The Comparative Method: Moving beyond Qualitative and Quantitative Strategies. Berkeley: University of California Press.
# example from Ragin (1987, p.99) DeMorgan("AC + B~C") # with different AND-operators DeMorgan("A*C + B*~C", and.split = "*") DeMorgan("A&C + B&~C", and.split = "&") # use solution object of class 'qca' returned by 'eQMC' function, # even with multiple models data(d.represent) KRO.ps <- eQMC(d.represent, outcome = "WNP") DeMorgan(KRO.ps)# example from Ragin (1987, p.99) DeMorgan("AC + B~C") # with different AND-operators DeMorgan("A*C + B*~C", and.split = "*") DeMorgan("A&C + B&~C", and.split = "&") # use solution object of class 'qca' returned by 'eQMC' function, # even with multiple models data(d.represent) KRO.ps <- eQMC(d.represent, outcome = "WNP") DeMorgan(KRO.ps)
This function performs the minimization. Although it is called 'eQMC', the implemented algorithm is different from the classical Quine-McCluskey (QMC) algorithm. Instead of QMC's approach of using positive minterms and remainders to perform minimization, eQMC uses positive and negative minterms, but no remainders. See Dusa and Thiem (2015) and Thiem (2015) for more details.
eQMC(data, outcome = c(""), neg.out = FALSE, exo.facs = c(""), relation = "suf", n.cut = 1, incl.cut1 = 1, incl.cut0 = 1, minimize = c("1"), sol.type = "ps", row.dom = FALSE, min.dis = FALSE, omit = c(), dir.exp = c(), details = FALSE, show.cases = FALSE, inf.test = c(""), use.tilde = FALSE, use.letters = FALSE, ...) is.qca(x)eQMC(data, outcome = c(""), neg.out = FALSE, exo.facs = c(""), relation = "suf", n.cut = 1, incl.cut1 = 1, incl.cut0 = 1, minimize = c("1"), sol.type = "ps", row.dom = FALSE, min.dis = FALSE, omit = c(), dir.exp = c(), details = FALSE, show.cases = FALSE, inf.test = c(""), use.tilde = FALSE, use.letters = FALSE, ...) is.qca(x)
data |
A truth table object or a set of configurational data (of class 'matrix' or 'data.frame'). |
outcome |
A character vector of outcomes. |
neg.out |
Logical, use negation of |
exo.facs |
A character vector with the names of the exogenous factors. |
relation |
The required relation of a model antecendent to the
|
n.cut |
The minimum number of cases with set membership score above 0.5 for an output function value of "0", "1" or "C"; an integer between 1 and the maximum number of cases for all non-remainder minterms. |
incl.cut1 |
The minimum sufficiency inclusion score for an output function value of "1". |
incl.cut0 |
The maximum sufficiency inclusion score for an output function value of "0". |
minimize |
A vector of output function values for which a solution is sought. |
sol.type |
A character scalar specifying the QCA solution type that should be applied; either "ps" (parsimonious solution), "ps+" (parsimonious solution including both positive and contradiction minterms), "cs" ( conservative solution) or "cs+" (conservative solution including both positive and contradiction minterms). Note that only "ps" and "ps+" generate correct solutions. |
row.dom |
Logical, impose row dominance as a constraint on the solution to
eliminate dominated inessential prime implicants. For causal data analysis,
this argument must be set to |
min.dis |
Logical, impose minimal disjunctivity as a constraint on the
solution to eliminate models with more prime implicants than the model(s)
with the fewest prime implicants. For causal data analysis, this argument
must be set to |
omit |
A vector of minterm index values or a matrix of minterms to be omitted from minimization. |
dir.exp |
A vector of directional expectations for deriving intermediate
solutions; can only be used in conjunction with |
details |
Logical, present solution details (inclusion, raw coverage and unique coverage scores). |
show.cases |
Logical, also print case names as part of a solution's details;
|
inf.test |
A vector of length two specifying the inference-statistical
test to be performed (currently only |
use.tilde |
Logical, use tilde operator ("~") for negation with bivalent (crisp-set and fuzzy-set) factors. |
use.letters |
Logical, use single letters (in alphabetical order) instead of original variable names. |
... |
Other arguments. |
x |
An object of class 'qca'. |
The argument data can be a truth table object (an object of class 'tt'
returned by the truthTable function) or a suitable data set. Suitable data
sets have the following structure: values of 0 and 1 for bivalent crisp-set factors,
values between 0 and 1 for bivalent fuzzy-set factors, and values beginning
with 0 at increments of 1 for multivalent crisp-set factors. The placeholders
"-" and "dc" indicate "don't cares" in auxiliary factors that specify temporal
order between other substantive factors in tQCA. These values lead to the
exclusion of the auxiliary factor from the computation of parameters of fit.
The argument outcome specifies the outcome to be analyzed, either in
curly-bracket notation (e.g., O{value}) if the outcome is from a multivalent
(or a bivalent) factor, or in upper-case notation if the outcome is from a bivalent
factor (e.g., O as a short-cut for O{1}). Outcomes from multivalent crisp-set factors always require curly-bracket notation. Outcomes can be single
levels of factors not simultaneously passed to exo.facs, or levels from
any subset of the factors specified in exo.facs if data is not a
truth table object. At least one outcome has to be specified.
If multiple outcomes are specified, their factors must also be specified in
exo.facs. In this case, solution details will not be printed by default
(see the example on mimicking Coincidence Analysis below).
The logical argument neg.out controls whether outcome is to be
analyzed or its negation. If outcome is a level from a multivalent factor,
neg.out = TRUE makes the disjunction of all remaining levels the outcome.
The argument exo.facs specifies the exogenous factors. If omitted, all
factors in data are used except that of the outcome. With multiple outcomes, all factors in data are used. Please note that computation times
may increase significantly beyond 17 exogenous factors, and that the computation
of a solution may not be possible at all depending on end-user machine constraints.
The argument relation specifies the relation between the antecedent of a
model and the outcome. It accepts either the value "suf" or "sufnec".
If relation = "suf" (default), only sufficiency is used as a criterion in
identifying a model. If relation = "sufnec", models must be sufficient and
necessary for the outcome to be identified. The argument incl.cut1 then
acts as the cut-off for the sufficiency inclusion of a minterm as well as the
necessity inclusion of the final model(s).
Minterms that contain fewer than n.cut cases with membership scores above
0.5 are coded as remainders (OUT = "?"). If the number of such cases is at
least n.cut, minterms with an inclusion score of at least incl.cut1
are coded positive (OUT = "1"), minterms with an inclusion score below
incl.cut1 but with at least incl.cut0 are coded as a contradiction
(OUT = "C"), and minterms with an inclusion score below incl.cut0
are coded negative (OUT = "0"). If incl.cut0 is not explicitly
changed, it is set equal to incl.cut1.
The argument minimize specifies a vector of suitable values of the output
function for which a solution is sought. Vectors of such values are "1"
(default; positive minterms), "C" (contradictions), "0" (negative
minterms), c("1", "C") and c("0", "C"), but not c("1", "0")
and c("1", "0", "C"). Note that for "0", "C" and
c("0", "C"), the respective minterms will be processed but no solution
details will be printed. Also note that minimize = "0" is not the same
as using neg.out = TRUE.
The argument sol.type specifies the QCA solution type that should be
generated. It accepts either "ps" (default, parsimonious solution),
"ps+" (parsimonious solution including both positive minterms and
contradictions), "cs" (conservative solution) or "cs+" (conservative
solution including both positive minterms and contradictions). As only the
parsimonious search strategy generates methodologically correct solutions (Baumgartner
and Thiem 2017a), sol.type should not normally be changed to generate conservative or intermediate solutions.
The logical argument row.dom controls whether the principle of row dominance
is imposed as a constraint on the solution. An inessential prime implicant
dominates another if all configurations covered by are also
covered by , but they are not interchangeable (cf. McCluskey 1956, 1425;
McCluskey 1965, 164-152). If row dominance is operative, models that contain
dominated prime implicants will not be returned. For purposes of causal data
analysis, row.dom must be set to FALSE.
The logical argument min.dis controls whether the principle of minimal
disjunctivity is imposed as a constraint on the solution (McCluskey 1965, 123-126).
If minimal disjunctivity is operative, models that contain more than the number
of prime implicants of the model(s) with the fewest prime implicants will not be
returned. For purposes of causal data analysis, both row.dom
and min.dis must be set to FALSE (Baumgartner and Thiem 2017b; Thiem 2014b).
The argument omit can be used to omit minterms from the minimization
process ex ante. It accepts a vector of row numbers from the truth table
or a matrix of minterms of the same order as passed to the truthTable
function (if the argument data is a truth table object) or as specified
in the argument exo.facs.
Neither the conservative nor the intermediate search strategy of QCA produce
correct solutions (Baumgartner and Thiem 2017a). The dir.exp argument is retained only for purposes of method evaluation in
relation to intermediate solutions. It specifies directional expectations for
separating easy from difficult counterfactuals in simplifying assumptions. For
bivalent crisp and fuzzy-set factors, expectations should be specified as a vector
of the same length and the same order of condition variables as provided in
exo.facs. For bivalent factors, a value of either "0" or "1" indicates
that the corresponding factor is expected to contribute to a positive output
function value, while a dash, "-", indicates that one or the other level of the
corresponding factor does so. For multivalent factors, multiple levels have to
be enclosed by double quotes and separated by a semicolon (see mvQCA example using
Hartmann and Kemmerzell (2010)
below). In some situations, directional expectations in mvQCA generate easy
counterfactuals that do not contribute to parsimony
(Thiem 2014a).
If details = TRUE, parameters of fit (inclusion, raw coverage, and unique
coverage) will be printed for each solution and its respective prime implicants.
Essential prime implicants are listed first in the solution output and in the top
part of the parameters-of-fit table. Inessential prime implicants are listed in
brackets in the solution output and in the middle part of the parameters-of-fit
table, together with their unique coverage scores under each individual model.
Inclusion and coverage scores for each model are provided in the bottom part
of the parameters-of-fit table.
The logical argument show.cases controls whether case names are displayed
next to their corresponding prime implicants (do not use with many cases and/or
long case names!). In the parameters-of-fit table, semicolons separate cases from
different minterms, whereas commas separate cases from the same minterm.
The argument inf.test provides functionality for basing output function
value codings on inference-statistical tests. Currently, only an exact binomial
test ("binom") is available, which requires the data to contain only
bivalent or multivalent crisp-set factors. The argument requires a vector of
length two, comprising the test and a critical significance level. If the
empirical inclusion score of a minterm is not significantly lower than
incl.cut1, it will be coded positive (OUT = "1"). If it is
significantly lower than incl.cut1 yet still significantly higher than
incl.cut0, it will be coded as a contradiction (OUT = "C"). If it
is not significantly higher than incl.cut0, it will be coded negative
(OUT = "0").
The argument use.tilde should only be used for bivalent factors. If the exogenous factors are already named with single letters, the argument
use.letters will have no effect when set to TRUE. Otherwise,
upper-case letters will replace original factor names in alphabetical order.
An object of class 'qca' for single outcomes and 'mqca' for multiple
outcomes. Objects of class 'qca' are lists with the following
ten main components:
tt |
The truth table object. |
excluded |
The line numbers of the negative minterms. |
initials |
The positive (non-remainder) minterms. |
PIs |
The prime implicants. |
PIchart |
The list of prime implicant charts. |
solution |
The list of solutions. |
essential |
The list of essential prime implicants. |
pims |
The list of model prime implicant set membership scores. |
SA |
The list of simplifying assumptions that would have been used by Quine-McCluskey minimization. |
i.sol |
A list of components specific to intermediate solution(s), including the prime implicant chart, model prime implicant membership scores, (non-simplifying) easy counterfactuals and difficult counterfactuals. |
| Dusa, Adrian | : development, programming |
| Thiem, Alrik | : development, documentation, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Baumgartner, Michael. 2009. “Inferring Causal Complexity.” Sociological Methods & Research 38 (1):71-101. DOI: 10.1177/0049124109339369.
Baumgartner, Michael, and Alrik Thiem. 2017a. “Often Trusted but Never (Properly) Tested: Evaluating Qualitative Comparative Analysis.” Sociological Methods & Research. Advance online publication. DOI: 10.1177/0049124117701487.
Baumgartner, Michael, and Alrik Thiem. 2017b. “Model Ambiguities in Configurational Comparative Research.” Sociological Methods & Research 46 (4):954-87. DOI: 10.1177/0049124115610351.
Dusa, Adrian, and Alrik Thiem. 2015. “Enhancing the Minimization of Boolean and Multivalue Output Functions with eQMC.” Journal of Mathematical Sociology 39 (2):92-108. DOI: 10.1080/0022250X.2014.897949.
Emmenegger, Patrick. 2011. “Job Security Regulations in Western Democracies: A Fuzzy Set Analysis.” European Journal of Political Research 50 (3):336-64. DOI: 10.1111/j.1475-6765.2010.01933.x.
Hartmann, Christof, and Joerg Kemmerzell. 2010. “Understanding Variations in Party Bans in Africa.” Democratization 17 (4):642-65. DOI: 10.1080/13510347.2010.491189.
McCluskey, Edward J. 1956. “Minimization of Boolean Functions.” Bell Systems Technical Journal 35 (6):1417-44. DOI: 10.1002/j.1538-7305.1956.tb03835.x.
McCluskey, Edward J. 1965. Introduction to the Theory of Switching Circuits. Princeton: Princeton University Press.
Krook, Mona Lena. 2010. “Women's Representation in Parliament: A Qualitative Comparative Analysis.” Political Studies 58 (5):886-908. DOI: 10.1111/j.1467-9248.2010.00833.x.
Ragin, Charles C. 2008. Redesigning Social Inquiry: Fuzzy Sets and Beyond. Chicago: University of Chicago Press. Link.
Schneider, Carsten Q., and Claudius Wagemann. 2012. Set-Theoretic Methods for the Social Sciences: A Guide to Qualitative Comparative Analysis (QCA). Cambridge: Cambridge University Press. Link.
Thiem, Alrik. 2014a. “Parameters of Fit and Intermediate Solutions in Multi-Value Qualitative Comparative Analysis.” Quality & Quantity 49 (2):657-74. DOI: 10.1007/s11135-014-0015-x.
Thiem, Alrik. 2014b. “Navigating the Complexities of Qualitative Comparative Analysis: Case Numbers, Necessity Relations, and Model Ambiguities.” Evaluation Review 38 (6):487-513. DOI: 10.1177/0193841x14550863.
Thiem, Alrik. 2015. “Using Qualitative Comparative Analysis for Identifying Causal Chains in Configurational Data: A Methodological Commentary on Baumgartner and Epple (2014).” Sociological Methods & Research 44 (4):723-36. DOI: 10.1177/0049124115589032.
# csQCA using Krook (2010) #------------------------- data(d.represent) head(d.represent) # solution with details and case names KRO <- eQMC(d.represent, outcome = "WNP", details = TRUE, show.cases = TRUE) KRO # check PI chart KRO$PIchart # solution with truth table object KRO.tt <- truthTable(d.represent, outcome = "WNP") KRO <- eQMC(KRO.tt) KRO # simplifying assumptions (SAs) that would have been used with Quine-McCluskey # optimization KRO$SA # fsQCA using Emmenegger (2011) #------------------------------ data(d.jobsecurity) head(d.jobsecurity) # solution with details EMM <- eQMC(d.jobsecurity, outcome = "JSR", incl.cut1 = 0.9, details = TRUE) EMM # are the model prime implicants also sufficient for the negation of the outcome? pof(EMM$pims, outcome = "JSR", d.jobsecurity, neg.out = TRUE, relation = "suf") # are the negations of the model prime implicants also sufficient for the outcome? pof(1 - EMM$pims, outcome = "JSR", d.jobsecurity, relation = "suf") # plot all three prime implicants of the solution PIsc <- EMM$pims par(mfrow = c(1, 3)) for(i in 1:3){ plot(PIsc[, i], d.jobsecurity$JSR, pch = 19, ylab = "JSR", xlab = names(PIsc)[i], xlim = c(0, 1), ylim = c(0, 1), main = paste("Prime Implicant", print(i))) mtext(paste( "Inclusion = ", round(EMM$IC$overall$incl.cov$incl[i], 3), "; Coverage = ", round(EMM$IC$overall$incl.cov$cov.r[i], 3)), cex = 0.7, line = 0.4) abline(h = 0.5, lty = 2, col = gray(0.5)) abline(v = 0.5, lty = 2, col = gray(0.5)) abline(0, 1) } # mvQCA using Hartmann and Kemmerzell (2010) #------------------------------------------- data(d.partybans) head(d.partybans) # specify exogenous factors beforehand exo.facs <- c("C", "F", "T", "V") # parsimonious solution with contradictions included HK.sol <- eQMC(d.partybans, outcome = "PB{1}", exo.facs = exo.facs, incl.cut0 = 0.4, sol.type = "ps+", details = TRUE) HK.sol # which are the two countries in T{2} but not PB{1}? rownames(d.partybans[d.partybans$T == 2 & d.partybans$PB != 1, ]) # QCA with multiple outcomes from multivalent variables #------------------------------------------------------ d.mmv <- data.frame(A = c(2,0,0,1,1,1,2,2), B = c(2,2,2,2,1,1,0,0), C = c(0,1,0,0,0,2,1,0), D = c(2,1,2,2,3,1,3,0), E = c(3,2,3,3,0,1,3,2), row.names = letters[1:8]) head(d.mmv) mmv.s <- eQMC(d.mmv, outcome = c("D{2}", "E{3}")) mmv.s # use quotes with curly-bracket notation to access solution component print(mmv.s$"E{3}", details = TRUE, show.cases = TRUE) # negation of outcome from multivalent factor is disjunction of all other # levels; high under-determination (18 models) mmv.s <- eQMC(d.mmv, outcome = "E{3}", neg.out = TRUE) mmv.s # causal chains with QCA (Thiem 2015); data from Baumgartner (2009) #----------------------------------------------------------------------------- d.Bau <- data.frame( U = c(1,1,1,1,0,0,0,0), D = c(1,1,0,0,1,1,0,0), L = c(1,1,1,1,1,1,0,0), G = c(1,0,1,0,1,0,1,0), E = c(1,1,1,1,1,1,1,0), row.names = letters[1:8]) head(d.Bau) # with multiple outcomes, no solution details are printed; # "causal-chain structure": (D + U <=> L) * (G + L <=> E) # "common-cause structure": (D + U <=> L) * (G + D + U <=> E) Bau.cna <- eQMC(d.Bau, outcome = names(d.Bau), relation = "sufnec") Bau.cna # get the truth table, solution details and case names for outcome "E" print(Bau.cna$E, details = TRUE, show.cases = TRUE) # examples relating to QCA method evaluation #------------------------------------------- # # is the conservative solution (QCA-CS) really "conservative"? #------------------------------------------------------------- # Ragin (2008, 173): "The complex [conservative] solution [...] does not # permit any counterfactual cases and thus no simplifying assumptions # regarding combinations of conditions that do not exist in the data."; # the conservative solution is "[c]onservative because [...] the # researcher [...] is exclusively guided by the empirical information # at hand" (Schneider and Wagemann 2012, 162) # # in fact, QCA-CS makes extremely strong assumptions on ALL remainders; # QCA-CS assumes every remainder exists at least 'freq.cut' times, # and occurs with the negation of the outcome more than # 'freq.cut' * (1 - 'incl.cut1') times # create a test data-set 'CS' with 32 cases and randomly assign values # on the endogenous factor 'Z' CS <- data.frame(mintermMatrix(rep(2,5))) CS$Z <- sample(0:1, 2^5, replace = TRUE) # randomly draw 20 cases to create a limitedly diverse data-set 'CS.LD' # and turn all 12 remainder minterms into observations that occur with # 'Z = 0' in original data-set 'CS' CS.LD <- CS[sample(1:2^5, 20), ] change <- as.numeric(setdiff(rownames(CS), rownames(CS.LD))) CS$Z[change] <- 0 # create the (conservative) solutions for 'CS' and 'CS.LD' CS.sol <- eQMC(CS, outcome = "Z") CS.LD.sol <- eQMC(CS.LD, outcome = "Z", sol.type = "cs") # test whether the two solutions are identical identical(unlist(CS.LD.sol$solution), unlist(CS.sol$solution)) # both solutions are identical, for two datasets that do not allow the same # causal inferences to be made; this indicates that QCA-CS draws causal inferences # beyond what the data warrants; the lower the diversity index (ratio of non-remainder # minterms to all minterms), the stronger the assumptions QCA-CS makes# csQCA using Krook (2010) #------------------------- data(d.represent) head(d.represent) # solution with details and case names KRO <- eQMC(d.represent, outcome = "WNP", details = TRUE, show.cases = TRUE) KRO # check PI chart KRO$PIchart # solution with truth table object KRO.tt <- truthTable(d.represent, outcome = "WNP") KRO <- eQMC(KRO.tt) KRO # simplifying assumptions (SAs) that would have been used with Quine-McCluskey # optimization KRO$SA # fsQCA using Emmenegger (2011) #------------------------------ data(d.jobsecurity) head(d.jobsecurity) # solution with details EMM <- eQMC(d.jobsecurity, outcome = "JSR", incl.cut1 = 0.9, details = TRUE) EMM # are the model prime implicants also sufficient for the negation of the outcome? pof(EMM$pims, outcome = "JSR", d.jobsecurity, neg.out = TRUE, relation = "suf") # are the negations of the model prime implicants also sufficient for the outcome? pof(1 - EMM$pims, outcome = "JSR", d.jobsecurity, relation = "suf") # plot all three prime implicants of the solution PIsc <- EMM$pims par(mfrow = c(1, 3)) for(i in 1:3){ plot(PIsc[, i], d.jobsecurity$JSR, pch = 19, ylab = "JSR", xlab = names(PIsc)[i], xlim = c(0, 1), ylim = c(0, 1), main = paste("Prime Implicant", print(i))) mtext(paste( "Inclusion = ", round(EMM$IC$overall$incl.cov$incl[i], 3), "; Coverage = ", round(EMM$IC$overall$incl.cov$cov.r[i], 3)), cex = 0.7, line = 0.4) abline(h = 0.5, lty = 2, col = gray(0.5)) abline(v = 0.5, lty = 2, col = gray(0.5)) abline(0, 1) } # mvQCA using Hartmann and Kemmerzell (2010) #------------------------------------------- data(d.partybans) head(d.partybans) # specify exogenous factors beforehand exo.facs <- c("C", "F", "T", "V") # parsimonious solution with contradictions included HK.sol <- eQMC(d.partybans, outcome = "PB{1}", exo.facs = exo.facs, incl.cut0 = 0.4, sol.type = "ps+", details = TRUE) HK.sol # which are the two countries in T{2} but not PB{1}? rownames(d.partybans[d.partybans$T == 2 & d.partybans$PB != 1, ]) # QCA with multiple outcomes from multivalent variables #------------------------------------------------------ d.mmv <- data.frame(A = c(2,0,0,1,1,1,2,2), B = c(2,2,2,2,1,1,0,0), C = c(0,1,0,0,0,2,1,0), D = c(2,1,2,2,3,1,3,0), E = c(3,2,3,3,0,1,3,2), row.names = letters[1:8]) head(d.mmv) mmv.s <- eQMC(d.mmv, outcome = c("D{2}", "E{3}")) mmv.s # use quotes with curly-bracket notation to access solution component print(mmv.s$"E{3}", details = TRUE, show.cases = TRUE) # negation of outcome from multivalent factor is disjunction of all other # levels; high under-determination (18 models) mmv.s <- eQMC(d.mmv, outcome = "E{3}", neg.out = TRUE) mmv.s # causal chains with QCA (Thiem 2015); data from Baumgartner (2009) #----------------------------------------------------------------------------- d.Bau <- data.frame( U = c(1,1,1,1,0,0,0,0), D = c(1,1,0,0,1,1,0,0), L = c(1,1,1,1,1,1,0,0), G = c(1,0,1,0,1,0,1,0), E = c(1,1,1,1,1,1,1,0), row.names = letters[1:8]) head(d.Bau) # with multiple outcomes, no solution details are printed; # "causal-chain structure": (D + U <=> L) * (G + L <=> E) # "common-cause structure": (D + U <=> L) * (G + D + U <=> E) Bau.cna <- eQMC(d.Bau, outcome = names(d.Bau), relation = "sufnec") Bau.cna # get the truth table, solution details and case names for outcome "E" print(Bau.cna$E, details = TRUE, show.cases = TRUE) # examples relating to QCA method evaluation #------------------------------------------- # # is the conservative solution (QCA-CS) really "conservative"? #------------------------------------------------------------- # Ragin (2008, 173): "The complex [conservative] solution [...] does not # permit any counterfactual cases and thus no simplifying assumptions # regarding combinations of conditions that do not exist in the data."; # the conservative solution is "[c]onservative because [...] the # researcher [...] is exclusively guided by the empirical information # at hand" (Schneider and Wagemann 2012, 162) # # in fact, QCA-CS makes extremely strong assumptions on ALL remainders; # QCA-CS assumes every remainder exists at least 'freq.cut' times, # and occurs with the negation of the outcome more than # 'freq.cut' * (1 - 'incl.cut1') times # create a test data-set 'CS' with 32 cases and randomly assign values # on the endogenous factor 'Z' CS <- data.frame(mintermMatrix(rep(2,5))) CS$Z <- sample(0:1, 2^5, replace = TRUE) # randomly draw 20 cases to create a limitedly diverse data-set 'CS.LD' # and turn all 12 remainder minterms into observations that occur with # 'Z = 0' in original data-set 'CS' CS.LD <- CS[sample(1:2^5, 20), ] change <- as.numeric(setdiff(rownames(CS), rownames(CS.LD))) CS$Z[change] <- 0 # create the (conservative) solutions for 'CS' and 'CS.LD' CS.sol <- eQMC(CS, outcome = "Z") CS.LD.sol <- eQMC(CS.LD, outcome = "Z", sol.type = "cs") # test whether the two solutions are identical identical(unlist(CS.LD.sol$solution), unlist(CS.sol$solution)) # both solutions are identical, for two datasets that do not allow the same # causal inferences to be made; this indicates that QCA-CS draws causal inferences # beyond what the data warrants; the lower the diversity index (ratio of non-remainder # minterms to all minterms), the stronger the assumptions QCA-CS makes
This function finds all possibilities for factorizing a configurational expression.
factorize(expression, and.split = "", sort.factorizing = FALSE, sort.factorized = FALSE)factorize(expression, and.split = "", sort.factorizing = FALSE, sort.factorized = FALSE)
expression |
A string representing a configurational expression or a QCA
solution object of class “qca” generated by |
and.split |
The AND-operator (if any). |
sort.factorizing |
Logical, sort results beginning with largest number of factorizing elements. |
sort.factorized |
Logical, sort results beginning with largest number of factorized elements. |
In Boolean algebra, the “*”-operator is distributive over the “+”-
operator such that for any three literals , and , the
following law holds:
(Hohn 1966, pp.78-80; South 1974, p.12). The 'factorize' function finds
all possible for any configurational expression. Factorized versions
of the initial expression(s) can be sorted in decreasing order by the number of
factorizing literals or in decreasing order by the number of factorized literals.
A list with the following components:
initial |
The initial expression. |
factored |
The factorizations of the initial expression. |
| Dusa, Adrian | : development, programming, testing |
| Thiem, Alrik | : development, documentation, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Hohn, Franz E. 1966. Applied Boolean Algebra: An Elementary Introduction. 2nd ed. New York: Macmillan.
South, G. F. 1974. Boolean Algebra and Its Uses. New York: Van Nostrand Reinhold.
# factorize a disjunction of two two-way conjunctions; # if single letters are used, argument "and.split" is not needed factorize("AB + AC") # "and.split" is needed in these cases factorize("one*TWO*four + one*THREE + THREE*four", and.split = "*") factorize("~ONE*TWO*~FOUR + ~ONE*THREE + THREE*~FOUR", and.split = "*") factorize("one&TWO&four + one&THREE + THREE&four", and.split = "&") # factorize solution objects directly data(d.represent) KRO.sol <- eQMC(d.represent, outcome = "WNP") factorize(KRO.sol)# factorize a disjunction of two two-way conjunctions; # if single letters are used, argument "and.split" is not needed factorize("AB + AC") # "and.split" is needed in these cases factorize("one*TWO*four + one*THREE + THREE*four", and.split = "*") factorize("~ONE*TWO*~FOUR + ~ONE*THREE + THREE*~FOUR", and.split = "*") factorize("one&TWO&four + one&THREE + THREE&four", and.split = "&") # factorize solution objects directly data(d.represent) KRO.sol <- eQMC(d.represent, outcome = "WNP") factorize(KRO.sol)
This function finds calibration thresholds for splitting base variables into the desired number of groups using cluster analysis.
findTh(x, groups = 2, hclustm = "complete", distm = "euclidean")findTh(x, groups = 2, hclustm = "complete", distm = "euclidean")
x |
An interval or ratio-scaled base variable. |
groups |
A vector of integers with the desired number of groups. |
hclustm |
The agglomeration (clustering) method to be used. |
distm |
The distance measure to be used. |
For more details about argument groups, see ?cutree. For more
details about argument hclustm, see ?hclust. For more details
about argument distm, see ?dist.
A numeric vector of suggested threshold(s) for dividing base variables into the desired number of groups.
| Dusa, Adrian | : programming |
| Thiem, Alrik | : development, documentation, testing |
Default values from the hclust method and the dist method
are used for both the distance measure distm and the clustering method
hclustm.
Alrik Thiem (Personal Website; ResearchGate Website)
# 15 random values between 1 and 100 x <- sample(1:100, size = 15) # split into two groups for csQCA findTh(x) # split into three groups for mvQCA findTh(x, groups = 3)# 15 random values between 1 and 100 x <- sample(1:100, size = 15) # split into two groups for csQCA findTh(x) # split into three groups for mvQCA findTh(x, groups = 3)
This function creates implicant matrices. An implicant matrix consists of all truth table minterms and their subsets, including the empty set.
implicantMatrix(noflevels, raw = FALSE, arrange = FALSE)implicantMatrix(noflevels, raw = FALSE, arrange = FALSE)
noflevels |
The number of levels for each exogenous factor. |
raw |
Logical, return implicant matrix with indicator for elimination. |
arrange |
Logical, arrange for easier visual inspection. |
An implicant matrix consists of all minterms and their subsets, including the
empty set (Dusa 2007, 2010; Thiem and Dusa 2015). The number of implicants is given by
,
where is the number of levels for factor
and is the total number of exogenous factors.
If raw = TRUE, the indicator for elimination (-1) is used.
A matrix with
rows and columns.
| Dusa, Adrian | : programming |
| Thiem, Alrik | : development, documentation, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Dusa, Adrian. 2007. Enhancing Quine-McCluskey. COMPASSS: Working Paper 2007-49. URL: http://www.compasss.org/wpseries/Dusa2007b.pdf.
Dusa, Adrian. 2010. “A Mathematical Approach to the Boolean Minimization Problem.” Quality & Quantity 44 (1):99-113. DOI: 10.1007/s11135-008-9183-x.
Dusa, Adrian, and Alrik Thiem. 2015. “Enhancing the Minimization of Boolean and Multivalue Output Functions with eQMC.” Journal of Mathematical Sociology 39 (2):92-108. DOI: 10.1080/0022250X.2014.897949.
# three exogenous factors with two levels each; # first row is empty set implicantMatrix(noflevels = rep(2, 3)) # two exogenous factors with three levels each implicantMatrix(noflevels = rep(3, 2)) # arranged differently implicantMatrix(noflevels = rep(3, 2), arrange = TRUE) # with internal indicator for eliminated values implicantMatrix(noflevels = rep(3, 2), raw = TRUE)# three exogenous factors with two levels each; # first row is empty set implicantMatrix(noflevels = rep(2, 3)) # two exogenous factors with three levels each implicantMatrix(noflevels = rep(3, 2)) # arranged differently implicantMatrix(noflevels = rep(3, 2), arrange = TRUE) # with internal indicator for eliminated values implicantMatrix(noflevels = rep(3, 2), raw = TRUE)
This evaluation function tests for the implicational independence between two factors. It has been programmed for Thiem and Baumgartner (2016).
implicIndep(expression, n.samples = 1, size.sample = 100, corr = "0")implicIndep(expression, n.samples = 1, size.sample = 100, corr = "0")
expression |
A string representing the Boolean function to be evaluated. |
n.samples |
The number of datasets to be sampled. |
size.sample |
The size of each data sample. |
corr |
The direction of correlation between the endogenous factor and the implicationally independent factor. |
Randomly sample n.samples different data-sets with uniform probability mass function (any other discrete function would do as well; proficient users may adjust this at the relevant places in the function); and run QCA for each dataset; check whether the irrelevant factor is eliminated and get the correlations between the irrelevant factor and the outcome factor.
The correlation can be controlled with corr: "0" means no correlation; "+" positive correlation, and "-" negative correlation. The larger the sample size, the larger the positive / negative correlation. The argument expression may represent any Boolean function in disjunctive normal form as shown below, including proper causal structures such as "(X1*X2 + X3*X4 <=> Y)*(Z1 + z1)" or non-causal structures such as "(x1*X2 + X1*x2 + X1*X3 + X2*X3 <=> Y)*(Z1 + z1)" (contains redundant prime implicants) or "(X3*x2 + X2 <=> Y)*(Z1 + z1)" (contains redundant conjuncts).
If expression is no causal structure, an additional note will be issued together with the test output for whether the irrelevant factor has been eliminated.
You can use the following possibilities for expression: "(X1X2 + X3X4 <=> Y)(Z1 + z1)" if a factor has one letter and a one-digit number, "(AB + CD <=> E)(F + f)" if a factor has one letter, "(X1*X2 + X3*X4 <=> Y)*(Z1 + z1)" or "(A*B + C*D <=> E)*(F + f)" (curly-bracket notation is not supported). Empty spaces and the type of the biconditional operator (<->/<=>) have no effect.
A list with the following five components:
tt |
The evaluated truth tables. |
dat.list |
The test datasets generated on the basis of the evaluaetd truth tables. |
sol.list |
The corresponding solutions. |
cor.list |
The correlations between the endogenous factor and the irrelevant factor. |
test |
The result for whether the irrelevant factor has been eliminated in all tests. |
| Baumgartner, Michael | : testing |
| Thiem, Alrik | : development, documentation, programming, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Thiem, Alrik, and Baumgartner, Michael. 2016. “Modeling Causal Irrelevance in Evaluations of Configurational Comparative Methods.” Sociological Methodology 46 (1):345-57. DOI: 10.1177/0081175016654736.
## Not run: # simulation with 10 sample datasets simulation <- vector(mode = "list", length = 3) n.samples <- 10 # directions of correlation and number of cases in each sample corr <- c("-", "0", "+") nofc <- c(40, 160, 640) simulation <- lapply(nofc, function (x) {lapply(corr, function (y) { implicIndep("(X1*X2 + X3*X4 <=> Y)*(Z1 + z1)", n.samples, x, y)})}) # has Z1 been eliminated in all data experiments of a block of tests? series.test <- matrix(sapply(1:length(corr), function (x) {sapply(1:length(nofc), function (y) {simulation[[x]][[y]]$test == "Z1 has been eliminated."})}), ncol = length(corr), dimnames = list(as.character(nofc), corr)) series.test ## End(Not run)## Not run: # simulation with 10 sample datasets simulation <- vector(mode = "list", length = 3) n.samples <- 10 # directions of correlation and number of cases in each sample corr <- c("-", "0", "+") nofc <- c(40, 160, 640) simulation <- lapply(nofc, function (x) {lapply(corr, function (y) { implicIndep("(X1*X2 + X3*X4 <=> Y)*(Z1 + z1)", n.samples, x, y)})}) # has Z1 been eliminated in all data experiments of a block of tests? series.test <- matrix(sapply(1:length(corr), function (x) {sapply(1:length(nofc), function (y) {simulation[[x]][[y]]$test == "Z1 has been eliminated."})}), ncol = length(corr), dimnames = list(as.character(nofc), corr)) series.test ## End(Not run)
This evaluation function computes all solutions and unique models that result when all n-tuples of minterms are systematically eliminated from a truth table. It has initially been programmed for Baumgartner and Thiem (2017) to test the correctness of QCA's three search strategies (conservative/complex, intermediate, parsimonious).
limitedDiversity(truth.tab, outcome = "", exo.facs = c(""), sol.type = "ps", dir.exp = c(), n.drop = 1, c.minterms = FALSE)limitedDiversity(truth.tab, outcome = "", exo.facs = c(""), sol.type = "ps", dir.exp = c(), n.drop = 1, c.minterms = FALSE)
truth.tab |
A truth table (either in plain format or a truth table object
of class "tt" generated by the |
outcome |
A character vector with the name of the outcome. |
exo.facs |
A character vector with the names of the exogenous factors. |
sol.type |
A character scalar specifying the QCA solution type that should be applied; either "ps" (parsimonious solution), "ps+" (parsimonious solution including both positive and contradiction minterms), "cs" ( conservative solution) or "cs+" (conservative solution including both positive and contradiction minterms). |
dir.exp |
A vector of directional expectations for deriving intermediate
solutions; can only be used in conjunction with |
n.drop |
The number of minterms to be dropped from the truth table. |
c.minterms |
Logical, should contradictions be treated as positive minterms. |
This function computes all solutions and unique models that result when all
n-tuples of observed minterms are systematically dropped from a truth table.
It has been programmed for Baumgartner and Thiem (2017) to test the correctness of QCA's three search strategies (conservative/complex, intermediate, parsimonious) in conjunction with the submodels function.
The argument truth.tab specifies the truth table from which minterms are
to be dropped. The truth table can either be in plain format or be a truth table
object of class "tt" generated by the truthTable function. If it
is a truth table object, the arguments outcome and exo.facs need
not be specified. The main difference between a truth table in plain format (as
also used by Coincidence Analysis, for example (Baumgartner 2009)), is that each minterm includes only cases that have identical values on the exogenous factors and the endogenous factor. A QCA truth table object, in contrast, consists of minterms that include both cases with the outcome being analyzed as well as cases with the negation of this outcome. The ratio between these cases is used as the basis for the output function value. Thus, dropping minterms from plain truth tables will drop all cases that are identical with respect to all factors in the factor frame, whereas dropping minterms from QCA truth table objects will drop all cases that are identical with respect to all exogenous factors in the factor frame.
The argument n.drop specifies the size of the tuples of minterms to be
dropped for generating limited empirical diversity. For example, if the truth
table has 16 observed minterms, n.drop = 2 creates 120 2-tuples,
n.drop = 3 creates 560 3-tuples, and so on.
The argument c.minterms specifies whether contradictions should be
treated as positive minterms (TRUE) or negative minterms (FALSE).
A list with the following three components:
model.shares |
All unique models for all n-tuples of dropped minterms and their occurrence shares. |
solutions |
The solutions for all n-tuples of eliminated minterms. |
tt |
The truth table. |
| Dusa, Adrian | : programming |
| Thiem, Alrik | : development, documentation, programming, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Baumgartner, Michael. 2009. “Inferring Causal Complexity.” Sociological Methods & Research 38 (1):71-101. DOI: 10.1177/0049124109339369.
Baumgartner, Michael, and Alrik Thiem. 2017. “Often Trusted but Never (Properly) Tested: Evaluating Qualitative Comparative Analysis.” Sociological Methods & Research. Advance online publication. DOI: 10.1177/0049124117701487.
## Not run: # number (n) of minterms (mt) and levels (lv) for each factor (exogenous # and endogenous) n.mt <- 2^5 n.lv <- rep(2, 5) # expand to unevaluated truth table and assign case/factor labels tt.unev <- data.frame(mintermMatrix(n.lv)) dimnames(tt.unev) <- list(1:n.mt, c(LETTERS[1:4], "Z")) # cull rows from tt.unev that are compatible with aB + Bc + D <=> Z # to produce evaluated truth table tt.ev tt.ev <- tt.unev[pmax(tt.unev$D, pmin(1 - tt.unev$A, tt.unev$B), pmin(tt.unev$B, 1 - tt.unev$C)) == tt.unev$Z, ] # conservative solutions for all 1-tuples (16) limitedDiversity(tt.ev, outcome = "Z", sol.type = "cs")$model.shares # using a truth table object of class 'tt' created by eQMC function #------------------------------------------------------------------ data(d.represent) tt <- truthTable(d.represent, outcome = "WNP") # with objects of class 'tt', exogenous factors and the outcome need not be # specified again limitedDiversity(tt) # proof that the conservative/complex solution type of QCA is incorrect, # (see Baumgartner and Thiem (2017) for more details) #----------------------------------------------------------------------- # 1. build truth table on the basis of reference model aB + Bc + D tt <- data.frame(mintermMatrix(rep(2, 5))) dimnames(tt) <- list(as.character(1:32), c(LETTERS[1:4], "OUT")) tt <- tt[pmax(pmin(1 - tt$A, tt$B), pmin(tt$B, 1 - tt$C), tt$D) == tt$OUT, ] # 2. generate all conservative/complex solutions for all 16 + 120 scenarios # of one/two dropped minterm/s sollist.cs <- vector("list", 2) sollist.cs <- lapply(1:2, function (x) { limitedDiversity(tt, outcome = "OUT", sol.type = "cs", n.drop = x) } ) # 3. compute in how many scenarios a correctness-preserving submodel of # the reference model was part of the solution (43.75% for one dropped # minterm and 16.67% for two dropped minterms) cs.correct <- numeric(2) cs.correct <- sapply(1:2, function (x) {round((sum(unlist(lapply( sollist.cs[[x]][[2]], function (y) {any( submodels("aB + Bc + D")$submodels %in% y)} ))) / choose(16, x))*100, 2)} ) cs.correct ## End(Not run)## Not run: # number (n) of minterms (mt) and levels (lv) for each factor (exogenous # and endogenous) n.mt <- 2^5 n.lv <- rep(2, 5) # expand to unevaluated truth table and assign case/factor labels tt.unev <- data.frame(mintermMatrix(n.lv)) dimnames(tt.unev) <- list(1:n.mt, c(LETTERS[1:4], "Z")) # cull rows from tt.unev that are compatible with aB + Bc + D <=> Z # to produce evaluated truth table tt.ev tt.ev <- tt.unev[pmax(tt.unev$D, pmin(1 - tt.unev$A, tt.unev$B), pmin(tt.unev$B, 1 - tt.unev$C)) == tt.unev$Z, ] # conservative solutions for all 1-tuples (16) limitedDiversity(tt.ev, outcome = "Z", sol.type = "cs")$model.shares # using a truth table object of class 'tt' created by eQMC function #------------------------------------------------------------------ data(d.represent) tt <- truthTable(d.represent, outcome = "WNP") # with objects of class 'tt', exogenous factors and the outcome need not be # specified again limitedDiversity(tt) # proof that the conservative/complex solution type of QCA is incorrect, # (see Baumgartner and Thiem (2017) for more details) #----------------------------------------------------------------------- # 1. build truth table on the basis of reference model aB + Bc + D tt <- data.frame(mintermMatrix(rep(2, 5))) dimnames(tt) <- list(as.character(1:32), c(LETTERS[1:4], "OUT")) tt <- tt[pmax(pmin(1 - tt$A, tt$B), pmin(tt$B, 1 - tt$C), tt$D) == tt$OUT, ] # 2. generate all conservative/complex solutions for all 16 + 120 scenarios # of one/two dropped minterm/s sollist.cs <- vector("list", 2) sollist.cs <- lapply(1:2, function (x) { limitedDiversity(tt, outcome = "OUT", sol.type = "cs", n.drop = x) } ) # 3. compute in how many scenarios a correctness-preserving submodel of # the reference model was part of the solution (43.75% for one dropped # minterm and 16.67% for two dropped minterms) cs.correct <- numeric(2) cs.correct <- sapply(1:2, function (x) {round((sum(unlist(lapply( sollist.cs[[x]][[2]], function (y) {any( submodels("aB + Bc + D")$submodels %in% y)} ))) / choose(16, x))*100, 2)} ) cs.correct ## End(Not run)
This function creates minterm and implicant matrices. It is mainly used for internal and demonstration purposes.
mintermMatrix(noflevels, logical = FALSE)mintermMatrix(noflevels, logical = FALSE)
noflevels |
The number of levels for each exogenous factor. |
logical |
Logical, return the matrix in logical values (only bivalent data). |
Minterm matrices contain all unique and complete conjunctions that can
be formed from all levels of factors (Dusa and Thiem 2015). The total
number of minterms is given by
, where
is the number of levels for exogenous factor and
is the total number of exogenous factors. A minterm matrix is an essential
part of a truth table.
| Dusa, Adrian | : development, programming |
| Thiem, Alrik | : development, documentation, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Dusa, Adrian, and Alrik Thiem. 2015. “Enhancing the Minimization of Boolean and Multivalue Output Functions with eQMC.” Journal of Mathematical Sociology 39 (2):92-108. DOI: 10.1080/0022250X.2014.897949.
# a minterm matrix with three bivalent exogenous factors noflevels <- rep(2, 3) mintermMatrix(noflevels) # with logical values mintermMatrix(noflevels, logical = TRUE)# a minterm matrix with three bivalent exogenous factors noflevels <- rep(2, 3) mintermMatrix(noflevels) # with logical values mintermMatrix(noflevels, logical = TRUE)
This function computes inclusion (consistency) and coverage scores.
pof(setms, outcome, data, neg.out = FALSE, relation = "suf", inf.test = "", incl.cut1 = 0.75, incl.cut0 = 0.5, ...) is.pof(x)pof(setms, outcome, data, neg.out = FALSE, relation = "suf", inf.test = "", incl.cut1 = 0.75, incl.cut0 = 0.5, ...) is.pof(x)
setms |
A data frame of set membership scores, or a matrix of implicants, or a vector of implicant matrix line numbers. |
outcome |
The name of the outcome. |
data |
The working data set. |
neg.out |
Logical, use negation of |
relation |
The set relation to |
inf.test |
The inference-statistical test to be performed (currently only
|
incl.cut1 |
The upper inclusion cut-off against which the
empirical inclusion score is tested if |
incl.cut0 |
The lower inclusion cut-off against which the
empirical inclusion score is tested if |
... |
Other arguments (not used in this function). |
x |
An object of class "pof". |
The argument setms specifies a data frame of set membership scores,
where set refers to any kind of set, including simple sets, combinations
returned by the superSubset function (coms), prime implicants returned
by the eQMC function (pims), or any other compound set.
The function also accepts a matrix of implicants with the level representation
of created by the mintermMatrix function, or even a corresponding vector
of implicant matrix line numbers.
The argument outcome specifies the outcome to be analyzed, either in
curly-bracket notation (e.g., O{value}) if the outcome is from a multivalent
(or a bivalent) factor, or in upper-case notation if the outcome is from a bivalent
factor (e.g., O as a short-cut for O{1}). Outcomes from multivalent crisp-set factors always require curly-bracket notation. Outcomes must be single
levels of factors not simultaneously passed to exo.facs.
The logical argument neg.out controls whether outcome is to be
analyzed or its negation. If outcome is a level from a multivalent factor,
neg.out = TRUE causes the disjunction of all remaining levels to become
the outcome to be analyzed.
The argument inf.test provides functionality for adjudicating between
rival hypotheses on the basis of inference-statistical tests. Currently, only an
exact binomial test ("binom") is available, which requires the data to
contain only bivalent or multivalent crisp-set factors. Two one-tailed tests
are performed. The null hypothesis with respect to incl.cut1 is that the
empirical inclusion score of each element in setms is not lower than the
upper critical inclusion cut-off provided in incl.cut1. The null hypothesis
with respect to incl.cut0 is that the empirical inclusion score of each
element in setms is not higher than the lower critical inclusion cut-off
provided in incl.cut0.
| Dusa, Adrian | : programming |
| Thiem, Alrik | : development, documentation, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Emmenegger, Patrick. 2011. “Job Security Regulations in Western Democracies: A Fuzzy Set Analysis.” European Journal of Political Research 50 (3):336-64. DOI: 10.1111/j.1475-6765.2010.01933.x.
Hartmann, Christof, and Joerg Kemmerzell. 2010. “Understanding Variations in Party Bans in Africa.” Democratization 17 (4):642-65. DOI: 10.1080/13510347.2010.491189.
Krook, Mona Lena. 2010. “Women's Representation in Parliament: A Qualitative Comparative Analysis.” Political Studies 58 (5):886-908. DOI: 10.1111/j.1467-9248.2010.00833.x.
# csQCA using Krook (2010) #------------------------- data(d.represent) head(d.represent) # solution with details KRO <- eQMC(d.represent, outcome = "WNP", incl.cut1 = 0.9, details = TRUE) KRO # exact binomial tests of sufficiency inclusion pof(KRO$pims, outcome = "WNP", d.represent, inf.test = c("binom", 0.1), incl.cut1 = 0.75, incl.cut0 = 0.5) # fsQCA using Emmenegger (2011) #------------------------------ data(d.jobsecurity) head(d.jobsecurity) # solution with details EMM.sol <- eQMC(d.jobsecurity, outcome = "JSR", incl.cut1 = 0.9, details = TRUE) EMM.sol # are the model prime implicants also sufficient for the negation # of the outcome? pof(EMM.sol$pims, outcome = "JSR", d.jobsecurity, neg.out = TRUE) # are the negations of the model prime implicants also sufficient # for the outcome? pof(1 - EMM.sol$pims, outcome = "JSR", d.jobsecurity) # parameters of fit for matrix of implicants; # "-1" is the placeholder for an eliminated variable; # e.g.: R*p*V and S*c*L*P*v # "S" "C" "L" "R" "P" "V" # [,1] [,2] [,3] [,4] [,5] [,6] #[1,] -1 -1 -1 1 0 1 #[2,] 1 0 1 -1 1 0 mat <- matrix(c(-1,-1,-1, 1, 0, 1, 1, 0, 1,-1, 1, 0), nrow = 2, byrow = TRUE) pof(mat, outcome = "JSR", d.jobsecurity) # or even vectors of line numbers from the implicant matrix pof(c(43, 57), "JSR", d.jobsecurity) # mv-data from Hartmann and Kemmerzell (2010) #------------------------------------------- data(d.partybans) head(d.partybans) # parameters of fit for several mv-expressions expr <- c("C{1}", "F{2}", "T{2}", "T{1}*V{0}") dat <- data.frame(ifelse(d.partybans$C == 1, 1, 0), ifelse(d.partybans$F == 2, 1, 0), ifelse(d.partybans$T == 2, 1, 0), ifelse(d.partybans$T == 1 & d.partybans$V == 0, 1, 0)) colnames(dat) <- expr pof(dat, outcome = "PB{1}", d.partybans) # miscellaneous #-------------- # parameters of fit for a data frame x <- data.frame(A = c(1,1,1,0,1), B = c(1,1,1,0,1), C = c(0,1,0,0,1), D = c(0,0,1,0,1), O = c(1,1,1,0,1)) pof(x[, -5], outcome = "O", x) # for a single column from that data frame pof(x$A, x$O) # for multiple columns from that data frame pof(x[, 1:2], outcome = "O", x)# csQCA using Krook (2010) #------------------------- data(d.represent) head(d.represent) # solution with details KRO <- eQMC(d.represent, outcome = "WNP", incl.cut1 = 0.9, details = TRUE) KRO # exact binomial tests of sufficiency inclusion pof(KRO$pims, outcome = "WNP", d.represent, inf.test = c("binom", 0.1), incl.cut1 = 0.75, incl.cut0 = 0.5) # fsQCA using Emmenegger (2011) #------------------------------ data(d.jobsecurity) head(d.jobsecurity) # solution with details EMM.sol <- eQMC(d.jobsecurity, outcome = "JSR", incl.cut1 = 0.9, details = TRUE) EMM.sol # are the model prime implicants also sufficient for the negation # of the outcome? pof(EMM.sol$pims, outcome = "JSR", d.jobsecurity, neg.out = TRUE) # are the negations of the model prime implicants also sufficient # for the outcome? pof(1 - EMM.sol$pims, outcome = "JSR", d.jobsecurity) # parameters of fit for matrix of implicants; # "-1" is the placeholder for an eliminated variable; # e.g.: R*p*V and S*c*L*P*v # "S" "C" "L" "R" "P" "V" # [,1] [,2] [,3] [,4] [,5] [,6] #[1,] -1 -1 -1 1 0 1 #[2,] 1 0 1 -1 1 0 mat <- matrix(c(-1,-1,-1, 1, 0, 1, 1, 0, 1,-1, 1, 0), nrow = 2, byrow = TRUE) pof(mat, outcome = "JSR", d.jobsecurity) # or even vectors of line numbers from the implicant matrix pof(c(43, 57), "JSR", d.jobsecurity) # mv-data from Hartmann and Kemmerzell (2010) #------------------------------------------- data(d.partybans) head(d.partybans) # parameters of fit for several mv-expressions expr <- c("C{1}", "F{2}", "T{2}", "T{1}*V{0}") dat <- data.frame(ifelse(d.partybans$C == 1, 1, 0), ifelse(d.partybans$F == 2, 1, 0), ifelse(d.partybans$T == 2, 1, 0), ifelse(d.partybans$T == 1 & d.partybans$V == 0, 1, 0)) colnames(dat) <- expr pof(dat, outcome = "PB{1}", d.partybans) # miscellaneous #-------------- # parameters of fit for a data frame x <- data.frame(A = c(1,1,1,0,1), B = c(1,1,1,0,1), C = c(0,1,0,0,1), D = c(0,0,1,0,1), O = c(1,1,1,0,1)) pof(x[, -5], outcome = "O", x) # for a single column from that data frame pof(x$A, x$O) # for multiple columns from that data frame pof(x[, 1:2], outcome = "O", x)
This evaluation function can be used to randomly build data-generating structures. It has initially been programmed for Baumgartner and Thiem (2017) to test the correctness of QCA's three search strategies (conservative/complex, intermediate, parsimonious).
randomDGS(n.DGS = 1, exo.facs = c(""), seed.1 = NULL, seed.2 = NULL, prob = 0.5, diversity = 1, delete.trivial = FALSE)randomDGS(n.DGS = 1, exo.facs = c(""), seed.1 = NULL, seed.2 = NULL, prob = 0.5, diversity = 1, delete.trivial = FALSE)
n.DGS |
The number of random data-generating structures to be built. |
exo.facs |
A character vector with the names of the exogenous factors. |
seed.1 |
The seed for the random generation of output function values. |
seed.2 |
The seed for the random selection of a DGS in cases of structural ambiguities. |
prob |
The probability of assigning a positive output function value to a minterm. |
diversity |
The diversity index value. |
delete.trivial |
Logical, delete "TRUE" and "FALSE" from set of structures. |
The argument n.DGS specifies the number of random data-generating structures to be built.
The argument exo.facs is a character vector with the names of the exogenous factors.
The argument seed.1 sets the seed for the random generation of output function values, whereas seed.2 sets the seed for the random selection of a DGS in cases of structural ambiguities.
The argument prob is the probability of assigning a positive output function value to a minterm.
The argument diversity specifies the diversity index value. It must be a number between 0 and 1.
The argument delete.trivial is logical, and specifies whether "TRUE" and "FALSE" should be deleted from the set of structures.
A list with the following two components:
DGS |
A vector of the data-generating structure(s). |
tt |
The corresponding truth table(s). |
| Thiem, Alrik | : development, documentation, programming, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Baumgartner, Michael, and Alrik Thiem. 2017. “Often Trusted but Never (Properly) Tested: Evaluating Qualitative Comparative Analysis.” Sociological Methods & Research. Advance online publication. DOI: 10.1177/0049124117701487.
# randomly generate three data-generating structures on the basis of four # exogenous factors str <- randomDGS(n.DGS = 3, exo.facs = LETTERS[1:4], seed.1 = 1375, seed.2 = 3917) str$DGS # all correctness-preserving submodels of DGS 2, bd + abC, can then be found with the # 'submodels' function submodels(str$DGS[2])$submodels# randomly generate three data-generating structures on the basis of four # exogenous factors str <- randomDGS(n.DGS = 3, exo.facs = LETTERS[1:4], seed.1 = 1375, seed.2 = 3917) str$DGS # all correctness-preserving submodels of DGS 2, bd + abC, can then be found with the # 'submodels' function submodels(str$DGS[2])$submodels
This evaluation function computes retention probabilities of QCA baseline solutions. It has been programmed for Thiem, Spoehel, and Dusa (2016).
retention(data, outcome = "", exo.facs = c(""), type = "corruption", assump = "DPA", n.cut = 1, incl.cut = 1, p.pert = 0.5, n.pert = 1)retention(data, outcome = "", exo.facs = c(""), type = "corruption", assump = "DPA", n.cut = 1, incl.cut = 1, p.pert = 0.5, n.pert = 1)
data |
A dataset of bivalent crisp-set factors. |
outcome |
The name of the outcome. |
exo.facs |
A character vector with the names of the exogenous factors. |
type |
Induce errors on the endogenous factor or delete cases. |
assump |
Assume dependent or independent perturbations. |
n.cut |
The minimum number of cases for a minterm not to be considered as a remainder. |
incl.cut |
The minimum sufficiency inclusion score for an output function value of "1". |
p.pert |
The probability of perturbation under independence. |
n.pert |
The number of perturbations under dependence. |
This function computes exact retention probabilities of QCA baseline solutions for saturated truth tables and truth tables with a two-difference restriction (every remainder differs on at least two positions from every positive minterm).
The argument data requires a suitable dataset. Suitable datasets have the following structure: values of "0" and "1" for bivalent crisp-set factors.
The argument exo.facs specifies the exogenous factors. If omitted, all
factors in data are used except that of the outcome.
The argument type specifies whether errors are to be induced in the endogenous factor ("1" is recoded to "0"; "0" is recoded to "1") of cases or whether entire cases are to be deleted from the data.
The argument assump specifies whether the perturbations detailed in type occur independently of each other or whether they are dependent on each other. Note that the assumption of dependence increases the consumption of computational resources significantly.
Minterms that contain fewer than n.cut cases with membership scores above 0.5 are coded as remainders (OUT = "?"). If the number of such cases is at least n.cut, minterms with an inclusion score of at least incl.cut are coded positive (OUT = "1"), and minterms with an inclusion score below incl.cut are coded negative (OUT = "0"). The possibility to specify contradictions using a second inclusion cut-off as in the truthTable function does not exist.
The argument p.pert specifies the probability of perturbation for type = "independent". For example, if p.pert = 1, each case is guaranteed to have measurement error on the endogenous factor.
The argument n.pert specifies the number of perturbations for type = "dependent". This must be an integer between zero (no case suffers from measurement error in the endogenous factor or no case gets deleted) and the total number of cases in data (all cases suffer from measurement error in the endogenous factor or all cases get deleted.)
| Dusa, Adrian | : programming, testing |
| Spoehel, Reto | : development |
| Thiem, Alrik | : development, documentation, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Hug, Simon. 2013. “Qualitative Comparative Analysis: How Inductive Use and Measurement Error lead to Problematic Inference.” Political Analysis 21 (2):252-65. DOI: 10.1093/pan/mps061.
Thiem, Alrik, Reto Spoehel, and Adrian Dusa. 2016. “Enhancing Sensitivity Diagnostics for Qualitative Comparative Analysis: A Combinatorial Approach.” Political Analysis 24 (1):104-20. DOI: 10.1093/pan/mpv028.
# replicate results from Hug (2013) for 2 deleted cases #------------------------------------------------------ dat <- data.frame(matrix(c( rep(1,25),rep(0,20),rep(c(0,0,1,0,0),3), 0,0,0,1,0,0,1,0,0,0,0,rep(1,7),0,1), nrow = 16, byrow = TRUE, dimnames = list(c( "AT","DK","FI","NO","SE","AU","CA","FR", "US","DE","NL","CH","JP","NZ","IE","BE"), c("P", "U", "C", "S", "W")) )) retention(dat, outcome = "W", type = "deletion", assump = "dependent", n.pert = 2)# replicate results from Hug (2013) for 2 deleted cases #------------------------------------------------------ dat <- data.frame(matrix(c( rep(1,25),rep(0,20),rep(c(0,0,1,0,0),3), 0,0,0,1,0,0,1,0,0,0,0,rep(1,7),0,1), nrow = 16, byrow = TRUE, dimnames = list(c( "AT","DK","FI","NO","SE","AU","CA","FR", "US","DE","NL","CH","JP","NZ","IE","BE"), c("P", "U", "C", "S", "W")) )) retention(dat, outcome = "W", type = "deletion", assump = "dependent", n.pert = 2)
This evaluation function computes all correctness-preserving submodels of a QCA reference model. It has initially been programmed for Baumgartner and Thiem (2015) to test the correctness of QCA's three search strategies (conservative/complex, intermediate, parsimonious).
submodels(expression, noflevels = c(), test = TRUE)submodels(expression, noflevels = c(), test = TRUE)
expression |
A string representing a csQCA or an fsQCA model, or a csQCA
or fsQCA solution object of class 'qca' (created by the
|
noflevels |
A numeric vector specifying the number of levels for each factor (experimental, can be ignored). |
test |
Logical, test whether |
This function has initially been programmed for Baumgartner and Thiem (2015) to
test the correctness of QCA's three solution types (conservative/complex,
intermediate, parsimonious). It computes all submodels of a csQCA or an fsQCA
reference model that do not violate the criterion of correctness (mvQCA models
are not yet supported). The following expression structures can be used:
"A*B + C*D <=> Y" or "AB + CD <=> Y". Empty spaces and the type
of conditional operator (<->/<=>/->/=>) are irrelevant,
but only single letters are allowed for exogenous factors. The full model need not
be provided; the antecedent also suffices (e.g., "AB + CD").
Objects of class 'qca', which are returned by the eQMC function,
are also accepted, provided that all exogenous factors have a single-letter label
(set the argument use.letters to TRUE in the function call to
eQMC if original factor labels are not single letters).
The argument noflevels expects a numeric vector of the number of factor
levels with a names attribute. Currently, this argument is experimental
and can be ignored.
The argument test specifies whether expression should be pre-tested
for its causal interpretability before forming submodels. The value to this argument
does not affect whether basic tests for likely typos in expressions such as
"abb <-> C" or "abB <-> C" are performed. If expression is
an object of class 'qca', test will be set to FALSE because QCA
models generated by the eQMC function at default argument settings are
always causally interpretable.
Note that for highly complex models containing many conjuncts within many disjuncts, computing times tend to increase considerably.
A list with the following four main components:
model |
The reference model. |
noflevels |
The number of levels for each factor in the factor frame of the model. |
outcome |
The outcome specified as part of the expression or a pseudo outcome if only an antecedent was specified. |
submodels |
A character vector of all correctness-preserving submodels. |
| Baumgartner, Michael | : development, testing |
| Thiem, Alrik | : development, documentation, programming, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Baumgartner, Michael, and Alrik Thiem. 2015. Often Trusted but Never (Properly) Tested: Evaluating Qualitative Comparative Analysis. Paper presented at the 12th Conference of the European Sociological Association, 25-28 August, Czech Technical University, Prague (Czech Republic). Link.
## Not run: # provide a) a full model as an equivalence and inspect its submodels models1 <- submodels("a*B + B*c + D <-> Z") models1$submodels # ... b) a full model with a negated outcome # submodels models2 <- submodels("AcD + BCD + abcd <=> e") length(models2$submodels) # ... c) or only an antecedent models3 <- submodels("aB + Bc + D") models3$submodels # directly provide an object of class 'qca' generated by the 'eQMC' function, # even when the solution comprises multiple models; specify # 'use.letters = TRUE' when the original exogenous factors have multi-letter # labels; for example: data(d.represent) sol1 <- eQMC(d.represent, outcome = "WNP", neg.out = TRUE, use.letters = TRUE) sol1 # M1: ae + cde + (bdE) <=> wnp # M2: ae + cde + (bcd) <=> wnp # M3: ae + cde + (Abc) <=> wnp # M1 has 138 submodels, M2 has 129, and M3 has 139 submodels models4 <- submodels(sol1) sapply(models4, "[") # when original labels of exogenous factors already consist of single # letters only, 'use.letters = TRUE' need not be specified data(d.napoleon) sol2 <- eQMC(d.napoleon, outcome = "O") sol2 models5 <- submodels(sol2) sapply(models5, "[") # prior testing is recommended because non-causal models can sometimes only # be identified computationally submodels("aB + Ac + Ad + bc + bd + CD") # can a + AbC => Y be an acceptable QCA solution as Schneider and Wagemann # (2012, p. 108) argue? No, because in Boolean algebra, it holds that # F + fG = (F + f) * (F + G) = 1*(F + G) = F + G by the laws of distribution, # complementarity, and identity submodels("a + AbC => Y", test = TRUE) # proof that the conservative/complex solution type of QCA is incorrect, # using model 3 from above (see Baumgartner and Thiem (2015) for more details) # 1. build saturated truth table on the basis of model 3: aB + Bc + D tt <- data.frame(mintermMatrix(rep(2, 5))) dimnames(tt) <- list(as.character(1:32), c(LETTERS[1:4], "OUT")) tt <- tt[pmax(pmin(1 - tt$A, tt$B), pmin(tt$B, 1 - tt$C), tt$D) == tt$OUT, ] # 2. use function 'limitedDiversity' to generate all conservative/complex # solutions for all 16 + 120 scenarios of one/two dropped minterm/s sollist.cs <- vector("list", 2) sollist.cs <- lapply(1:2, function (x) { limitedDiversity(tt, outcome = "OUT", sol.type = "cs", n.drop = x) } ) # 3. compute in how many scenarios a correctness-preserving submodel of # model 3 was part of the solution (43.75% for one dropped minterm and # 16.67% for two dropped minterms) cs.correct <- numeric(2) cs.correct <- sapply(1:2, function (x) {round((sum(unlist(lapply( sollist.cs[[x]][[2]], function (y) {any(models3$submodels %in% y)} ))) / choose(16, x))*100, 2)} ) cs.correct ## End(Not run)## Not run: # provide a) a full model as an equivalence and inspect its submodels models1 <- submodels("a*B + B*c + D <-> Z") models1$submodels # ... b) a full model with a negated outcome # submodels models2 <- submodels("AcD + BCD + abcd <=> e") length(models2$submodels) # ... c) or only an antecedent models3 <- submodels("aB + Bc + D") models3$submodels # directly provide an object of class 'qca' generated by the 'eQMC' function, # even when the solution comprises multiple models; specify # 'use.letters = TRUE' when the original exogenous factors have multi-letter # labels; for example: data(d.represent) sol1 <- eQMC(d.represent, outcome = "WNP", neg.out = TRUE, use.letters = TRUE) sol1 # M1: ae + cde + (bdE) <=> wnp # M2: ae + cde + (bcd) <=> wnp # M3: ae + cde + (Abc) <=> wnp # M1 has 138 submodels, M2 has 129, and M3 has 139 submodels models4 <- submodels(sol1) sapply(models4, "[") # when original labels of exogenous factors already consist of single # letters only, 'use.letters = TRUE' need not be specified data(d.napoleon) sol2 <- eQMC(d.napoleon, outcome = "O") sol2 models5 <- submodels(sol2) sapply(models5, "[") # prior testing is recommended because non-causal models can sometimes only # be identified computationally submodels("aB + Ac + Ad + bc + bd + CD") # can a + AbC => Y be an acceptable QCA solution as Schneider and Wagemann # (2012, p. 108) argue? No, because in Boolean algebra, it holds that # F + fG = (F + f) * (F + G) = 1*(F + G) = F + G by the laws of distribution, # complementarity, and identity submodels("a + AbC => Y", test = TRUE) # proof that the conservative/complex solution type of QCA is incorrect, # using model 3 from above (see Baumgartner and Thiem (2015) for more details) # 1. build saturated truth table on the basis of model 3: aB + Bc + D tt <- data.frame(mintermMatrix(rep(2, 5))) dimnames(tt) <- list(as.character(1:32), c(LETTERS[1:4], "OUT")) tt <- tt[pmax(pmin(1 - tt$A, tt$B), pmin(tt$B, 1 - tt$C), tt$D) == tt$OUT, ] # 2. use function 'limitedDiversity' to generate all conservative/complex # solutions for all 16 + 120 scenarios of one/two dropped minterm/s sollist.cs <- vector("list", 2) sollist.cs <- lapply(1:2, function (x) { limitedDiversity(tt, outcome = "OUT", sol.type = "cs", n.drop = x) } ) # 3. compute in how many scenarios a correctness-preserving submodel of # model 3 was part of the solution (43.75% for one dropped minterm and # 16.67% for two dropped minterms) cs.correct <- numeric(2) cs.correct <- sapply(1:2, function (x) {round((sum(unlist(lapply( sollist.cs[[x]][[2]], function (y) {any(models3$submodels %in% y)} ))) / choose(16, x))*100, 2)} ) cs.correct ## End(Not run)
This helper function finds all combinations of conditions among all possible combinations that optimize the fulfilment of the specified criteria for a superset (necessity) or subset (sufficiency) relation to the outcome.
superSubset(data, outcome = "", neg.out = FALSE, exo.facs = c(""), relation = "nec", incl.cut = 1, cov.cut = 0, use.tilde = FALSE, use.letters = FALSE, ...)superSubset(data, outcome = "", neg.out = FALSE, exo.facs = c(""), relation = "nec", incl.cut = 1, cov.cut = 0, use.tilde = FALSE, use.letters = FALSE, ...)
data |
A dataset of bivalent or multivalent crisp-set factor or bivalent fuzzy-set variables. |
outcome |
The name of the outcome. |
neg.out |
Logical, use negation of |
exo.facs |
A character vector with the names of the exogenous factors. |
relation |
The relation to |
incl.cut |
The minimal inclusion score of the relation. |
cov.cut |
The minimal coverage score of the relation. |
use.tilde |
Logical, use "~" for negation with bivalent variables. |
use.letters |
Logical, use simple letters instead of original factor names. |
... |
Other arguments for backward compatibility. |
This helper function to the testTESA function returns a list of those of the
potential value combinations, where is the number of values
for exogenous variable and is the number of exogenous
variables, that define minimal condition sets for the specified inclusion
(consistency) and coverage score cut-offs with respect to an outcome.
If relation = "nec" (default), the function finds (combinations of)
conditions that are supersets of (necessary for) the outcome. It starts with an
initiation set, which is comprised of all simple
condition sets. This set is expanded by incrementally forming set-theoretic
intersections of a higher order as long as incl.cut and cov.cut
are still met (the former always takes precedence over the latter). If suitable
conjunctions exist, they will be returned, together with all their lower-order
conjuncts.
If none of the simple conditions or their negations in the initiation set passes
incl.cut, disjunctions instead of conjunctions are formed until
incl.cut and cov.cut will have been met. Only the disjunctions thus
found will be returned.
If relation = "suf", the function finds (combinations of)
conditions that are subsets of (sufficient for) the outcome. The initiation set
is comprised of all
intersections of order . This set is reduced by incrementally forming
intersections of a lower order as long as incl.cut and cov.cut are
still met. Only the intersections of the lowest order will be printed. For more
details, see Thiem and Dusa (2013). For relation = "necsuf" and
relation = "sufnec", incl.cut will be applied to each relation and
cov.cut has no effect.
The argument outcome specifies the outcome. Outcomes from multivalent
variables require curly-bracket notation (X{value}).
The logical argument neg.out controls whether outcome is to be
used or its negation. If outcome is from a multivalent crisp-set factor,
neg.out = TRUE has the effect that the disjunctions of all remaining values
becomes the new outcome.
The argument exo.facs specifies the names of the exogenous factors.
If omitted, all factors in data are used except the factor of which
outcome is a level.
The argument use.tilde only applies to bivalent factors. If factors are
already named with single letters, the argument use.letters has no effect.
A list with the following two main components:
incl.cov |
A data frame with the parameters of fit. |
coms |
A data frame with the combination membership scores. |
| Dusa, Adrian | : development, programming |
| Thiem, Alrik | : development, documentation, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Ragin, Charles C. 2009. “Qualitative Comparative Analysis Using Fuzzy Sets (fsQCA).” In Configurational Comparative Methods: Qualitative Comparative Analysis (QCA) and Related Techniques, ed. B. Rihoux and C. C. Ragin. London: Sage Publications, pp. 87-121.
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. DOI: 10.1177/1065912912468269.
Thiem, Alrik. 2015. Standards of Good Practice and the Methodology of Necessary Conditions in Qualitative Comparative Analysis: A Critical View on Schneider and Wagemann's Theory-Guided/Enhanced Standard Analysis. COMPASSS WP Series 2015-83. URL: http://www.compasss.org/wpseries/Thiem2015.pdf.
# Schneider and Wagemann (2013, 212), using data from Ragin # (2009, 95), only present G and L as minimally necessary conditions #------------------------------------------------------------------- LIP <- data.frame( D = c(0.81,0.99,0.58,0.16,0.58,0.98,0.89,0.04,0.07, 0.72,0.34,0.98,0.02,0.01,0.01,0.03,0.95,0.98), U = c(0.12,0.89,0.98,0.07,0.03,0.03,0.79,0.09,0.16, 0.05,0.10,1.00,0.17,0.02,0.03,0.30,0.13,0.99), L = c(0.99,0.98,0.98,0.98,0.99,0.99,0.99,0.13,0.88, 0.98,0.41,0.99,0.59,0.01,0.17,0.09,0.99,0.99), I = c(0.73,1.00,0.90,0.01,0.08,0.81,0.96,0.36,0.07, 0.01,0.47,0.94,0.00,0.11,0.00,0.21,0.67,1.00), G = c(0.43,0.98,0.91,0.91,0.58,0.95,0.31,0.43,0.13, 0.95,0.58,0.99,0.00,0.01,0.84,0.20,0.91,0.98), S = c(0.05,0.95,0.89,0.12,0.77,0.95,0.05,0.06,0.42, 0.92,0.05,0.95,0.12,0.05,0.21,0.06,0.95,0.95) ) rownames(LIP) <- c("AT","BE","CZ","EE","FI","FR","DE","GR","HU", "IE","IT","NL","PL","PT","RO","ES","SE","UK") rownames(superSubset(LIP, outcome = "S", incl.cut = 0.9)$incl.cov) # with mv-data from Hartmann and Kemmerzell (2010) #------------------------------------------------- data(d.partybans) head(d.partybans) HK <- superSubset(d.partybans, outcome = "PB", exo.facs = c("C", "F", "T", "V"), incl.cut = 0.75) HK # combination membership scores for all cases (only first four # combinations and first ten lines displayed) HK$coms[1:10, 1:4, drop = FALSE]# Schneider and Wagemann (2013, 212), using data from Ragin # (2009, 95), only present G and L as minimally necessary conditions #------------------------------------------------------------------- LIP <- data.frame( D = c(0.81,0.99,0.58,0.16,0.58,0.98,0.89,0.04,0.07, 0.72,0.34,0.98,0.02,0.01,0.01,0.03,0.95,0.98), U = c(0.12,0.89,0.98,0.07,0.03,0.03,0.79,0.09,0.16, 0.05,0.10,1.00,0.17,0.02,0.03,0.30,0.13,0.99), L = c(0.99,0.98,0.98,0.98,0.99,0.99,0.99,0.13,0.88, 0.98,0.41,0.99,0.59,0.01,0.17,0.09,0.99,0.99), I = c(0.73,1.00,0.90,0.01,0.08,0.81,0.96,0.36,0.07, 0.01,0.47,0.94,0.00,0.11,0.00,0.21,0.67,1.00), G = c(0.43,0.98,0.91,0.91,0.58,0.95,0.31,0.43,0.13, 0.95,0.58,0.99,0.00,0.01,0.84,0.20,0.91,0.98), S = c(0.05,0.95,0.89,0.12,0.77,0.95,0.05,0.06,0.42, 0.92,0.05,0.95,0.12,0.05,0.21,0.06,0.95,0.95) ) rownames(LIP) <- c("AT","BE","CZ","EE","FI","FR","DE","GR","HU", "IE","IT","NL","PL","PT","RO","ES","SE","UK") rownames(superSubset(LIP, outcome = "S", incl.cut = 0.9)$incl.cov) # with mv-data from Hartmann and Kemmerzell (2010) #------------------------------------------------- data(d.partybans) head(d.partybans) HK <- superSubset(d.partybans, outcome = "PB", exo.facs = c("C", "F", "T", "V"), incl.cut = 0.75) HK # combination membership scores for all cases (only first four # combinations and first ten lines displayed) HK$coms[1:10, 1:4, drop = FALSE]
This evaluation function can be used to test the implications of Schneider and Wagemann's Theory-Guided/Enhanced Standard Analysis (T/ESA; Schneider and Wagemann 2013), and in particular, the procedure's first two stages, with respect to the extent of remainders that would have to be declared insufficient for the outcome. It has been programmed for Thiem (2016).
testTESA(data, outcome = "", neg.out = FALSE, exo.facs = c(""), n.cut = 1, incl.cut1 = 1, incl.cut0 = 1)testTESA(data, outcome = "", neg.out = FALSE, exo.facs = c(""), n.cut = 1, incl.cut1 = 1, incl.cut0 = 1)
data |
A dataset of bivalent crisp-set factors or bivalent fuzzy-set factors or multivalent crisp-set factors. |
outcome |
The name of the outcome. |
neg.out |
Logical, use negation of |
exo.facs |
A character vector with the names of the exogenous factors. |
n.cut |
The minimum number of cases with set membership score above 0.5 for an output function value of "0", "1" or "C". |
incl.cut1 |
The minimum sufficiency inclusion score for an output function value of "1". |
incl.cut0 |
The maximum sufficiency inclusion score for an output function value of "0". |
The arguments data, outcome, exo.facs, n.cut, incl.cut1 and incl.cut0 are those of the eQMC function.
A numeric vector with the percentages of remainder minterms that would have been used as simplifying assumptions by Quine-McCluskey optimization but that were declared to be insufficient for the outcome by T/ESA.
| Thiem, Alrik | : development, documentation, programming, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Ragin, Charles C. 2009. “Qualitative Comparative Analysis Using Fuzzy Sets (fsQCA).” In Configurational Comparative Methods: Qualitative Comparative Analysis (QCA) and Related Techniques, ed. B. Rihoux and C. C. Ragin. London: Sage Publications, pp. 87-121.
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. DOI: 10.1177/1065912912468269.
Thiem, Alrik. 2016. “Standards of Good Practice and the Methodology of Necessary Conditions in Qualitative Comparative Analysis.” Political Analysis 24 (4):478-84. DOI: 10.1093/pan/mpw024.
# Schneider and Wagemann (2013, 212), using data from Ragin # (2009, 95), only present L and S as minimally necessary conditions #------------------------------------------------------------------- LIP <- data.frame( D = c(0.81,0.99,0.58,0.16,0.58,0.98,0.89,0.04,0.07, 0.72,0.34,0.98,0.02,0.01,0.01,0.03,0.95,0.98), U = c(0.12,0.89,0.98,0.07,0.03,0.03,0.79,0.09,0.16, 0.05,0.10,1.00,0.17,0.02,0.03,0.30,0.13,0.99), L = c(0.99,0.98,0.98,0.98,0.99,0.99,0.99,0.13,0.88, 0.98,0.41,0.99,0.59,0.01,0.17,0.09,0.99,0.99), I = c(0.73,1.00,0.90,0.01,0.08,0.81,0.96,0.36,0.07, 0.01,0.47,0.94,0.00,0.11,0.00,0.21,0.67,1.00), G = c(0.43,0.98,0.91,0.91,0.58,0.95,0.31,0.43,0.13, 0.95,0.58,0.99,0.00,0.01,0.84,0.20,0.91,0.98), S = c(0.05,0.95,0.89,0.12,0.77,0.95,0.05,0.06,0.42, 0.92,0.05,0.95,0.12,0.05,0.21,0.06,0.95,0.95) ) rownames(LIP) <- c("AT","BE","CZ","EE","FI","FR","DE","GR","HU", "IE","IT","NL","PL","PT","RO","ES","SE","UK") superSubset(LIP, outcome = "S", incl.cut = 0.9) testTESA(LIP, outcome = "S", incl.cut1 = 0.75)# Schneider and Wagemann (2013, 212), using data from Ragin # (2009, 95), only present L and S as minimally necessary conditions #------------------------------------------------------------------- LIP <- data.frame( D = c(0.81,0.99,0.58,0.16,0.58,0.98,0.89,0.04,0.07, 0.72,0.34,0.98,0.02,0.01,0.01,0.03,0.95,0.98), U = c(0.12,0.89,0.98,0.07,0.03,0.03,0.79,0.09,0.16, 0.05,0.10,1.00,0.17,0.02,0.03,0.30,0.13,0.99), L = c(0.99,0.98,0.98,0.98,0.99,0.99,0.99,0.13,0.88, 0.98,0.41,0.99,0.59,0.01,0.17,0.09,0.99,0.99), I = c(0.73,1.00,0.90,0.01,0.08,0.81,0.96,0.36,0.07, 0.01,0.47,0.94,0.00,0.11,0.00,0.21,0.67,1.00), G = c(0.43,0.98,0.91,0.91,0.58,0.95,0.31,0.43,0.13, 0.95,0.58,0.99,0.00,0.01,0.84,0.20,0.91,0.98), S = c(0.05,0.95,0.89,0.12,0.77,0.95,0.05,0.06,0.42, 0.92,0.05,0.95,0.12,0.05,0.21,0.06,0.95,0.95) ) rownames(LIP) <- c("AT","BE","CZ","EE","FI","FR","DE","GR","HU", "IE","IT","NL","PL","PT","RO","ES","SE","UK") superSubset(LIP, outcome = "S", incl.cut = 0.9) testTESA(LIP, outcome = "S", incl.cut1 = 0.75)
This function creates truth tables from configurational data.
truthTable(data, outcome = "", neg.out = FALSE, exo.facs = c(""), n.cut = 1, incl.cut1 = 1, incl.cut0 = 1, complete = FALSE, show.cases = FALSE, sort.by = c(""), decreasing = TRUE, inf.test = c(""), use.letters = FALSE, ...) is.tt(x)truthTable(data, outcome = "", neg.out = FALSE, exo.facs = c(""), n.cut = 1, incl.cut1 = 1, incl.cut0 = 1, complete = FALSE, show.cases = FALSE, sort.by = c(""), decreasing = TRUE, inf.test = c(""), use.letters = FALSE, ...) is.tt(x)
data |
A set of configurational data (of class 'matrix' or 'data.frame'). |
outcome |
The name of the outcome. |
neg.out |
Logical, use the negation of |
exo.facs |
A character vector with the names of the exogenous factors. |
n.cut |
The minimum number of cases with set membership score above 0.5 for an output function value of "0", "1" or "C"; an integer between 1 and the maximum number of cases for all non-remainder minterms. |
incl.cut1 |
The minimum sufficiency inclusion score for an output function value of "1". |
incl.cut0 |
The maximum sufficiency inclusion score for an output function value of "0". |
complete |
Logical, print the complete truth table. |
show.cases |
Logical, print case names (do not use this option with many cases and/or long case names). |
sort.by |
Sort the truth table by inclusion scores and/or number of cases. |
decreasing |
Sort in decreasing or increasing order of value(s) passed to
|
inf.test |
A vector of length two specifying the inference-statistical
test to be performed (currently only |
use.letters |
Logical, use single letters (in alphabetical order) instead of original variable names. |
... |
Other arguments. |
x |
An object of class 'tt'. |
The argument data can be a truth table object (an object of class 'tt'
returned by the truthTable function) or a suitable data set. Suitable data
sets have the following structure: values of 0 and 1 for bivalent crisp-set factors,
values between 0 and 1 for bivalent fuzzy-set factors, and values beginning
with 0 at increments of 1 for multivalent crisp-set factors. The placeholders
"-" and "dc" indicate "don't cares" in auxiliary factors that specify temporal
order between other substantive factors in tQCA. These values lead to the
exclusion of the auxiliary factor from the computation of parameters of fit.
The argument outcome specifies the outcome to be analyzed, either in
curly-bracket notation (e.g., O{value}) if the outcome is from a multivalent
(or a bivalent) factor, or in upper-case notation if the outcome is from a bivalent
factor (e.g., O as a short-cut for O{1}). Outcomes from multivalent crisp-set factors always require curly-bracket notation. Outcomes must be single
levels of factors not simultaneously passed to exo.facs.
The logical argument neg.out controls whether outcome is to be
analyzed or its negation. If outcome is a level from a multivalent factor,
neg.out = TRUE causes the disjunction of all remaining levels to become
the outcome to be analyzed.
The argument exo.facs specifies the exogenous factors. If omitted, all
factors in data are used except that of the outcome. Please note
that computation times may increase significantly beyond 17 exogenous factors,
and that the computation of a solution may not be possible at all depending on
end-user machine constraints.
Minterms that contain fewer than n.cut cases with membership scores above
0.5 are coded as remainders (OUT = "?"). If the number of such cases is at
least n.cut, minterms with an inclusion score of at least incl.cut1
are coded positive (OUT = "1"), minterms with an inclusion score below
incl.cut1 but with at least incl.cut0 are coded as a contradiction
(OUT = "C"), and minterms with an inclusion score below incl.cut0
are coded negative (OUT = "0"). If incl.cut0 is not explicitly
changed, it is set equal to incl.cut1.
The logical argument show.cases controls whether case names are displayed
next to their corresponding minterm (do not use this option with many cases
and/or long case names).
The sort.by argument orders all minterms by their inclusion scores
(incl) or the number of cases with membership above 0.5 they contain
(n) or both, in either order.
If the exogenous factors are already named with single letters, the argument
use.letters will have no effect when set to TRUE. Otherwise,
upper-case letters will replace original factor names in alphabetical order.
The argument inf.test provides functionality for basing output function
value codings on inference-statistical tests. Currently, only an exact binomial
test ("binom") is available, which requires the data to contain only
bivalent or multivalent crisp-set factors. The argument requires a vector of
length two, comprising the test and a critical significance level. If the
empirical inclusion score of a minterm is not significantly lower than
incl.cut1, it will be coded positive (OUT = "1"). If it is
significantly lower than incl.cut1 yet still significantly higher than
incl.cut0, it will be coded as a contradiction (OUT = "C"). If it
is not significantly higher than incl.cut0, it will be coded negative
(OUT = "0").
An object of class 'tt', which is a list with the following six main
components:
tt |
The truth table. |
indexes |
The minterm line numbers. |
noflevels |
A vector with the number of levels of the exogenous factors. |
initial.data |
The initial data. |
recoded.data |
Recoded data (if crisp, same as |
cases |
The cases with membership above 0.5 in a minterm. |
| Dusa, Adrian | : development, programming |
| Thiem, Alrik | : development, documentation, programming, testing |
Alrik Thiem (Personal Website; ResearchGate Website)
Emmenegger, Patrick. 2011. “Job Security Regulations in Western Democracies: A Fuzzy Set Analysis.” European Journal of Political Research 50 (3):336-64. DOI: 10.1111/j.1475-6765.2010.01933.x.
Hartmann, Christof, and Joerg Kemmerzell. 2010. “Understanding Variations in Party Bans in Africa.” Democratization 17 (4):642-65. DOI: 10.1080/13510347.2010.491189.
Krook, Mona Lena. 2010. “Women's Representation in Parliament: A Qualitative Comparative Analysis.” Political Studies 58 (5):886-908. DOI: 10.1111/j.1467-9248.2010.00833.x.
Ragin, Charles C., and Sarah Ilene Strand. 2008. “Using Qualitative Comparative Analysis to Study Causal Order: Comment on Caren and Panofsky (2005).” Sociological Methods & Research 36 (4):431-41. DOI: 10.1177/0049124107313903.
# csQCA using Krook (2010) #------------------------- data(d.represent) head(d.represent) # print truth table; if all factors except that of the outcome in # the data should be included as exogenous factors, then these need # not be specified separately truthTable(d.represent, outcome = "WNP") # print complete truth table, show cases, and first sort by # inclusion scores, then by number of cases truthTable(d.represent, outcome = "WNP", complete = TRUE, show.cases = TRUE, sort.by = c("incl", "n")) # code minterms with a single case as remainders (note: use of # 'n.cut' should be well justified) KRO.tt <- truthTable(d.represent, outcome = "WNP", n.cut = 2, show.cases = TRUE) KRO.tt # print cases that were assigned to remainders based on argument 'n.cut' KRO.tt$excluded # fsQCA using Emmenegger (2011) #------------------------------ data(d.jobsecurity) head(d.jobsecurity) # code non-remainder minterms with inclusion scores between 0.4 # and 0.8 as contradictions (note: these are not 'contradictions' # in the logical sense of the word but minterms that can neither # be coded as sufficient nor as insufficient for the outcome) truthTable(d.jobsecurity, outcome = "JSR", incl.cut1 = 0.8, incl.cut0 = 0.4) # truth table based on the negated outcome truthTable(d.jobsecurity, outcome = "JSR", neg.out = TRUE, incl.cut1 = 0.8, incl.cut0 = 0.4) # mvQCA using Hartmann and Kemmerzell (2010) #------------------------------------------- data(d.partybans) head(d.partybans) # code non-remainder minterms with inclusion scores below 1 # but above 0.4 as contradictions HK.tt <- truthTable(d.partybans, outcome = "PB", exo.facs = c("C","F","T","V"), incl.cut0 = 0.4) HK.tt # list the number of levels for the exogenous factors HK.tt$noflevels # which minterms have more than 2 cases? HK.tt$tt[which(HK.tt$tt$n > 2), ] # code output function values in truth table based on # exact binomial test truthTable(d.partybans, outcome = "PB", exo.facs = c("C","F","T"), incl.cut1 = 0.9, incl.cut0 = 0.4, show.cases = TRUE, inf.test = c("binom", 0.1)) # tQCA using Ragin and Strand (2008) #----------------------------------- data(d.graduate) head(d.graduate) # tQCA truth table with "don't care" values truthTable(d.graduate, outcome = "REC")# csQCA using Krook (2010) #------------------------- data(d.represent) head(d.represent) # print truth table; if all factors except that of the outcome in # the data should be included as exogenous factors, then these need # not be specified separately truthTable(d.represent, outcome = "WNP") # print complete truth table, show cases, and first sort by # inclusion scores, then by number of cases truthTable(d.represent, outcome = "WNP", complete = TRUE, show.cases = TRUE, sort.by = c("incl", "n")) # code minterms with a single case as remainders (note: use of # 'n.cut' should be well justified) KRO.tt <- truthTable(d.represent, outcome = "WNP", n.cut = 2, show.cases = TRUE) KRO.tt # print cases that were assigned to remainders based on argument 'n.cut' KRO.tt$excluded # fsQCA using Emmenegger (2011) #------------------------------ data(d.jobsecurity) head(d.jobsecurity) # code non-remainder minterms with inclusion scores between 0.4 # and 0.8 as contradictions (note: these are not 'contradictions' # in the logical sense of the word but minterms that can neither # be coded as sufficient nor as insufficient for the outcome) truthTable(d.jobsecurity, outcome = "JSR", incl.cut1 = 0.8, incl.cut0 = 0.4) # truth table based on the negated outcome truthTable(d.jobsecurity, outcome = "JSR", neg.out = TRUE, incl.cut1 = 0.8, incl.cut0 = 0.4) # mvQCA using Hartmann and Kemmerzell (2010) #------------------------------------------- data(d.partybans) head(d.partybans) # code non-remainder minterms with inclusion scores below 1 # but above 0.4 as contradictions HK.tt <- truthTable(d.partybans, outcome = "PB", exo.facs = c("C","F","T","V"), incl.cut0 = 0.4) HK.tt # list the number of levels for the exogenous factors HK.tt$noflevels # which minterms have more than 2 cases? HK.tt$tt[which(HK.tt$tt$n > 2), ] # code output function values in truth table based on # exact binomial test truthTable(d.partybans, outcome = "PB", exo.facs = c("C","F","T"), incl.cut1 = 0.9, incl.cut0 = 0.4, show.cases = TRUE, inf.test = c("binom", 0.1)) # tQCA using Ragin and Strand (2008) #----------------------------------- data(d.graduate) head(d.graduate) # tQCA truth table with "don't care" values truthTable(d.graduate, outcome = "REC")