Find Superset and Subset Relations
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, ...)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
∏_{j = 1}^{k}{(p_{j} + 1) - 1}
potential value combinations, where p_{j} is the number of values
for exogenous variable j and k 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 ∑_{j = 1}^{k}{p_{j}} 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 ∏_{j = 1}^{k}{p_{j}}
intersections of order k. 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]Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.