| truthTable {QCApro} | R Documentation |
Create a Truth Table
Description
This function creates truth tables from configurational data.
Usage
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)
Arguments
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'. |
Details
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").
Value
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. |
Contributors
| Dusa, Adrian | : development, programming |
| Thiem, Alrik | : development, documentation, programming, testing |
Author(s)
Alrik Thiem (Personal Website; ResearchGate Website)
References
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.
Examples
# 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")