QCA (version 1.1-2)

truthTable: Create a Truth Table

Description

This function creates truth tables from any kind of common input data. For crisp set variables, cases are assigned directly to their respective configuration. For fuzzy set variables, the function first finds the configuration in which a case has membership above 0.5 before assigning it.

Usage

truthTable(data, outcome = c(""), neg.out = FALSE, conditions = c(""), 
           n.cut = 1, incl.cut1 = 1, incl.cut0 = 1, complete = FALSE, 
           show.cases = FALSE, sort.by = c(""), decreasing = TRUE, 
           use.letters = FALSE, inf.test = c(""), ...)

is.tt(x)

Arguments

data

A data set of bivalent crisp or fuzzy set variables or multivalent crisp set variables.

outcome

The name of the outcome set.

neg.out

Logical, use negation of outcome set.

conditions

A vector of condition sets.

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".

complete

Logical, print complete truth table.

show.cases

Logical, print case names.

sort.by

Sort truth table by inclusion scores and/or number of cases.

decreasing

Sort in decreasing or increasing order of value(s) passed to sort.by.

use.letters

Logical, use simple letters instead of original variable names.

inf.test

A vector specifying the inference-statistical test to be performed (currently only "binom") and the critical significance level.

...

Other arguments (for backward compatibility).

x

An object of class "tt".

Value

• An object of class "tt", which is a list with the following components:
• tt
  The truth table.
• indexes
  The configuration line numbers.
• noflevels
  A vector with the number of condition variable values.
• initial.data
  The initial data.
• recoded.data
  Recoded data (if crisp, same as initial.data; if fuzzy, dichotomized version of initial.data).
• cases
  The cases with membership above 0.5 in each configuration.

Details

The argument data requires a suitable data set. Suitable data sets have the following structure: values of 0 and 1 for bivalent crisp set variables, values between 0 and 1 for bivalent fuzzy set variables, and values beginning with 0 at increments of 1 for multivalent crisp set variables. The placeholder "-" indicates a "don't care" value in auxiliary conditions that specify temporal order between other substantive conditions in tQCA. These values lead to the exclusion of the auxiliary condition from the computation of parameters of fit. The argument conditions specifies the condition variables. If omitted, all variables in data are used except outcome. Configurations that contain fewer than n.cut cases with membership scores above 0.5 are coded as logical remainders (OUT = "?"). If the number of such cases is at least n.cut, configurations with an inclusion score of at least incl.cut1 are coded positive (OUT = "1"), configurations with an inclusion score below incl.cut1 but with at least incl.cut0 are coded as a contradiction (OUT = "C"), and configurations with an inclusion score below incl.cut0 are coded negative (OUT = "0"). If incl.cut0 is unspecified, it is set equal to incl.cut1 and no contradictions can occur. The logical argument show.cases controls whether case names are displayed next to their corresponding configuration (do not use with many cases and/or long case names). The sort.by argument orders all configurations 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 conditions are already named with single letters, the argument use.letters will have no effect. The argument inf.test provides functionality for basing output function value codings on inference-statistical tests of the observed configurations for (bivalent and multivalent) crisp set variables. It requires a vector of length two, comprising the test (currently only exact binomial: "binom") and a significance level. If the empirical inclusion score of a configuration is not significantly lower than incl.cut1, it will be coded positive (OUT = "1"). If it is significantly lower than incl.cut1 but 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"). For backward compatibility, the logical argument PRI returns PRI (proportional reduction in inconsistency) scores (see Schneider and Wagemann 2012, pp. 241-249; Thiem and Dusa 2013, pp. 63-64, 78-79). However, note that direct tests on negated outcomes and/or conditions should be preferred.

References

Emmenegger, Patrick. 2011. Job Security Regulations in Western Democracies: A Fuzzy Set Analysis. European Journal of Political Research 50 (3):336-64. Hartmann, Christof, and Joerg Kemmerzell. 2010. Understanding Variations in Party Bans in Africa. Democratization 17 (4):642-65. Krook, Mona Lena. 2010. Women's Representation in Parliament: A Qualitative Comparative Analysis. Political Studies 58 (5):886-908. Ragin, Charles C. 1987. The Comparative Method: Moving beyond Qualitative and Quantitative Strategies. Berkeley: University of California 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. 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. Thiem, Alrik, and Adrian Dusa. 2013. Qualitative Comparative Analysis with R: A User's Guide. New York: Springer.

See Also

eqmcc

Examples

# csQCA using Krook (2010)
#-------------------------
data(d.Kro)
head(d.Kro)

# print truth table
truthTable(d.Kro, outcome = "WNP")

# print complete truth table, show cases, and first sort by 
# inclusion scores, then by number of cases
truthTable(d.Kro, outcome = "WNP", complete = TRUE, 
  show.cases = TRUE, sort.by = c("incl", "n"))

# code configurations with single case as remainders
Kro.tt <- truthTable(d.Kro, outcome = "WNP", n.cut = 2, 
  show.cases = TRUE)
Kro.tt

# print cases that were assigned to remainders based on n.cut
Kro.tt$excluded

# fsQCA using Emmenegger (2011)
#------------------------------
data(d.Emm)
head(d.Emm)

# code non-remainder configurations with inclusion scores 
# between 0.5 and 0.9 as contradictions
Emm.tt <- truthTable(d.Emm, outcome = "JSR", incl.cut1 = 0.9, 
  incl.cut0 = 0.5)
Emm.tt

# truth table based on negated outcome set
Emm.tt <- truthTable(d.Emm, outcome = "JSR", neg.out = TRUE, 
  incl.cut1 = 0.9, incl.cut0 = 0.5)
Emm.tt

# mvQCA using Hartmann and Kemmerzell (2010)
#-------------------------------------------
data(d.HK)
head(d.HK)

# code non-remainder configurations with inclusion scores below 1 
# but above 0.4 as contradictions 
HK.tt <- truthTable(d.HK, outcome = "PB", 
  conditions = c("C","F","T","V"), incl.cut0 = 0.4)
HK.tt

# list the number of levels (values)  
HK.tt$noflevels

# which configurations 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 (condition variable V dropped)
HK.tt <- truthTable(d.HK, outcome = "PB", 
  conditions = c("C","F","T"), incl.cut1 = 0.9, incl.cut0 = 0.4, 
  show.cases = TRUE, inf.test = c("binom", 0.1))
HK.tt

# tQCA using Ragin and Strand (2008)
#-----------------------------------
data(d.RS)
head(d.RS)

# tQCA truth table with "don't care" values
truthTable(d.RS, outcome = "REC")