QCA (version 1.0-4)

truthTable: Create a Truth Table

Description

A truth table lists every configuration (combination of condition literals) and its outcome value. This function creates truth tables from any kind of common input data. For crisp-set data (binary and multi-value), cases are assigned directly to the unique configuration in which they have membership. For fuzzy-set data, the function first detects in which configuration a case has membership above 0.5 before assigning it to this configuration. is.tt() checkes whether an object has class "tt" (truth table); such an object is created by truthTable()

Usage

truthTable(mydata, outcome = "", 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, ...)
is.tt(x)

Arguments

mydata

A dataset of (binary or multi-value) crisp or fuzzy-set data

outcome

The name of the outcome set

neg.out

Logical, use negation of outcome set

conditions

The names of the conditions

n.cut

The minimum number of cases with membership > 0.5 for an outcome value of "0", "1" or "C"

incl.cut1

The minimum sufficiency inclusion score for an outcome value of "1"

incl.cut0

The maximum sufficiency inclusion score for an outcome 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 letters instead of set names

x

An object of class "tt"

...

Other arguments (used internally)

Value

• An object of class "tt", which is a list with the following components: lll{ tt the truth table indexes the configuration line numbers noflevels a vector with the number of condition levels 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 dataset specifed as mydata has to have the following structure: values of 0 and 1 for binary-value crisp sets, values between 0 and 1 for fuzzy set data, and values beginning with 0 and increments of 1 for mutli-value crisp set data. "Don't care" values are indicated by a dash "-", the placeholder "dc" or any negative integer. These values are ignored in the minimization. Sets which contain these values are excluded from the computation of parameters of fit.

If the argument conditions is not specified, all sets in mydata but the outcome are included as conditions.

Configurations that contain fewer than n.cut cases with membership above 0.5 are coded as logical remainders ("?"). If the number of such cases is at least n.cut, configurations with an inclusion score of at least incl.cut1 are coded as true ("1"), configuration with an inclusion score below incl.cut1 but with at least incl.cut0 are coded as a contradiction ("C"), and configurations with an inclusion score below incl.cut0 are coded as false ("0"). If incl.cut0 is not specified, it is set equal to incl.cut1 and no contradictions can occur.

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.

References

P. Emmenegger. Job Security Regulations in Western Democracies: A Fuzzy Set Analysis. European Journal of Political Research, 50(3):336-364, 2011.

C. Hartmann and J. Kemmerzell. Understanding Variations in Party Bans in Africa. Democratization, 17(4):642-665, 2010.

M. L. Krook. Women's Representation in Parliament: A Qualitative Comparative Analysis. Political Studies, 58(5):886-908, 2010.

C. C. Ragin. The Comparative Method: Moving beyond Qualitative and Quantitative Strategies. University of California Press, Berkeley, 1987.

C. C. Ragin. Redesigning Social Inquiry: Fuzzy Sets and Beyond. University of Chicago Press, Chicago, 2008.

C. C. Ragin and S. I. Strand. Using Qualitative Comparative Analysis to Study Causal Order: Comment on Caren and Panofsky (2005). Sociological Methods & Research, 36(4):431-441, 2008.

A. Thiem and A. Dusa. Qualitative Comparative Analysis with R: A User's Guide. Springer, New York, 2012.

See Also

eqmcc

Examples

# csQCA using Krook (2010)
#-------------------------
data(Krook)
Krook

# print the truth table
truthTable(Krook, outcome = "WNP")

# print the complete truth table, show cases, sort by inclusions
# scores and then number of cases
truthTable(Krook, outcome = "WNP", complete = TRUE, show.cases = TRUE,
  sort.by = c("incl", "n"))

# code configurations with 1 case as remainders
KrookTT <- truthTable(Krook, outcome = "WNP", n.cut = 2, show.cases = TRUE)
KrookTT

# print the cases that were assigned to remainders based on n.cut
KrookTT$excluded

# fsQCA using Emmenegger (2011)
#------------------------------
data(Emme)
Emme

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

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

# get the raw truth table as a component of the truth table object EmmeTT
EmmeTT$tt 

# mvQCA using Hartmann and Kemmerzell (2010)
#-------------------------------------------
data(HarKem)
HarKem

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

# list the number of condition levels  
HarKemTT$noflevels

# which configurations have more than 2 cases
which(HarKemTT$tt$n > 2)

# tQCA using Ragin and Strand (2008)
#-----------------------------------
data(RagStr)
RagStr

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