QCAGUI (version 2.2)

truthTable: Create a truth table

Description

This function creates a truth table from all types of calibrated data (binary crisp, multi-value crisp and fuzzy). For fuzzy data, Ragin's (2008) procedure is applied to assign cases to the vector space corners (the truth table rows, combinations of causal conditions).

Usage

truthTable(data, outcome = "", conditions = "", n.cut = 1,
    incl.cut = 1, complete = FALSE,  show.cases = FALSE,
    sort.by = "", use.letters = FALSE, inf.test = "", ...)

is.tt(x)

Arguments

data

A data frame containing calibrated causal conditions and an outcome

outcome

String, the name of the outcome.

conditions

A single string containing the conditions' (columns) names separated by commas, or a character vector of conditions' names.

n.cut

The minimum number of cases under which a truth table row is declared as a remainder.

incl.cut

The inclusion cutoff(s): either a single value for the presence of the output, or a vector of length 2, the second for the absence of the output.

complete

Logical, print complete truth table.

show.cases

Logical, print case names.

sort.by

Sort the truth table according to various columns.

use.letters

Logical, use letters instead of causal conditions' names.

inf.test

Specifies the statistical inference test to be performed (currently only "binom") and the critical significance level. It can be either a vector of length 2, or a single string containing both, separated by a comma.

...

Other arguments (mainly for backward compatibility).

x

An object of class tt.

Value

• An object of class tt, a list containing the following components: rl{ tt The truth table itself. indexes The line numbers for the observed causal configurations. noflevels A vector with the number of values for each causal condition. initial.data The initial data. recoded.data The crisp version of the initial.data, if fuzzy. cases The cases for each observed causal configuration. options The command options used. rowsorder The order of the rows after sorting, if using sort.by. } For reasons related to compatibility with other packages, the optios component with temporarily contain both forms of notation for the inclusion cuttofs: in addition to incl.cut it will also contain incl.cut1 and incl.cut0 (but will soon be deprecated).

Details

The data should always be provided as a data frame, with calibrated columns. Calibration can be either crisp, with 2 or more values starting from 0, or fuzzy with continous scores from 0 to 1. Raw data containing relative frequencies can also be continous between 0 and 1, but these are not calibrated, fuzzy data. Some columns can contain the placeholder "-" indicating a don't care, which is used to indicate the temporal order between other columns in tQCA. These special columns are not causal conditions, hence no parameters of fit will be calculated for them. The argument outcome specifies the column name to be explained. If the outcome is a multivalue column, it can be specified in curly bracket notation, indicating the value to be explained (the others being automatically converted to zero). The outcome can be negated using a tilde operator ~X. The logical argument neg.out is now deprecated, but still backwards compatible. Replaced by the tilde in front of the outcome name, it controls whether outcome is to be explained or its negation. If the outcome column is multi-value, the argument outcome should use the standard curly-bracket notation X{value}. Multiple values are allowed, separated by a comma (for example X{1,2}). Negation of the outcome can also be performed using the tilde ~ operator, for example ~X{1,2}, which is interpreted as: "all values in X except 1 and 2" and it becomes the new outcome to be explained. Using both neg.out = TRUE and a tilde ~ in the outcome name don't cancel each other out, either one (or even both) signaling if the outcome should be negated. The argument conditions specifies the causal conditions' names among the other columns in the data. When this argument is not specified, all other columns except for the outcome are taken as causal conditions. A good practice advice is to specify both outcome and conditions as upper case letters. It is possible, in a next version, to negate outcomes using lower case letters, situation in which it really does matter how the outcome and/or conditions are specified. The argument n.cut specifies the frequency threshold under which a truth table row is coded as a remainder, irrespective of its inclusion score. The argument incl.cut replaces the (deprecated, but still backwards compatible) former arguments incl.cut1 and incl.cut0. Most of the analyses use the inclusion cutoff for the presence of the output (code "1"). When users need both inclusion cutoffs (see below), incl.cut can be specified as a vector of length 2, in the form: c(ic1, ic0) where: rl{ ic1 is the inclusion cutoff for the presence of the output, a minimum sufficiency inclusion score above which the output value is coded with "1". ic0 is the inclusion cutoff for the absence of the output, a maximum sufficiency inclusion score below which the output value is coded with "0". } If not specifically declared, the argument ic0 is automatically set equal to ic1, but otherwise ic0 should always be lower than ic1. Using these two cutoffs, the observed combinations are coded with: rl{ "1" if they have an inclusion score above ic1 "C" if they have an inclusion score below ic1 and above ic0 (contradiction) "0" if they have an inclusion score below ic0 } When argument show.cases is set to TRUE, the case names will be printed at their corresponding row in the truth table. The resulting object always contains the cases for each causal combination, even if not printed on the screen (the print function can later be used to print them). The sort.by argument orders all configurations by any of the columns present in the truth table. Typically, sorting occurs by their outcome value, and/or by their inclusion score, and/or by their frequency, in any order. sort.by can also be a named logical vector, with the names indicating the columns to sort and the logical value indicating a decreasing order (TRUE) or not. The order specified in this vector is the order in which the configurations will be sorted. When sorting based on the OUTput column, remainders will always be sorted last. Aternatively, the (deprecated) decreasing argument can be used either as a logical vector of the same length as sort.by, or a single logical value which will be used for all columns in sort.by. If the length of the decreasing is shorter than sort.by's, it will be augmented with TRUE values. If sort.by is already defined as a logical vector, decreasing will be ignored. The argument use.letters controls using the original names of the causal conditions, or replace them by single letters in alphabetical order. If the causal conditions are already named with single letters, the original letters will be used. The argument inf.test combines the inclusion score with a statistical inference test, in order to assign values in the output column OUT. For the moment, it is only the binomial test, which needs crisp data (it doesn't work with fuzzy sets). Following a similar logic as above, for a given (specified) critical significance level, the output for a truth table row will be coded as: rl{ "1" if the true inclusion score is significanly higher than ic1, "C" contradiction, if the true inclusion score is not significantly higher than ic1 but significantly higher than ic0, "0" if the true inclusion score is not significantly higher than ic0. } It should be noted that statistical tests perform well only when the number of cases is large, otherwise they are usually not significant. For a low number of cases, depending on the inclusion cutoff value(s), it will be harder to code a value of "1" in the output, and also harder to obtain contradictions if the true inclusion is not signficantly higher than ic0. The argument complete controls how to print the table on the screen, either complete (when set to TRUE), or just the observed combinations (default). For up to 7 causal conditions, the resulting object will always contain the complete truth table, even if it's not printed on the screen. This is useful for multiple reasons: researchers like to manually change output values in the truth table (sometimes including in this way a remainder, for example), and it is also useful to plot Venn diagrams, each truth table row having a correspondent intersection in the diagram.

References

Cronqvist, L.; Berg-Schlosser, D. (2009) Multi-Value QCA (mvQCA), in Rihoux, B.; Ragin, C. (eds.) Configurational Comparative Methods. Qualitative Comparative Analysis (QCA) and Related Techniques, SAGE. Lipset, S.M. (1959) Some Social Requisites of Democracy: Economic Development and Political Legitimacy, American Political Science Review vol.53, pp.69-105. Ragin, C.C. (1987) The Comparative Method: Moving beyond Qualitative and Quantitative Strategies. Berkeley: University of California Press. Ragin, C.C. (2008) Redesigning Social Inquiry: Fuzzy Sets and Beyond. Chicago: University of Chicago Press. Ragin, C.C.; Strand, S.I. (2008) Using Qualitative Comparative Analysis to Study Causal Order: Comment on Caren and Panofsky (2005). Sociological Methods & Research vol.36, no.4, pp.431-441. Schneider, C.Q.; Wagemann, C. (2012) Set-Theoretic Methods for the Social Sciences: A Guide to Qualitative Comparative Analysis (QCA). Cambridge: Cambridge University Press. Thiem, A.; Dusa, A. (2013) Qualitative Comparative Analysis with R: A User's Guide. New York: Springer.

See Also

eqmcc

Examples

# -----
# Lipset binary crisp data
data(LC)
ttLC <- truthTable(LC, "SURV")

# inspect the truth table
ttLC

# print the cases too, even if not specifically asked for
print(ttLC, show.cases = TRUE)

# the printing function also supports the complete version
print(ttLC, show.cases = TRUE, complete = TRUE)

# formally asking the complete version
truthTable(LC, "SURV", complete = TRUE)

# sorting by multiple columns, decreasing by default
# equivalent to the (now obsolete) argument decreasing = TRUE
truthTable(LC, "SURV", complete = TRUE, sort.by = "incl, n")

# sort the truth table decreasing for inclusion, and increasing for n
# "n = FALSE" is equivalent to using "decreasing = FALSE"
truthTable(LC, "SURV", complete = TRUE, sort.by = "incl, n = FALSE")



# -----
# Lipset multi-value crisp data (Cronqvist & Berg-Schlosser 2009, p.80)
data(LM)
truthTable(LM, "SURV", sort.by = "incl")

# using a frequency cutoff equal to 2 cases
ttLM <- truthTable(LM, "SURV", n.cut = 2, sort.by = "incl = TRUE")
ttLM

# the observed combinations coded as remainders
ttLM$excluded



# -----
# Cebotari & Vink fuzzy data
data(CVF)
ttCVF <- truthTable(CVF, "PROTEST", incl.cut = 0.8, sort.by="incl")

# view the Venn diagram for this truth table
library(venn)
venn(ttCVF)

# each intersection transparent by its inclusion score
venn(ttCVF, transparency = ttCVF$tt$incl)

# the truth table negating the outcome
truthTable(CVF, "~PROTEST", incl.cut = 0.8, sort.by="incl")

# allow contradictions
truthTable(CVF, "PROTEST", incl.cut = c(0.8, 0.75), sort.by="incl")



# -----
# Ragin and Strand data with temporal QCA
data(RS)

# truth table containing the "-" placeholder as a "don't care"
truthTable(RS, "REC")