cna (version 1.0-3)

truthTab: Generate a truth table

Description

This function builds a truth table from a Boolean data frame.

Usage

truthTab(x, frequency = NULL, switch = FALSE, case.cutoff = 0)
"print"(x, row.names = FALSE, show.cases = FALSE, ...)

Arguments

x

A Boolean data frame, i.e. a data frame or a matrix with 0 and 1 as entries.

frequency

Numeric vector of length nrow(x). All elements must be non-negative.

switch

Vector (integer, logical or character) specifying the columns in x to be switched, i.e. the columns where 1 is replaced by 0 and vice versa.

case.cutoff

Minimum number of occurrences (cases) of a configuration in x. Configurations with fewer than case.cutoff occurrences (cases) are not included in the truth table.

show.cases

Logical; specifies whether the attribute “cases” is printed.

row.names,...

Are passed to print.data.frame.

Value

truthTab returns a data frame of class “truthTab” with attributes “n” and “cases”.

Details

The truthTab function merges multiple rows of a data frame x featuring the same configuration into one row, such that each row of the resulting truth table corresponds to one determinate configuration of the factors in x. The number of occurrences (cases) and an enumeration of the cases are saved as attributes “n” and “cases”, respectively. The attribute “n” is always printed in the output of truthTab, the attribute “cases” is not printed by default but can be recovered by the show.cases argument of the print function.

Instead of multiply listing identical configurations in x, the frequency argument can be used to indicate the frequency of each configuration in the data frame. frequency takes a numeric vector of length nrow(x) as value. For instance, truthTab(x, frequency = c(3,4,2,3)) determines that the first configuration in x is featured in 3 cases, the second in 4, the third in 2, and the fourth in 3 cases.

The switch argument serves the purpose of switching all values of a factor in its column of x from 1 to 0 and vice versa. Thereby, the corresponding factor is re-categorized. For instance, truthTab(x, switch = c("SP")) re-categorizes the factor "superior performance" into the factor "inferior performance".

The case.cutoff argument is used to stipulate that configurations are only included in the truth table if they are instantiated at least as many times in x as the number assigned to case.cutoff. Or differently, configurations that are instantiated less than the number given to case.cutoff are excluded from the truth table. For instance, truthTab(x, case.cutoff = 3) entails that configurations with less than 3 cases are excluded.

The row.names argument of the print function determines whether the row names of x are printed or not. The default is FALSE.

References

Greckhamer, Thomas, Vilmos F. Misangyi, Heather Elms, and Rodney Lacey. 2008. “Using Qualitative Comparative Analysis in Strategic Management Research: An Examination of Combinations of Industry, Corporate, and Business-Unit Effects.” Organizational Research Methods 11 (4):695-726.

See Also

cna, condition, d.performance

Examples

# User defined data input
#------------------------
dat1 <- data.frame(
A = c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0),
B = c(1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0),
C = c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0),
D = c(1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0),
E = c(1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0)
)

# Default return of the truthTab function.
truthTab(dat1)

# By means of the print function, the cases featuring each configuration can be recovered.
print(truthTab(dat1), show.cases = TRUE)

# The same truth table as before can be generated by using the frequency argument while
# listing each configuration only once.
dat1 <- data.frame(
A = c(1,1,1,1,1,1,0,0,0,0,0),
B = c(1,1,1,0,0,0,1,1,1,0,0),
C = c(1,1,1,1,1,1,1,1,1,0,0),
D = c(1,0,0,1,0,0,1,1,0,1,0),
E = c(1,1,0,1,1,0,1,0,1,1,0)
)
truthTab(dat1, frequency = c(4,3,1,3,4,1,4,1,3,3,3))

# Truth tables generated by truthTab can be input into the cna function.
dat1_tt <- truthTab(dat1, frequency = c(4,3,1,3,4,1,4,1,3,3,3))
cna(dat1_tt, con = 0.85)

# By means of the case.cutoff argument configurations with less than 2 cases can
# be excluded, which maneuver yields perfect consistency and coverage scores for dat1.
dat1_tt <- truthTab(dat1, frequency = c(4,3,1,3,4,1,4,1,3,3,3), case.cutoff = 2)
cna(dat1_tt)


# Greckhamer et al. (2008) on the causal conditions for superior business-unit performance
#-----------------------------------------------------------------------------------------
# Load dataset. 
data(d.performance)
truthTab(d.performance[1:8], frequency = d.performance$frequency)

# Eliminate configurations with less than 5 cases.
truthTab(d.performance[1:8], frequency = d.performance$frequency, case.cutoff = 5)

# Switch the factor "superior performance" into the factor "inferior performance".
truthTab(d.performance[1:8], frequency = d.performance$frequency, switch = c("SP"))

# Various large-n CNAs of d.performance with varying case, consistency, and coverage
# cut-offs.
cna(truthTab(d.performance[1:8], frequency = d.performance$frequency, case.cutoff = 5),
       con = 0.8, cov = 0.8)
cna(truthTab(d.performance[1:8], frequency = d.performance$frequency, case.cutoff = 5),
       con = 0.75, cov = 0.75)
cna(truthTab(d.performance[1:8], frequency = d.performance$frequency, case.cutoff = 10),
       con = 0.75, cov = 0.75)
print(cna(truthTab(d.performance[1:8], frequency = d.performance$frequency,
       case.cutoff = 7), con = 0.65, cov = 0.75, what = "c"), nsolutions = "all")