qmcc: Find a minimum solution in a boolean procedure, using the Quine-McCluskey algorithm

Description

This function is the core of the QCA (Qualitative Comparative Analysis) package. The QCA is the bridge between the qualitative and quantitative worlds, and its fundamental philosophy is based on Mill's methods of inductive inquiry. Given a dataset with cases on the rows (or better said, case studies) and various conditions on the columns, this function finds which condition (or combination of conditions) is necessary and/or sufficient to trigger the outcome. As of version 0.6-0, qmcc() is explicitely working with binary data only.

Usage

qmcc(mydata, outcome = "", conditions = c(""), incl.rem = FALSE,
     expl.1 = FALSE, expl.0 = FALSE, expl.ctr = FALSE, expl.mo = FALSE,
     incl.1 = FALSE, incl.0 = FALSE, incl.ctr = FALSE, incl.mo = FALSE,
     quiet = FALSE, details = TRUE, chart = FALSE, use.letters = TRUE,
     show.cases = FALSE, diffmat=TRUE)

Arguments

mydata

the dataset used for minimization (dataframe or matrix)

outcome

the name of the outcome variable from the dataset

conditions

a string vector containing the conditions' names from the dataset (if not specified, all variables but the outcome are included)

incl.rem

include the remainders in the minimization procedure

expl.1

explain the outcomes equal to 1

expl.0

explain the outcomes equal to 0

expl.ctr

explain the contradictions

expl.mo

explain the missing outcomes (not implemented yet)

incl.1

include the outcomes equal to 1 in the minimization procedure

incl.0

include the outcomes equal to 0 in the minimization procedure

incl.ctr

include the contradictions in the minimization procedure

incl.mo

include the missing outcome in the minimization procedure (not implemented yet)

quiet

prints the solution without any other information

details

prints some relevant details (set to FALSE if quiet is TRUE

chart

print the prime implicants chart

use.letters

should letters be used instead of column names

show.cases

show the lines corresponding to every minimized prime implicant

diffmat

generate the differences matrix

Value

an invisible list with five components: initial combinations, minimised PIs, the raw PI chart, the number of k PIs to solve the PI chart and the solution(s)

References

Ragin, Charles C. (1987) The Comparative Method. Moving beyond qualitative and quantitative strategies, Berkeley: University of California Press

Dusa, Adrian (2010) A mathematical approach to the boolean minimization problem, Quality & Quantity vol.44, no.1, pp.99-113

Examples

Run this code

data(Osa)

# find a solution using the Quine-McCluskey (qmcc) algorithm
# explaining only the presence of the outcome
qmcc(Osa, outcome="OUT", expl.1=TRUE)

# now including the remainers and the contradictions
qmcc(Osa, outcome="OUT", expl.1=TRUE, incl.rem=TRUE, incl.ctr=TRUE)

# the same as above, but we want to see the prime implicants chart
qmcc(Osa, outcome="OUT", expl.1=TRUE, incl.rem=TRUE, incl.ctr=TRUE, chart=TRUE)

# even more details
qmcc(Osa, outcome="OUT", expl.1=TRUE, incl.rem=TRUE, incl.ctr=TRUE, details=TRUE)

# printing the lines corresponding to each prime implicant
qmcc(Osa, outcome="OUT", expl.1=TRUE, incl.rem=TRUE, incl.ctr=TRUE, show.cases=TRUE)

# now explaining the absence of the outcome
qmcc(Osa, outcome="OUT", expl.0=TRUE, incl.rem=TRUE, incl.ctr=TRUE, show.cases=TRUE)