conCovOpt_utils {cnaOpt}

Build disjunctive normal forms realizing con-cov optima

Description

reprodAssign generates the output values of disjunctive normal forms (DNFs) reaching con-cov optima. DNFbuild builds a DNF realizing a targeted con-cov optimum; it only works for crisp-set and multi-value data (cf. Baumgartner and Ambuehl 2021).

Usage

reprodAssign(x, outcome = names(x), id = xi$id)
DNFbuild(x, outcome = names(x), reduce = c("ereduce", "rreduce", "none"), 
         id = xi$id, maxCombs = 1e7)

Arguments

x

An object produced by selectMax.

outcome

A character string specifying one outcome value in attr(x, "configTable").

id

An integer vector referring to the identifier of the targeted con-cov optimum or optima.

reduce

A character string: if "ereduce" or "rreduce", the canonical DNF realizing the con-cov optimum is freed of redundancies using ereduce or rreduce, respectively; if "none", the unreduced canonical DNF is returned. reduce=TRUE is interpreted as "rreduce", reduce=FALSE and reduce=NULL as "none".

maxCombs

Passed to ereduce if reduce = "ereduce"; ignored otherwise. (See ereduce for details.)

Details

An atomic CNA model (asf) accounts for the behavior of the outcome in terms of a redundancy-free DNF. reprodAssign generates the output values such a DNF has to return in order to reach a con-cov optimum stored in an object of class 'selectMax'. If the data stored in attr(x, "configTable") are crisp-set or multi-value, DNFbuild builds the DNFs realizing the targeted con-cov optimum. (For fuzzy-set data an error is returned.) If reduce = "ereduce" (default), all redundancy-free DNFs are built using ereduce; if reduce = "rreduce" (more computationally efficient), one (randomly selected) redundancy-free DNF is built using rreduce; if reduce = "none", the non-reduced canonical DNF is returned. The argument id allows for selecting a targeted con-cov optimum via its identifier (see examples below).

Value

reprodAssign: A matrix of scores. DNFbuild: A Boolean formula in disjunctive normal form (DNF).

References

Baumgartner, Michael and Mathias Ambuehl. 2021. “Optimizing Consistency and Coverage in Configurational Causal Modeling.” Sociological Methods & Research.
doi:10.1177/0049124121995554.

See Also

conCovOpt, selectMax, condTbl

Examples

# CS data, d.educate
cco1 <- conCovOpt(d.educate)
best1 <- selectMax(cco1)
reprodAssign(best1, outcome =  "E")
DNFbuild(best1, outcome =  "E")
DNFbuild(best1, outcome =  "E", reduce = FALSE) # canonical DNF
DNFbuild(best1, outcome =  "E", reduce = "ereduce") # all redundancy-free DNFs
DNFbuild(best1, outcome =  "E", reduce = "rreduce") # one redundancy-free DNF
DNFbuild(best1, outcome =  "E", reduce = "none") # canonical DNF

# Simulated mv data
datMV <- data.frame(
  A = c(3,2,1,1,2,3,2,2,2,1,1,2,3,2,2,2,1,2,3,3,3,1,1,1,3,1,2,1,2,3,3,2,2,2,1,2,2,3,2,1,2,1,3,3),
  B = c(1,2,3,2,1,1,2,1,2,2,3,1,1,1,2,3,1,3,3,3,1,1,3,2,2,1,1,3,3,2,3,1,2,1,2,2,1,1,2,2,3,3,3,3),
  C = c(1,3,3,3,1,1,1,2,2,3,3,1,1,2,2,2,3,1,1,2,1,2,2,3,3,1,2,2,2,3,2,1,1,2,2,2,1,1,1,2,2,1,1,2),
  D = c(3,1,2,2,1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,1,1,1,1,1,2,2,2,2,2,3,1,1,1,1,1,2,2,2,2,2,3,3,3),
  E = c(3,2,2,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3)
)

# Apply conCovOpt and selectMax.
(cco2 <- conCovOpt(datMV))
(best2 <- selectMax(cco2))

# Apply DNFbuild to build the redundancy-free DNFs reaching best2.
(formula1 <- DNFbuild(best2, outcome = "D=3"))
# Both DNFs in formula1 reache the con-cov score stored in best2 for outcome "D=3".
condTbl(paste0(formula1, "<-> D=3"), datMV)
# Build only one redundancy-free DNF reaching best2.
DNFbuild(best2, outcome = "D=3", reduce = "rreduce")
# Any factor value in datMV can be treated as outcome.
(formula2 <- DNFbuild(best2, outcome =  "E=3", reduce = "rreduce"))
condTbl(paste0(formula2, "<-> E=3"), datMV)
# Any con-cov optimum in cco2 can be targeted via its identifier.
(formula3 <- DNFbuild(best2, outcome =  "E=3", id = 508))
condTbl(paste0(formula3, "<-> E=3"), datMV)

# Simulated fs data
datFS <- data.frame(
  A = c(.73, .85, .94, .36, .73, .79, .39, .82, .15, .12, .67, .27, .3), 
  B = c(.21, .03, .91, .64, .39, .12, .06, .7,  .73, .15, .88, .73, .36), 
  C = c(.61,  0,  .61,  1,  .94, .15, .88, .27, .12, .12, .27, .15, .15), 
  D = c(.64, .67, .3,  .06, .33, .03, .76, .94, .67, .76, .18, .27, .36), 
  E = c(.91, .94, .67, .85, .73, .79, .24, .09, .03, .21, .33, .36, .27)
)

# Apply conCovOpt and selectMax.
(cco3 <- conCovOpt(datFS, outcome = "E"))
(best3 <- selectMax(cco3))

# Apply reprodAssign.
reprodAssign(best3, outcome = "E")
# Select a con-cov optimum in cco3 via its identifier.
reprodAssign(best3, outcome = "E", id = 252)

# DNFbuild does not work for fs data; it generates an error.
try(DNFbuild(best3, outcome = "E"))