allCombs: Generate all logically possible value configurations of a given set of factors

Description

The function allCombs generates a data frame of all possible value configurations of length(x) factors, the first factor having x[1] values, the second x[2] values etc. The factors are labeled using capital letters.

Usage

allCombs(x)

Value

A data frame.

Arguments

x: Integer vector with values >0

Details

In combination with selectCases. makeFuzzy, and is.submodel, allCombs is useful for simulating data, which are needed for inverse search trials benchmarking the output of cna. In a nutshell, allCombs generates the space of all logically possible configurations of the factors in an analyzed factor set, selectCases selects those configurations from this space that are compatible with a given data generating causal structure (i.e. the ground truth, which can be randomly generated using randomConds), makeFuzzy fuzzifies those data, and is.submodel checks whether the models returned by cna are true of the ground truth.

The cna package provides another function to the same effect, full.ct, which is more flexible than allCombs.

Examples

Run this code

# Generate all logically possible configurations of 5 dichotomous factors named "A", "B",
# "C", "D", and "E". 
allCombs(c(2, 2, 2, 2, 2)) - 1
# allCombs(c(2, 2, 2, 2, 2)) generates the value space for values 1 and 2, but as it is
# conventional to use values 0 and 1 for Boolean factors, 1 must be subtracted from
# every value output by allCombs(c(2, 2, 2, 2, 2)) to yield a Boolean data frame.

# Generate all logically possible configurations of 5 multi-value factors named "A", "B",
# "C", "D", and "E", such that A can take on 3 values {1,2,3}, B 4 values {1,2,3,4},
# C 3 values etc.
dat0 <- allCombs(c(3, 4, 3, 5, 3))
head(dat0)
nrow(dat0) # = 3*4*3*5*3

# Generate all configurations of 5 dichotomous factors that are compatible with the causal
# chain (A*b + a*B <-> C)*(C*d + c*D <-> E).
dat1 <- allCombs(c(2, 2, 2, 2, 2)) - 1
(dat2 <- selectCases("(A*b + a*B <-> C)*(C*d + c*D <-> E)", dat1))

# Generate all configurations of 5 multi-value factors that are compatible with the causal
# chain (A=2*B=1 + A=3*B=3 <-> C=1)*(C=1*D=2 + C=4*D=4 <-> E=3).
dat1 <- allCombs(c(3, 3, 4, 4, 3))
dat2 <- selectCases("(A=2*B=1 + A=3*B=3 <-> C=1)*(C=1*D=2 + C=4*D=4 <-> E=3)", dat1)
nrow(dat1)
nrow(dat2)                    

# Generate all configurations of 5 fuzzy-set factors that are compatible with the causal
# structure A*b + C*D <-> E, such that con = .8 and cov = .8.
dat1 <- allCombs(c(2, 2, 2, 2, 2)) - 1
dat2 <- makeFuzzy(dat1, fuzzvalues = seq(0, 0.45, 0.01))
(dat3 <- selectCases1("A*b + C*D <-> E", con = .8, cov = .8, dat2))

# Inverse search for the data generating causal structure A*b + a*B + C*D <-> E from
# fuzzy-set data with non-perfect consistency and coverage scores.
set.seed(3)
groundTruth <- "A*b + a*B + C*D <-> E"
dat1 <- allCombs(c(2, 2, 2, 2, 2)) - 1
dat2 <- makeFuzzy(dat1, fuzzvalues = 0:4/10)
dat3 <- selectCases1(groundTruth, con = .8, cov = .8, dat2)
ana1 <- cna(dat3, outcome = "E", con = .8, cov = .8)
any(is.submodel(asf(ana1)$condition, groundTruth))