full.ct: Generate the logically possible value configurations of a given set of factors

Description

The function full.ct generates a configTable with all (or a specified number of) logically possible value configurations of the factors defined in the input x. It is more flexible than allCombs. x can be a configTable, a data frame, an integer, a list specifying the factors' value ranges, or a character string expressing a condition featuring all admissible factor values.

Usage

full.ct(x, ...)
# S3 method for default
full.ct(x, type = "auto", cond = NULL, nmax = NULL, ...)
# S3 method for configTable
full.ct(x, cond = NULL, nmax = NULL, ...)
# S3 method for cti
full.ct(x, cond = NULL, nmax = NULL, ...)

Value

A configTable of type "cs" or "mv" with the full enumeration of combinations of the factor values.

Arguments

x: A configTable, a data frame, a matrix, an integer, a list specifying the factors' value ranges, or a character vector featuring all admissible factor values (see the details and examples below).
type: Character vector specifying the type of x: "auto" (automatic detection; default), "cs" (crisp-set), "mv" (multi-value), or "fs" (fuzzy-set). (Manual specification of the type only has an effect if x is a data frame or matrix.)
cond: Optional character vector containing conditions in the syntax of msc, asf or csf. If it is not NULL, only factors appearing in cond are used.
nmax: Maximal number of rows in the output configTable. If nmax is smaller than the total number of logically possible configurations, a random sample of configurations is drawn. The default nmax = NULL selects all logically possible configurations.
...: Further arguments passed to methods.

Details

full.ct generates all or nmax logically possible value configurations of the factors defined in x, which can either be a character vector or an integer or a list or a data frame or a matrix.

If x is a character vector, it can be a condition of any of the three types of conditions, boolean, atomic or complex (see condition). x must contain at least one factor. Factor names and admissible values are guessed from the Boolean formulas. If x contains multi-value factors, only those values are considered admissible that are explicitly contained in x. Accordingly, in case of multi-value factors, full.ct should be given the relevant factor definitions by means of a list (see below).
If x is an integer, the output is a configuration table of type "cs" with x factors. If x <= 26, the first x capital letters of the alphabet are used as the names of the factors. If x > 26, factors are named "X1" to "Xx".
If x is a list, x is expected to have named elements each of which provides the factor names with corresponding vectors enumerating their admissible values (i.e. their value ranges). These values must be non-negative integers.
If x is a configTable, data frame, or matrix, colnames(x) are interpreted as factor names and the rows as enumerating the admissible values (i.e. as value ranges). If x is a data frame or a matrix, x is first converted to a configTable (the function configTable is called with type as specified in full.ct), and the configTable method of full.ct is then applied to the result. The configTable method uses all factors and factor values occurring in the configTable. If x is of type "fs", 0 and 1 are taken as the admissible values.

The computational demand of generating all logically possible configurations increases exponentially with the number of factors in x. In order to get an output in reasonable time, even when x features more than about 15 factors, the argument nmax allows for specifying a maximal number of configurations to be returned (by random sampling).

If not all factors specified in x are of interest but only those in a given msc, asf, or csf, full.ct can be correspondingly restricted via the argument cond. For instance, full.ct(d.educate, cond = "D + L <-> E") generates the logically possible value configurations of the factors in the set {D, L, E}, even though d.educate contains further factors. The argument cond is primarily used internally to speed up the execution of various functions in case of high-dimensional data.

The main area of application of full.ct is data simulation in the context of inverse search trials benchmarking the output of cna (see examples below). While full.ct generates the relevant space of 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), that is, it selects the empirically possible configurations.

The method for class "cti" is for internal use only.

Examples

Run this code

# x is a character vector.
full.ct("A + B*c")
full.ct("A=1*C=3 + B=2*C=1 + A=3*B=1") 
full.ct(c("A + b*C", "a*D"))
full.ct("!A*-(B + c) + F")
full.ct(c("A=1", "A=2", "B=1", "B=0", "C=13","C=45"))

# x is a data frame.
full.ct(d.educate)
full.ct(d.jobsecurity)
full.ct(d.pban)

# x is a configTable.
full.ct(configTable(d.jobsecurity))
full.ct(configTable(d.pban), cond = "C=1 + F=0 <-> V=1") 

# x is an integer.
full.ct(6)
# Constrain the number of configurations to 1000.
full.ct(30, nmax = 1000) 

# x is a list.
full.ct(list(A = 0:1, B = 0:1, C = 0:1))  # cs
full.ct(list(A = 1:2, B = 0:1, C = 23:25))  # mv

# Simulating crisp-set data.
groundTruth.1 <- "(A*b + C*d <-> E)*(E*H + I*k <-> F)"
fullData <- ct2df(full.ct(groundTruth.1))
idealData <- ct2df(selectCases(groundTruth.1, fullData))
# Introduce 20% data fragmentation.
fragData <- idealData[-sample(1:nrow(idealData), nrow(idealData)*0.2), ] 
# Add 10% random noise.
incompData <- dplyr::setdiff(fullData, idealData)
(realData <- rbind(incompData[sample(1:nrow(incompData), nrow(fragData)*0.1), ], 
  fragData))

# Simulating multi-value data.
groundTruth.2 <- "(JO=3 + TS=1*PE=3 <-> ES=1)*(ES=1*HI=4 + IQ=2*KT=5 <-> FA=1)"
fullData <- ct2df(full.ct(list(JO=1:3, TS=1:2, PE=1:3, ES=1:2, HI=1:4, IQ=1:5, KT=1:5, FA=1:2)))
idealData <- ct2df(selectCases(groundTruth.2, fullData))
# Introduce 20% data fragmentation.
fragData <- idealData[-sample(1:nrow(idealData), nrow(idealData)*0.2), ] 
# Add 10% random noise.
incompData <- dplyr::setdiff(fullData, idealData)
(realData <- rbind(incompData[sample(1:nrow(incompData), nrow(fragData)*0.1), ], 
  fragData))