QCA (version 3.22)

generate: Generate a custom data structure

Description

This function acts as a DGS - Data Generating Structure for a certain SOP expression.

Usage

generate(expression = "", snames = "", noflevels, ...)

Value

A data frame.

Arguments

expression

String: a SOP - sum of products expression.

snames

A string containing the sets' names, separated by commas.

noflevels

Numerical vector containing the number of levels for each set.

...

Other arguments, mainly for internal use.

Author

Adrian Dusa

Details

Using the power of SOP expressions, this function can generate the data for any type of expressions, either Boolean or multi-value.

Causal conditions should always be separated by a product sign "*", unless: - they are single letters, or - the set names are provided, or - the expression is multi-value

All conditions are considered binary crisp, unless the number of levels are provided in conjunction with the set names, in the order of their specification from the snames argument.

This is an extension of the function expand() from package admisc, the process of data generating process being essentially a Quine expansion to a Disjunctive Normal Form.

Examples

generate(D + ~AB + B~C -> Z)

# the positive configurations in their complete DNF expansion:
expanded <- expand(D + ~AB + B~C, snames = c(A, B, C, D))
# ~A~B~CD + ~A~BCD + ~AB~CD + ~ABCD + A~B~CD + A~BCD +
# AB~CD + ABCD + ~AB~C~D + ~ABC~D + AB~C~D

# which has the equivalent simpler, initial expression:
simplify(expanded)
# D + ~AB + B~C

# same structure with different set names
# (note the mandatory use of the product sign *)
generate(Alpha + ~Beta*Gamma + Gamma*~Delta -> Omicron)

# introducing an additional, irrelevant condition
# (note the product sign is not mandatory if providing the set names)
setnames <- "Alpha, Beta, Gamma, Delta, Epsilon"
dat <- generate(Alpha + ~BetaGamma + Gamma~Delta -> Omicron, snames = setnames)

head(dat)

#   Alpha Beta Gamma Delta Epsilon Omicron
# 1     0    0     0     0       0       0
# 2     0    0     0     0       1       0
# 3     0    0     0     1       0       0
# 4     0    0     0     1       1       0
# 5     0    0     1     0       0       1
# 6     0    0     1     0       1       1

minimize(dat, outcome = Omicron)

# M1: Alpha + ~Beta*Gamma + Gamma*~Delta <-> Omicron