QCAGUI (version 2.4)

Interpret SOP expressions: translate, compute, findRows: Functions to interpret a SOP expression

Description

These functions interpret an expression written in a SOP (sum of products) form, for both crisp and multivalue QCA. The function translate() translates the expression into a standard (canonical) SOP form using a matrix of implicants, while compute() uses the first to compute the scores based on a particular dataset.

The function findRows() takes a QCA expression written in SOP form, and applies it on a truth table to find all rows that match the pattern in the expression.

For crisp sets notation, upper case letters are considered the presence of that causal condition, and lower case letters are considered the absence of the respective causal condition. Tilde is recognized as a negation, even in combination with upper/lower letters.

Functions similar to translate() and compute() have initially been written by Jirka Lewandowski (2015) but the actual code in these functions has been completely re-written to integrate it with the package QCAGUI, and expanded with more extensive functionality (see details and examples below).

Usage

translate(expression = "", snames = "")
compute(expression = "", data, separate = FALSE)
findRows(expression = "", ttobj, remainders = FALSE)

Arguments

expression

String: a QCA expression written in sum of products form.

snames

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

data

A dataset with binary cs, mv and fs data.

separate

Logical, perform computations on individual, separate paths.

ttobj

A truth table, an object of class "tt".

remainders

Logical, find remainders only.

Value

A standard of implicants, with the following codes:

0

absence of a causal condition

1

presence of a causal condition

-1

causal condition was eliminated

The matrix was also assigned a class "translate", to eliminate the -1 codes when printed.

Details

A SOP ("sum of products") is also known as a DNF ("disjunctive normal form"), or in other words a "union of intersections", for example A*D + B*c.

The same expression can be written in multivalue notation: A{1}*D{1} + B{1}*C{0}. Both types of expressions are valid, and yield the same result on the same dataset.

For multivalue notation, expressions can contain multiple values to translate, separated by a comma. If B was a multivalue causal condition, an expression could be: A{1} + B{1,2}*C{0}.

In this example, all values in B equal to either 1 or 2 will be translated to 1, and the rest of the (multi)values will be translated to 0.

In multivalue notation, causal snames are expected as upper case letters, and they will be converted to upper case by default.

The function automatically detects the use of tilde "~" as a negation for a particular causal condition. ~A does two things: it identifies the presence of causal condition A (because it was specified as upper case) and it recognizes that it must be negated, because of the tilde. It works even combined with lower case names: ~a, which is interpreted as A.

For multivalue notation, a pseudo-standard is applied. For a binary causal condition, A{0} is the negation of A, and ~A{0} can be interpreted as the presence of A. Starting from these two agreed statements, when multiple values are supplied, the pseudo-standard interprets anything that contains a value of 0 as the absence of causal condition: A{0,2} will be translated as 0, and upon recoding in the real data, values 0 and 2 will be recoded to 0 and the rest of the values to 1.

Similarly, negations work with multivalue snames: ~A{1,2} is be interpreted as "all values except 1 and 2 should be translated as 0", whereas ~A{0,2} will be translated as 1, and all other values except 0 and 2 will be recoded to 0.

The use of the product operator * is redundant when causal snames' names are single letters (for example AD + Bc), and is also redundant for multivalue data, where product terms can be separated by using the curly brackets notation.

When causal snames are binary and their names have multiple letters (for example AA + CC*bb), the use of the product operator * is preferable but the function manages to translate an expression even without it (AA + CCbb) by searching deep in the space of the conditions' names, at the cost of slowing down for a high number of causal conditions. For this reason, an arbitrary limit of 7 causal snames is imposed, to write an expression with.

References

Jirka Lewandowski (2015) QCAtools: Helper functions for QCA in R. R package version 0.1

Examples

if (require("QCA")) {

translate("A + B*C")

# same thing in multivalue notation
translate("A{1} + B{1}*C{1}")

# using upper/lower letters
translate("A + b*C")

# the negation with tilde is recognised
translate("~A + b*C")

# even in combination of upper/lower letters
translate("~A + ~b*C")

# and even for multivalue variables
translate("~A{1} + ~B{0}*C{1}")

# in multivalue notation, the product sign * is redundant
translate("C{1} + T{2} + T{1}V{0} + C{0}")

# multiple values can be specified
translate("C{1} + T{1,2} + T{1}V{0} + C{0}")

# or even negated
translate("C{1} + ~T{1,2} + T{1}V{0} + C{0}")

# if the expression does not contain the product sign *
# snames are required to complete the translation 
translate("AB + cD", "A, B, C, D")

# snames are not required
translate("PER*FECT + str*ing")

# snames are required
translate("PERFECT + string", "PER, FECT, STR, ING")

# it works even with overlapping columns
# SU overlaps with SUB in SUBER, but the result is still correct
translate("SUBER + subset", "SU, BER, SUB, SET")

## Not run: 
# # error because combinations of condition names clash
# translate("SUPER + subset", "SUP, ER, SU, PER, SUB, SET")
# ## End(Not run)

# to print _all_ codes from the standard output matrix
(obj <- translate("A + b*C"))
print(obj, original = TRUE) # also prints the -1 code



# for compute()
data(CVF)
compute("natpride + GEOCON", data = CVF)

# calculating individual paths
compute("natpride + GEOCON", data = CVF, separate = TRUE)



# for findRows()
data(LC)
ttLC <- truthTable(LC, "SURV", show.cases = TRUE)

findRows("DEV*ind*STB", ttLC)


findRows("DEV*ind*STB", ttLC, remainders = TRUE)
}