coherence {cna}

Calculate the coherence of complex solution formulas

Description

Calculates the coherence measure of complex solution formulas (csf).

Usage

coherence(x, ...)
## Default S3 method:
coherence(x, ct, type, ..., tt)

Arguments

x

Character vector specifying an asf or csf.

ct

Data frame or configTable.

type

Character vector specifying the type of x: "auto" (automatic detection; default), "cs" (crisp-set), "mv" (multi-value), or "fs" (fuzzy-set).

...

Arguments passed to methods.

tt

Argument tt is deprecated in coherence(); use x instead.

Details

Coherence is a measure for model fit that is custom-built for complex solution formulas (csf). It measures the degree to which the atomic solution formulas (asf) combined in a csf cohere, i.e. are instantiated together in x rather than independently of one another. More concretely, coherence is the ratio of the number of cases satisfying all asf contained in a csf to the number of cases satisfying at least one asf in the csf. For example, if the csf contains the three asf asf1, asf2, asf3, coherence amounts to | asf1 * asf2 * asf3 | / | asf1 + asf2 + asf3 |, where |...| expresses the cardinality of the set of cases in x instantiating the corresponding expression. For asf, coherence returns 1. For boolean conditions (see condition), the coherence measure is not defined and coherence hence returns NA. For multiple csf that do not have a factor in common, coherence returns the minimum of the separate coherence scores.

Value

Numeric vector of coherence values to which cond is appended as a "names" attribute. If cond is a csf "asf1*asf2*asf3" composed of asf that do not have a factor in common, the csf is rendered with commas in the "names" attribute: "asf1, asf2, asf3".

See Also

cna, condition, selectCases, allCombs, full.ct, condTbl

Examples

# Perfect coherence.
dat1 <- selectCases("(A*b <-> C)*(C + D <-> E)")
coherence("(A*b <-> C)*(C + D <-> E)", dat1)
csf(cna(dat1, details = "coherence"))

# Non-perfect coherence.
dat2 <- selectCases("(a*B <-> C)*(C + D <-> E)*(F*g <-> H)")
dat3 <- rbind(ct2df(dat2), c(0,1,0,1,1,1,0,1))
coherence("(a*B <-> C)*(C + D <-> E)*(F*g <-> H)", dat3)
csf(cna(dat3, con = .88, details = "coherence"))