coherence: Calculate the coherence of complex solution formulas

In cna: Causal Modeling with Coincidence Analysis

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 = "auto", ...)

Arguments

x	Character vector specifying an asf or csf.
ct	Data frame or configTable.
type	Character string specifying the type of x: "auto" (automatic detection; default), "cs" (crisp-set), "mv" (multi-value), or "fs" (fuzzy-set).
...	Arguments passed to methods.

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. Boolean conditions are rejected: coherence expects atomic or complex solution formulas in standard form. 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 x is appended as a "names" attribute. If x 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, configTable, 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")) 

cna documentation built on Oct. 28, 2026, 9:07 a.m.