List Implied Vanishing Tetrads

Description

Interpret the given graph as a structural equation model and list all the vanishing tetrads that it implies.

Usage

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Arguments

x

the input graph, a DAG.

type

restrict output to one level of Kenny's tetrad typology. Possible values are "within" (homogeneity within constructs; all four variables have the same parents), "between" (homogeneity between constructs; two pairs of variables each sharing one parent) and "epistemic" (consistency of epistemic correlations; three variables have the same parent). By default, all tetrads are listed.

Value

a data frame with four columns, where each row of the form i,j,k,l means that the tetrad Cov(i,j)Cov(k,l) - Cov(i,k)Cov(j,l) vanishes (is equal to 0) according to the model.

References

Kenny, D. A. (1979), Correlation and Causality. Wiley, New York.

Examples

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# Specify two-factor model with 4 indicators each
g <- dagitty("dag{{x1 x2 x3 x4} <- x <-> y -> {y1 y2 y3 y4}}")
latents(g) <- c("x","y")

# Check how many tetrads are implied
nrow(vanishingTetrads(g))
# Check how these distribute across the typology
nrow(vanishingTetrads(g,"within"))
nrow(vanishingTetrads(g,"between"))
nrow(vanishingTetrads(g,"epistemic"))