vanishing.tetrads: Vanishing Tetrads Algorithm

In BillShipley/CauseAndCorrelation: Functions for Path Analysis and SEM

Vanishing Tetrads Algorithm

Description

For each unique set of four variables in the input data, this function tests if these four variables possess "vanishing" tetrads. A tetrad is a product of two correlations that exactly equals a second product of two correlations, each involving the same four variables. Each set of four variables has three possible tetrad equations (tetrad triplets). If a tetrad vanishes, but every variable of the four is dependent on every other, conditional on every possible set of the other variables, then there must be a latent variable generating these correlations. This is the Tetrad Representation Theorem whose proof is given in Spirtes et al. (1993), page 196-197.

Usage

vanishing.tetrads(dat, sig = 0.05)

Arguments

dat	a matrix or data frame containing only numeric values
sig	the asymptotic significance level for testing the equality of the tetrad components

Details

The test assumes multivariate normality and linearity. It is also an asymptotic test and so is biased in small samples.

Value

Each unique tetrad is tested and the outcome given along with the null probability.

Author(s)

Bill Shipley

References

Spirtes, P., Glymour, C., Scheines, R. 1993. Causation, prediction, and search. Lecture Notes in Statistics 81. Springer-Verlag.

Shipley, B. 2016. Cause and correlation in biology: A user's guide to path analysis, structural equations and causal inference in R. Cambridge University Press.

Examples

set.seed(123)
dat <- gen.data()
vanishing.tetrads(dat[,c(1,3,4,5)])

BillShipley/CauseAndCorrelation documentation built on Jan. 31, 2023, 4:20 a.m.