ggm (version 0.5)

shipley.test: Test of all independencies implied by a DAG

Description

Computes a simultaneous test of all independence relationships implied by a given Gaussian model defined according to a directed acyclic graph, based on the sample covariance matrix.

Usage

shipley.test(S, n, A)

Arguments

S

a symmetric positive definite matrix, the sample covariance matrix.

n

a positive integer, the sample size.

A

a square Boolean matrix, of the same dimension as S, representing the edge matrix of a DAG.

Value

• ctest
  Test statistic $C$.
• df
  Degrees of freedom.
• pvalue
  The P-value of the test, assuming a two-sided alternative.

Details

The test statistic is $C = -2 \sum \ln p_j$ where $p_j$ are the p-values of tests of conditional independence in the basis set computed by basiSet(A). The p-values are independent uniform variables on $(0,1)$ and the statistic has exactly a chi square distribution on $2k$ degrees of freedom where $k$ is the number of elements of the basis set. Shipley (2002) calls this test Fisher's C test.

References

Shipley, B. (2000). A new inferential test for path models based on directed acyclic graphs. Structural Equation Modeling, 7(2), 206--218.

See Also

basiSet, pcor.test

Examples

## A decomposable model for the mathematics marks data
data(marks)
dag <- DAG(mec ~ vec+alg, vec ~ alg, sta ~ alg+ana, ana ~ alg)
shipley.test(cov(marks), n=88, dag)