ggm (version 2.5.1)

fitConGraph: Fitting a Gaussian concentration graph model

Description

Fits a concentration graph (a covariance selection model).

Usage

fitConGraph(amat, S, n, cli = NULL, alg = 3, pri = FALSE, tol = 1e-06)

Value

Shat

the fitted covariance matrix.

dev

the `deviance' of the model.

df

the degrees of freedom.

it

the iterations.

Arguments

amat

a square Boolean matrix representing the adjacency matrix of an UG

S

the sample covariance matrix

n

an integer denoting the sample size

cli

a list containing the cliques of the graph. The components of the list are character vectors containing the names of the nodes in the cliques. The names must match the names of the vertices. The knowledge of the cliques is not needed. If the cliques are not specified the function uses the algorithm by Hastie et al. (2009, p. 446).

alg

The algorithm used.

pri

If TRUE is verbose

tol

a small positive number indicating the tolerance used in convergence tests.

Author

Giovanni M. Marchetti

Details

The algorithms for fitting concentration graph models by maximum likelihood are discussed in Speed and Kiiveri (1986). If the cliques are known the function uses the iterative proportional fitting algorithm described by Whittaker (1990, p. 184). If the cliques are not specified the function uses the algorithm by Hastie et al. (2009, p. 631ff).

References

Cox, D. R. & Wermuth, N. (1996). Multivariate dependencies. London: Chapman & Hall.

Hastie, T., Tibshirani, R. and Friedman, J. (2009). The elements of statistical learning. Springer Verlag: New York.

Speed, T.P. and Kiiveri, H (1986). Gaussian Markov distributions over finite graphs. Annals of Statistics, 14, 138--150.

Whittaker, J. (1990). Graphical models in applied multivariate statistics. Chichester: Wiley.

See Also

UG, fitDag, marks

Examples

## A model for the mathematics marks (Whittaker, 1990)
data(marks)
## A butterfly concentration graph
G <- UG(~ mechanics*vectors*algebra + algebra*analysis*statistics)
fitConGraph(G, cov(marks), nrow(marks))
## Using the cliques

cl = list(c("mechanics", "vectors",   "algebra"), c("algebra", "analysis" ,  "statistics"))
fitConGraph(G, S = cov(marks), n = nrow(marks), cli = cl)