ggm (version 1.0.4)

fitCovGraph: Fitting of Gaussian covariance graph models

Description

Fits a Gaussian covariance graph by maximum likelihood.

Usage

fitCovGraph(amat, S, n, alg = "icf", dual.alg = 2, start.icf = NULL, tol = 1e-06)

Arguments

amat

A symmetric Booloean matrix with dimnames representing the adjacency matrix of the graph.

S

A symmetric positive definite matrix with dimnames, the sample covariance matrix

n

A positive integer, the sample size.

alg

A character string, the algorithm used. If alg="icf" (the default) the algorithm is based on iterative conditional fitting (see Drton and Richardson, 2003). In this case the ML estimates are returned. If alg="dual"

dual.alg

And integer equal to 1 or 2. It is used if alg="dual". In this case a concentration graph model is fitted to the inverse of the sample covariance matrix, and dual.alg is passed to fitConGraph to

start.icf

A symmetric matrix used as starting value of the algorithm. If start=NULL the starting value is a diagonal matrix with diagonal entries equal to sample variances.

tol

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

Value

• Shat
  the fitted covariance matrix.
• dev
  the `deviance' of the model.
• df
  the degrees of freedom.
• it
  the iterations.

Details

A covariance graph is an undirected graph in which the variables associated to two non-adjacent nodes are marginally independent. The edges of these models are represented by bidirected edges (Drton & Richardson, 2003) or by dashed lines (Cox & Wermuth, 1996).

By default, this function gives the ML estimates in the covariance graph model, by a new iterative method (Drton & Richardson, 2003). If desired then estimates from a ``dual likelihood'' heuristic (Kauermann, 1996; Edwards, 2000, section 7.4).

References

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

Drton, M. & Richardson, T. S. (2003). A new algorithm for maximum likelihood estimation in Gaussian graphical models for marginal independence. Proceedings of the Nineteenth Conference on Uncertainty in Artificial Intelligence, 184--191. Kauermann, G. (1996). On a dualization of graphical Gaussian models. Scandinavian Journal of Statistics. 23, 105--116.

See Also

fitConGraph, icf

Examples

## Correlations among four strategies to cope with stress for 
## 72 students. Cox & Wermuth (1996), p. 73.
##  Y = cognitive avoidance
##  X = vigilance
##  V = blunting
##  U = monitoring

R <- matrix(c(
   1.00, -0.20,  0.46,  0.01,
  -0.20,  1.00,  0.00,  0.47,
   0.46,  0.00,  1.00, -0.15,
   0.01,  0.47, -0.15,  1.00), 4, 4)
nam <- c("Y", "X", "V", "U") 
dimnames(R) <- list(nam, nam)

## A chordless 4-cycle covariance graph
gr <- UG(~ Y*X + X*U + U*V + V*Y)
fitCovGraph(gr, R, n=72)
fitCovGraph(gr, R, n=72, alg="dual")