fitCovGraph {ggm} | R Documentation |
Fits a Gaussian covariance graph by maximum likelihood.
fitCovGraph(amat, S, n, alg = "icf", dual.alg = 2, start.icf = NULL, tol = 1e-06)
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" the algorithm is based on the dual
likelihood (see Kauermann, 1996). The fitted values are not
true ML estimates.
|
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
specify the algorithm used in fitConGraph .
|
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. |
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, S 7.4).
Shat |
the fitted covariance matrix. |
dev |
the `deviance' of the model. |
df |
the degrees of freedom. |
it |
the iterations. |
Mathias Drton
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.
## 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")