fitDagLatent {ggm} | R Documentation |
Fits by maximum likelihood a Gaussian DAG model where one of the nodes of the graph is latent and it is marginalised over.
fitDagLatent(gmat, Syy, n, latent, norm = 1, seed = 144, maxit = 9000, tol = 1e-06, pri = TRUE)
gmat |
a square Boolean matrix with dimnames, the edge matrix of the DAG. |
Syy |
a symmetric positive definite matrix, with dimnames, the sample covariance
matrix. The order of the rows needs not match the order of the nodes
of the graph. However, the set of nodes of the graph must be a subset
of the set of the names of the variables in Syy . |
n |
a positive integer, the sample size. |
latent |
the name of the hidden node. |
norm |
an integer, the kind of normalization of the latent
variable.
If norm=1 , the latent is scaled to have unit variance. If
norm=2 , the latent is scaled to have unit partial variance
given its parents. |
seed |
an integer, used by set.seed to specify a random
starting point of the EM algorithm. |
maxit |
an integer denoting the maximum number of iterations allowed for the EM algorithm. If the convergence criterion is not satisfied within maxit iterations the algorithms stops and a warning message is returned. |
tol |
a small real value, denoting the tolerance used in testing convergence. |
pri |
logical, if pri=TRUE then the value of the deviance at
each iteration is printed. |
The EM algorithm used is due to Kiivery (1987).
Shat |
a symmetric matrix, the fitted covariance matrix of all the variables including the latent one. |
Khat |
a symmetric matrix, the fitted concentration matrix,
i.e. the inverse of Shat .
|
A |
a square matrix with ones along the diagonal,
resulting from the triangular decomposition
of Shat . The non diagonal entries are partial regression
coefficients, with sign changed, attached to the edges of the fitted
DAG.
|
Delta |
a numeric vector resulting from triangular decomposition of
Shat . The values are the partial variances.
|
dev |
the `deviance' (-2 log L) of the model. |
it |
a positive integer, the number of EM algorithm iterations at convergence. |
df |
a positive integer, degrees of freedom of the model. |
Giovanni M. Marchetti
Kiiveri,H. T. (1987). An incomplete data approach to the analysis of covariance structures. Psychometrika, 52, 4, 539554.
J"oreskog, K.G. & Goldberger, A.S. (1975). Estimation of a model with multiple indicators and multiple causes of a single latent variable. Journal of the American Statistical Association, 10, 631639.
## data from Joreskog and Goldberger (1975) V <- matrix(c(1, 0.36, 0.21, 0.10, 0.156, 0.158, 0.36, 1, 0.265, 0.284, 0.192, 0.324, 0.210, 0.265, 1, 0.176, 0.136, 0.226, 0.1, 0.284, 0.176, 1, 0.304, 0.305, 0.156, 0.192, 0.136, 0.304, 1, 0.344, 0.158, 0.324, 0.226, 0.305, 0.344, 1), 6,6) nod <- c("y1", "y2", "y3", "x1", "x2", "x3") dimnames(V) <- list(nod,nod) dag <- DAG(y1 ~ z, y2 ~ z, y3 ~ z, z ~ x1 + x2 + x3, x1~x2+x3, x2~x3) fitDagLatent(dag, V, n=530, latent="z", seed=4564) fitDagLatent(dag, V, n=530, latent="z", norm=2, seed=145)