fitDag function

Fitting of Gaussian DAG models

Fits linear recursive regressions with independent residuals specified by a DAG.

fitDag(amat, S, n)

Arguments

• amat: a square matrix with dimnames representing the adjacency matrix of the DAG
• S: a symmetric positive definite matrix, the sample covariance matrix
• n: an integer > 0, the sample size

Details

fitDag checks if the order of the nodes in adjacency matrix is the same of S and if not it reorders the adjacency matrix to match the order of the variables in S. The nodes of the adjacency matrix may form a subset of the variables in S.

Returns

• Shat: the fitted covariance matrix.

• Ahat: a square matrix of the fitted regression coefficients. The entry Ahat[i,j] is minus the regression coefficient of variable i in the regression equation j. Thus there is a non zero partial regression coefficient Ahat[i,j]

  corresponding to each non zero value amat[j,i] in the adjacency matrix.

• Dhat: a vector containing the partial variances of each variable given the parents.

• dev: the `deviance' of the model.

• df: the degrees of freedom.

References

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

Author(s)

Giovanni M. Marchetti

See Also

DAG, swp.

Examples

dag <- DAG(y ~ x+u, x ~ z, z ~ u)
"S" <- structure(c(2.93, -1.7, 0.76, -0.06,
                   -1.7, 1.64, -0.78, 0.1,
                    0.76, -0.78, 1.66, -0.78,
                    -0.06, 0.1, -0.78, 0.81), .Dim = c(4,4),
         .Dimnames = list(c("y", "x", "z", "u"), c("y", "x", "z", "u")))
fitDag(dag, S, 200)