pdLogChol General Positive-Definite Matrix

Description

This function is a constructor for the pdLogChol class, representing a general positive-definite matrix. If the matrix associated with object is of dimension n, it is represented by n*(n+1)/2 unrestricted parameters, using the log-Cholesky parametrization described in Pinheiro and Bates (1996).

• When value is numeric(0), an uninitialized pdMat object, a one-sided formula, or a character vector, object is returned as an uninitialized pdLogChol object (with just some of its attributes and its class defined) and needs to have its coefficients assigned later, generally using the coef or matrix replacement functions.

• If value is an initialized pdMat object, object will be constructed from as.matrix(value).

• Finally, if value is a numeric vector, it is assumed to represent the unrestricted coefficients of the matrix-logarithm parametrization of the underlying positive-definite matrix.

Usage

pdLogChol(value, form, nam, data)

Arguments

value	an optional initialization value, which can be any of the following: a pdMat object, a positive-definite matrix, a one-sided linear formula (with variables separated by +), a vector of character strings, or a numeric vector. Defaults to numeric(0), corresponding to an uninitialized object.
form	an optional one-sided linear formula specifying the row/column names for the matrix represented by object. Because factors may be present in form, the formula needs to be evaluated on a data frame to resolve the names it defines. This argument is ignored when value is a one-sided formula. Defaults to NULL.
nam	an optional character vector specifying the row/column names for the matrix represented by object. It must have length equal to the dimension of the underlying positive-definite matrix and unreplicated elements. This argument is ignored when value is a character vector. Defaults to NULL.
data	an optional data frame in which to evaluate the variables named in value and form. It is used to obtain the levels for factors, which affect the dimensions and the row/column names of the underlying matrix. If NULL, no attempt is made to obtain information on factors appearing in the formulas. Defaults to the parent frame from which the function was called.

Details

Internally, the pdLogChol representation of a symmetric positive definite matrix is a vector starting with the logarithms of the diagonal of the Choleski factorization of that matrix followed by its upper triangular portion.

Value

a pdLogChol object representing a general positive-definite matrix, also inheriting from class pdMat.

Author(s)

José Pinheiro and Douglas Bates [email protected]

References

Pinheiro, J.C. and Bates., D.M. (1996) Unconstrained Parametrizations for Variance-Covariance Matrices, Statistics and Computing 6, 289–296.

Pinheiro, J.C., and Bates, D.M. (2000) Mixed-Effects Models in S and S-PLUS, Springer.

See Also

as.matrix.pdMat, coef.pdMat, pdClasses, matrix<-.pdMat

Examples

(pd1 <- pdLogChol(diag(1:3), nam = c("A","B","C")))

(pd4 <- pdLogChol(1:6))
(pd4c <- chol(pd4)) # -> upper-tri matrix with off-diagonals  4 5 6
pd4c[upper.tri(pd4c)]
log(diag(pd4c)) # 1 2 3