Class "pdLogChol", positive-definite matrices

Description

A class of general, positive-definite symmetric matrices parameterized by the non-zero elements in the Cholesky decomposition. The diagonal elements are represented by their logarithms in the first q positions of the parameter vector. The strict upper triangle of the factor is in the last q(q-1)/2 positions.

Objects from the Class

Objects of class pdLogChol can be created by calls of the form new("pdLogChol", ...) or by the generic constructor function pdLogChol. Frequently the constructor is given a formula only, creating an uninitialized pdLogChol object which is later assigned a value.

pdLogChol objects are primarily used to represent the variance-covariance matrix or the precision matrix of random-effects terms in mixed-effects models.

Slots

form:

Object of class "formula", from class "pdMat", a formula for the object

Names:

Object of class "character", from class "pdMat", names for the rows (and columns) of the positive-definite matrix.

param:

Object of class "numeric", from class "pdMat", a parameter vector of length [q(q+1)]/2 where q is Ncol, the number of columns (and rows) in the positive-definite matrix.

Ncol:

Object of class "integer", from class "pdMat", number of columns (and rows) in the positive-definite matrix.

factor:

Object of class "matrix", from class "pdMat", a square root factor of the positive-definite matrix.

logDet:

Object of class "numeric", from class "pdMat" the logarithm of the absolute value of the determinant of the square root factor or, equivalently, half the logarithm of the determinant of the positive-definite matrix.

Extends

Class "pdMat", directly.

Methods

EMupdate<-

signature(x = "pdLogChol", nlev = "numeric", value = "matrix"): update the pdLogChol object in the EM algorithm for a mixed-effects model.

LMEgradient

signature(x = "pdLogChol", A = "matrix", nlev = "numeric"): evaluate the gradient of the log-likelihood in a linear mixed-effects model.

coef<-

signature(object = "pdLogChol", value = "numeric"): assign the parameter.

coerce

signature(from = "pdLogChol", to = "pdmatrix"): extract the positive-definite matrix represented by the object.

pdgradient

signature(x = "pdLogChol"): the gradient of the positive definite matrix with respect to the parameter vector.

solve

signature(a = "pdLogChol", b = "missing"): a pdLogChol object representing the inverse of the positive-definite matrix represented by this object.

summary

signature(object = "pdLogChol"): summarize the object.

See Also

pdMat-class

Examples

m1 <- pdLogChol(~ age)
coef(m1) <- rnorm(3)
print(m1)
solve(m1)