pdLogChol-class {lme4} | R Documentation

## 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)

[Package Contents]