pdNatural-class {lme4} | R Documentation

## Class "pdNatural", positive-definite matrices

### Description

A class of general, positive-definite symmetric matrices parameterized by the logarithm of the diagonal elements and Fisher's z transformation of the correlations.

### Objects from the Class

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

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

### Slots

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

### Extends

Class `"pdMat"`, directly.

### Methods

EMupdate<-
  `signature(x = "pdNatural", nlev = "numeric", value = "matrix")`: update the `pdNatural` object in the EM algorithm for a mixed-effects model.
LMEgradient
  `signature(x = "pdNatural", A = "matrix", nlev = "numeric")`: evaluate the gradient of the log-likelihood in a linear mixed-effects model.
coef
  `signature(object = "pdNatural")`: extract the parameter.
coef<-
  `signature(object = "pdNatural", value = "numeric")`: assign the parameter.
coerce
  `signature(from = "pdNatural", to = "pdmatrix")`: extract the positive-definite matrix represented by the object.
coerce
  `signature(from = "pdNatural", to = "pdfactor")`: extract a square-root factor of the matrix represented by the object. This factor has a `logDet` attribute giving the logarithm of its determinant. In the case of `pdNatural` these are both scalars and the `logDet` attribute is the logarithm of the absolute value of the factor.
dim
  `signature(x = "pdNatural")`: the dimensions of the positive-definite matrix represented by the object.
isInitialized
  `signature(object = "pdNatural")`: a logical scalar indicating if the object is initialized.
logDet
  `signature(object = "pdNatural", covariate = "missing")`: the logarithm of the determinant of the factor of the positive-definite matrix represented by the object.
pdgradient
  `signature(x = "pdNatural")`: the gradient of the positive definite matrix with respect to the parameter vector.
solve
  `signature(a = "pdNatural", b = "missing")`: a `pdNatural` object representing the inverse of the positive-definite matrix represented by this object.
summary
  `signature(object = "pdNatural")`: summarize the object.

### See Also

`pdMat-class`

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