pdNatural {nlme} | R Documentation |

This function is a constructor for the `pdNatural`

class,
representing a general positive-definite matrix, using a natural
parametrization . If the matrix associated with `object`

is of
dimension *n*, it is represented by *n*(n+1)/2*
parameters. Letting *S(i,j)* denote the *ij*-th
element of the underlying positive definite matrix and
*r(i,j) =
S(i,j)/sqrt(S(i,i)S(j,j)), i not equal to j* denote the associated
"correlations", the "natural" parameters are given by
*sqrt(Sii), i=1,..,n* and
*log((1+r(i,j))/(1-r(i,j))), i not equal to j*. Note that all
natural parameters are individually unrestricted, but not jointly
unrestricted (meaning that not all unrestricted vectors would give
positive-definite matrices). Therefore, this parametrization should
NOT be used for optimization. It is mostly used for deriving
approximate confidence intervals on parameters following the
optimization of an objective function. When `value`

is
`numeric(0)`

, an uninitialized `pdMat`

object, a one-sided
formula, or a vector of character strings, `object`

is returned
as an uninitialized `pdSymm`

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 natural parameters of the
underlying positive-definite matrix.

pdNatural(value, form, nam, data)

`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 vector of character strings 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 vector of character strings. 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. |

a `pdNatural`

object representing a general positive-definite
matrix in natural parametrization, also inheriting from class
`pdMat`

.

Jose Pinheiro Jose.Pinheiro@pharma.novartis.com and Douglas Bates bates@stat.wisc.edu

Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer, esp. p. 162.

`as.matrix.pdMat`

,
`coef.pdMat`

,
`pdClasses`

,
`matrix<-.pdMat`

pdNatural(diag(1:3))

[Package *nlme* version 3.1-80 Index]