pdSymm {nlme} | R Documentation

## General Positive-Definite Matrix

### Description

This function is a constructor for the `pdSymm` 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 matrix-logarithm parametrization described in Pinheiro and Bates (1996). 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 unrestricted coefficients of the matrix-logarithm parametrization of the underlying positive-definite matrix.

### Usage

    pdSymm(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 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.

### Value

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

### Author(s)

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

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

[Package nlme version 3.1-86 Index]