pdLogChol: General Positive-Definite Matrix

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

This function is a constructor for the pdLogChol 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 log-Cholesky parametrization described in Pinheiro and Bates (1996).

Usage

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pdLogChol(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 character vector 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 character vector. 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.

Details

Internally, the pdLogChol representation of a symmetric positive definite matrix is a vector starting with the logarithms of the diagonal of the Choleski factorization of that matrix followed by its upper triangular portion.

Value

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

Author(s)

José Pinheiro 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

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

(pd4 <- pdLogChol(1:6))
(pd4c <- chol(pd4)) # -> upper-tri matrix with off-diagonals  4 5 6
pd4c[upper.tri(pd4c)]
log(diag(pd4c)) # 1 2 3

Example output

Positive definite matrix structure of class pdLogChol representing
  A B C
A 1 0 0
B 0 2 0
C 0 0 3
Positive definite matrix structure of class pdLogChol representing
          [,1]     [,2]      [,3]
[1,]  7.389056 10.87313  13.59141
[2,] 10.873127 70.59815  64.33434
[3,] 13.591409 64.33434 464.42879
         [,1]     [,2]     [,3]
[1,] 2.718282 4.000000  5.00000
[2,] 0.000000 7.389056  6.00000
[3,] 0.000000 0.000000 20.08554
[1] 4 5 6
[1] 1 2 3

nlme documentation built on Feb. 4, 2021, 9:06 a.m.

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