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Cholesky: Construct a Valid Variance - Covariance Matrix

Description

Constructs a valid variance - covariance matrix by using the Cholesky LDL decomposition.

Usage

Cholesky(param = NULL, format = NULL, decompositions = TRUE)

Value

A valid variance - covariance matrix. If decompositions = TRUE then it returns a list containing:

• cov_mat: The variance - covariance matrix.

• loading_matrix: The loading matrix of the Cholesky decomposition.

• diagonal_matrix: The diagonal matrix of the Cholesky decomposition.

• correlation_matrix: Matrix containing the correlations.

• stdev_matrix: Matrix containing the standard deviations on the diagonal.

Arguments

param

Vector containing the parameters used to construct the variance - covariance matrix.

format

Matrix representing the format for the Loading matrix L and Diagonal matrix D. The lower triangular part of the format is used as the format for the Loading matrix L. The diagonal of the format is used as the format for the Diagonal matrix D. Must be a matrix.

decompositions

Boolean indicating whether the loading and diagonal matrix of the Cholesky decomposition, and the correlation matrix and standard deviations should be returned.

Author

Dylan Beijers,

Details

format is used to specify which elements of the loading and diagonal matrix should be non-zero. The elements of param are then distributed along the non-zero elements of the loading and diagonal matrix. The parameters for the diagonal matrix are transformed using exp(2 * x).

Examples

format <- diag(1, 2, 2)
format[2, 1] <- 1
Cholesky(param = c(2, 4, 1), format = format, decompositions = TRUE)