Covariance matrix from upper-triangular elements

Conversion between covariance matrices and their upper-triangular elements

Usage

vec2sigma(x, groups = NULL, visits = NULL, simplify = FALSE)

sigma2vec(x)

Arguments

x

(numeric) for vec2sigma, the vector of upper-triangular elements of \(G\) \(p\times p\) matrices (length \(G p (p + 1) / 2\)). For sigma2vec, a matrix or a (named) list of matrices.

groups

(character) group names of the covariance matrices. If NULL, the groups are derived from the names of x, which must be of the form <group><index> (e.g., grpA1, ..., grpAk, grpB1, ..., grpBk).

visits

(character) optional row and column names of the matrices.

simplify

(logical) if TRUE and there is only a single group, the matrix is returned instead of a list.

Value

vec2sigma: list of matrices named by group (or a matrix if simplify = TRUE and there is a single group). sigma2vec: numeric vector with the upper-triangular elements of each matrix.

Details

vec2sigma constructs symmetric (covariance) matrices from a vector of upper-triangular elements (column-major, including the diagonal), e.g., the covariance parameters returned by estimate(fit, sigma = TRUE) for an mmrm model. The vector may contain the elements of several matrices of the same dimension (one per group), stacked after each other. sigma2vec is the inverse operation.

Examples

S <- matrix(c(2, 1, 1, 3), 2)
x <- sigma2vec(list(sigma = S))
x
#> sigma1 sigma2 sigma3 
#>      2      1      3 
vec2sigma(x)
#> $sigma
#>      [,1] [,2]
#> [1,]    2    1
#> [2,]    1    3
#> 
vec2sigma(x, groups = "sigma", visits = c("v1", "v2"), simplify = TRUE)
#>    v1 v2
#> v1  2  1
#> v2  1  3

## Two groups
vec2sigma(c(1, 0.5, 2, 3, 1, 4), groups = c("A", "B"))
#> $A
#>      [,1] [,2]
#> [1,]  1.0  0.5
#> [2,]  0.5  2.0
#> 
#> $B
#>      [,1] [,2]
#> [1,]    3    1
#> [2,]    1    4
#>