glmmTMB (version 1.1.7)

get_cor: translate vector of correlation parameters to correlation values

Description

translate vector of correlation parameters to correlation values

Usage

get_cor(theta)
put_cor(C)

Value

a vector of correlation values (get_cor) or glmmTMB scaled-correlation parameters (put_cor)

Arguments

theta

vector of internal correlation parameters (elements of scaled Cholesky factor, in row-major order)

C

a correlation matrix

Details

These functions follow the definition at http://kaskr.github.io/adcomp/classdensity_1_1UNSTRUCTURED__CORR__t.html: if \(L\) is the lower-triangular matrix with 1 on the diagonal and the correlation parameters in the lower triangle, then the correlation matrix is defined as \(\Sigma = D^{-1/2} L L^\top D^{-1/2}\), where \(D = \textrm{diag}(L L^\top)\). For a single correlation parameter \(\theta_0\), this works out to \(\rho = \theta_0/\sqrt{1+\theta_0^2}\). The get_cor function returns the elements of the lower triangle of the correlation matrix, in column-major order.

Examples

th0 <- 0.5
stopifnot(all.equal(get_cor(th0),th0/sqrt(1+th0^2)))
get_cor(c(0.5,0.2,0.5))
C <- matrix(c(1,  0.2,  0.1,
             0.2,  1, -0.2,
             0.1,-0.2,   1),
           3, 3)
## test: round-trip (almostl results in lower triangle only)
stopifnot(all.equal(get_cor(put_cor(C)),
                   C[lower.tri(C)]))