QGglmm (version 0.8.0)

QGmvpsi: Compute a multivariate "Psi" (used to compute the additive genetic variance on the observed scale).

Description

This function computes a multivariate version of the parameter "Psi" which relates the additive genetic variance-covariance matrix on the latent scale to the additive genetic variance-covariance matrix on the observed scale: G.obs = Psi %*% G %*% t(Psi)

Usage

QGmvpsi(mu = NULL, vcov, d.link.inv, predict = NULL, 
        rel.acc = 0.001, width = 10, compound = NULL, mask = NULL)

Value

This function yields the matrix "Psi". (numeric)

Arguments

mu

Vector of latent intercepts estimated from a GLMM (ignored if predict is not NULL). (numeric)

vcov

Latent total phenotypic variance-covariance matrix estimated from a GLMM. Usually, the sum of all the estimated variance-covariance matrices. (numeric)

d.link.inv

Derivative of the inverse-link functions. This function should accept a vector and yield a vector of the same length, see Details and Example below. (function)

predict

Optional matrix of predicted values on the latent scale (each trait in each column). The latent predicted values must be computed while only accounting for the fixed effects (marginal to the random effects). (numeric)

rel.acc

Relative accuracy of the integral approximation. (numeric)

width

Parameter for the integral computation. The default value is 10, which should be sensible for most models. (numeric)

compound

A vector of two indices, or list of such vectors (e.g. list(c(1,2), c(4,5))), providing the locations of "compound" distributions in the input (i.e. the dimensions that need to be "merged" into one in the output). The input must be ordered so that the first component (1 and 4 in the example above) is the latent trait for positive values and the second (2 and 5 in the example above) is the latent trait for the zero-component. (integer of length 2, or list of such vectors)

mask

Masking filter for removing predictions that don't exist in the population (e.g. female predictions for males for a sex-based bivariate model). Should the same dimensions as predict and values should be FALSE when the predictions should be filtered out.

Author

Pierre de Villemereuil & Michael B. Morrissey

Details

The multivariate parameter "Psi" is a diagonal matrix which elements are the average of the derivative of the inverse-link function. The additive genetic variance-covariance matrix on the latent scale G is linked to the additive genetic variance-covariance matrix on the observed scale G.obs through Psi: G.obs = Psi %*% G %*% t(Psi).

This function requires the derivatives of the inverse-link functions (d.link.inv). For an analysis with d traits, the function given to the d.link.inv argument should use a vector of length d and yield a vector of length d (see Example below). When using compound, the function corresponding to the compound distribution should accept a 2-rows input and yield a 2-rows output.

See Also

QGpsi, QGmvparams, QGlink.funcs, QGvcov, QGmvpsi

Examples

## Example using a bivariate model (Binary trait/Gaussian trait)
# Parameters
mu <- c(0, 1)
G <- diag(c(0.5, 2))
P <- diag(c(1, 4))

# Setting up the derivatives of the inverse-link functions
dinvs <- function(mat) {matrix(c(dnorm(mat[1, ]), rep(1, length(mat[2, ]))),
                               nrow = 2, 
                               byrow = TRUE)}
# The derivative of pnorm() is dnorm(), and the derivative of the identity is 1

# Computing Psi
Psi <- QGmvpsi(mu = mu, vcov = P, d.link.inv = dinvs)
# Computing genetic additive variance-covariance matrix on the observed scale
Psi
G.obs <- Psi %*% G %*% t(Psi)

QGparams(mu = 0, var.a = 0.5, var.p = 1, model = "binom1.probit")
# Same additive variance than trait 1
# Reminder: the results are the same here because we have no correlation between the two traits