grfx {nadiv}

Simulated genetic random effects

Description

This function simulates effects for random terms in a linear mixed model based on relatedness matrices. The intended purpose is for simulating genetic and environmental effects from a pedigree.

Usage

grfx(n, G, incidence = NULL, output = "matrix", stdnorms = NULL, warn = TRUE)

Arguments

n

The number of individuals for which to simulate effects

G

The variance-covariance matrix to model the effects after

incidence

A matrix of the covariance structure of the 'n' individuals or the Cholesky factorization of class CHMfactor for this structure.

output

Format for the output

stdnorms

Standard normal deviates to use

warn

Should a warning message be produced when the function interprets what to do based on the object class supplied to incidence

Details

The total number of effects simulated will be n*d, where d is the number of columns in the 'G' matrix. The standard normal deviates can be supplied instead of generated within the function when stdnorms != NULL. The length of this vector must be n*nrow(G).

Supplied incidence matrices should be n-by-n symmetric matrices or cholesky factorizations that resulted from a call to Matrix::Cholesky(). For simulated random effects using design matrices, see drfx. If no incidence matrix is supplied, incidence = NULL, the Identity matrix is used, which assumes that all 'n' random effects are independently and identically distributed (default to Identity matrix).

See examples for how to make and use a Cholesky factorized incidence matrix, for instance in a Monte Carlo simulation. Whether such an approach results in performance of speed improvements within the Monte Carlo simulation, by avoiding a Cholesky decomposition of a large matrix at each iteration, has not been tested. Setting warn = FALSE will suppress the warnings that the function is assuming a Cholesky factorization is contained in the object supplied to the incidence argument. Currently, Cholesky factorizations must inherit from the class “CHMfactor”.

If G = x, where 'x' is a single number, then 'x' should still be specified as a 1-by-1 matrix (e.g., matrix(x)). Note, the G-matrix should never have a structure which produces a correlation exactly equal to 1 or -1. Instead, covariances should be specified so as to create a correlation of slightly less than (greater than) 1 (-1). For example: 0.9999 or -0.9999.

Value

The random effects coerced to be in the format specified by output. The default is a "matrix".

Author(s)

[e-mail]

See Also

MCMCglmm, drfx, makeA, makeAA, makeD, makeDomEpi, makeDsim, makeS

Examples

# Create additive genetic breeding values for 2 uncorrelated traits
# with different additive genetic variances
  A <- makeA(warcolak[1:200, 1:3])
  Gmat <- matrix(c(20, 0, 0, 10), 2, 2)
  breedingValues <- grfx(n = 200, G = Gmat, incidence = A)

 # Now with a user supplied set of standard normal deviates
  snorms <- rnorm(nrow(warcolak[1:200,]) * ncol(Gmat))
  breedingValues2a <- grfx(n = 200, G = Gmat, incidence = A, stdnorms = snorms)
  breedingValues2b <- grfx(n = 200, G = Gmat, incidence = A, stdnorms = snorms)
  identical(breedingValues2a, breedingValues2b)  #<-- TRUE
  var(breedingValues2a)
  var(breedingValues2b)

 # User supplied Cholesky factorization of the incidence matrix from above
  cA <- Cholesky(A, LDL = FALSE, super = FALSE) 
    inherits(cA, "CHMfactor")  #<-- TRUE
  breedingValues3 <- grfx(n = 200, G = Gmat, incidence = cA, stdnorms = snorms)
  all.equal(breedingValues2a, breedingValues3)  #<-- TRUE