gsolve {qgg}

Solve linear mixed model equations

Description

The gsolve function is used for solving of linear mixed model equations. The algorithm used to solve the equation system is based on a Gauss-Seidel (GS) method (matrix-free with residual updates) that handles large data sets.

The linear mixed model fitted can account for multiple traits, multiple genetic factors (fixed or random genetic marker effects), adjust for complex family relationships or population stratification, and adjust for other non-genetic factors including lifestyle characteristics. Different genetic architectures (infinitesimal, few large and many small effects) is accounted for by modeling genetic markers in different sets as fixed or random effects and by specifying individual genetic marker weights.

Usage

gsolve(
  y = NULL,
  X = NULL,
  GRM = NULL,
  va = NULL,
  ve = NULL,
  Glist = NULL,
  W = NULL,
  ids = NULL,
  rsids = NULL,
  sets = NULL,
  scale = TRUE,
  lambda = NULL,
  weights = FALSE,
  maxit = 500,
  tol = 1e-05,
  method = "gsru",
  ncores = 1
)

Arguments

y

vector or matrix of phenotypes

X

design matrix of fixed effects

GRM

genetic relationship matrix

va

genetic variance

ve

residual variance

Glist

list of information about genotype matrix stored on disk

W

matrix of centered and scaled genotypes

ids

vector of individuals used in the analysis

rsids

vector of marker rsids used in the analysis

sets

list containing marker sets rsids

scale

logical if TRUE the genotypes in Glist will be scaled to mean zero and variance one

lambda

overall shrinkage factor

weights

vector of single marker weights used in BLUP

maxit

maximum number of iterations used in the Gauss-Seidel procedure

tol

tolerance, i.e. the maximum allowed difference between two consecutive iterations of the solver to declare convergence

method

used in solver (currently only methods="gsru": gauss-seidel with resiudal update)

ncores

number of cores used in the analysis

Author(s)

Peter Soerensen

Examples

# Simulate data
W <- matrix(rnorm(1000000), ncol = 1000)
	colnames(W) <- as.character(1:ncol(W))
	rownames(W) <- as.character(1:nrow(W))
m <- ncol(W)
causal <- sample(1:ncol(W),50)
y <- rowSums(W[,causal]) + rnorm(nrow(W),sd=sqrt(50))

X <- model.matrix(y~1)

Sg <- 50
Se <- 50
h2 <- Sg/(Sg+Se)
lambda <- Se/(Sg/m)
lambda <- m*(1-h2)/h2

# BLUP of single marker effects and total genomic effects based on Gauss-Seidel procedure
fit <- gsolve( y=y, X=X, W=W, lambda=lambda)