lmm.restricted.likelihood: Likelihood of a linear mixed model

In gaston: Genetic Data Handling (QC, GRM, LD, PCA) & Linear Mixed Models

Likelihood of a linear mixed model

Description

Compute the Restricted or the Full Likelihood of a linear mixed model.

Usage

 
 lmm.restricted.likelihood(Y, X = matrix(1, nrow = length(Y)), K, tau, s2)
 lmm.profile.restricted.likelihood(Y, X = matrix(1, nrow = length(Y)), K, h2) 

Arguments

Y	Phenotype vector
X	Covariable matrix
K	A positive definite matrix or a list of such matrices
tau	Value(s) of parameter(s) tau
s2	Value of parameter s2
h2	Value(s) of heritability

Details

Theses function respectively compute the Restricted and the Profile Likelihood under the linear mixed model

Y =X beta + omega_1 + ... + omega_k + epsilon

with omega_i ~ N(0, tau_i K_i) for i \in 1, …,k and epsilon ~ N(0, sigma^2 I_n).

The variance matrices K_1, ..., K_k, are specified through the parameter K. The parameter tau should be a vector of length k.

The function lmm.restricted.likelihood computes the restricted likelihood for the given values of tau and s2. Whenever k = 1, it is similar to lmm.diago.likelihood(tau, s2, Y = Y, X = X, eigenK = eigen(K)) which should be prefered (with a preliminary computation of eigen(K)).

The function lmm.profile.restricted.likelihood computes a profile restricted likelihood: the values of tau and sigma^2 which maximizes the likelihood are computed under the constraint tau/(tau + sigma^2) = h^2, and the profiled likelihood value for these parameters is computed. Whenever k = 1, it is similar to lmm.diago.likelihood(h2 = h2, Y = Y, X = X, eigenK = eigen(K)).

Value

The restricted likelihood value.

Author(s)

Hervé Perdry and Claire Dandine-Roulland

See Also

lmm.diago.likelihood, lmm.diago, lmm.aireml

Examples

# Load data
data(AGT)
x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim)

# Compute Genetic Relationship Matrix and its eigen decomposition
K <- GRM(x)
eiK <- eigen(K)

# simulate a phenotype
set.seed(1)
y <- 1 + lmm.simu(tau = 1, sigma2 = 2, eigenK = eiK)$y

# compute restricted likelihood for tau = 0.2 and s2 = 0.8
lmm.restricted.likelihood(y, K=K, tau = 0.2, s2 = 0.8)

# compute profile restricted likelihood for h2 = 0.2
lmm.profile.restricted.likelihood(y, K=K, h2 = 0.2)

# identity with the values computed with the diagonalisation trick
lmm.diago.likelihood(tau = 0.2, s2 = 0.8, Y = y, eigenK = eiK)
lmm.diago.likelihood(h2 = 0.2, Y = y, eigenK = eiK)

gaston documentation built on Dec. 28, 2022, 1:30 a.m.