lme4GS (version 0.1)

lmerUvcov: Fits a linear mixed model with user specified variance covariance-matrices.

Description

Fits a linear mixed model with user specified variance covariance-matrices.

Usage

lmerUvcov(formula, data = NULL, Uvcov = NULL,verbose=0L)

Value

An object of class merMod (more specifically, an object of subclass

lmerMod), for which many methods are available (e.g. methods(class="merMod"))

Arguments

formula

a two-sided linear formula object describing both the fixed-effects and random-effects part of the model, with the response on the left of a `~' operator and the terms, separated by `+' operators, on the right. Random-effects terms are distinguished by vertical bars (`|') separating expressions for design matrices from grouping factors.

data

an optional data frame containing the variables named in `formula'.

Uvcov

list.

verbose

integer scalar, verbose output from optimizeLmer function?. If '> 0' verbose output is generated during the optimization of the parameter estimates, default value is 0L.

Author

Paulino Perez-Rodriguez

Details

The routine fits the linear mixed model:

y=Xβ + Z₁ u₁ + ... + Z_q u_q + e,

where \(\boldsymbol y\) is the response vector, \(\boldsymbol X\) is the matrix for fixed effects, β is the vector of fixed effects, Z_j is a design matrix for random effects, u_j is a vector of random effects, \(j=1,\dots,q\). We assume that u_j~N(0,σ²_j K _j), \(j=1,\dots,q\) and e~N(0,σ²_eI).

The linear mixed model can be re-written as:

y=Xβ + Z₁^* u₁^*+...+Z_q^* u_q^*+e,

where Z_j^*=Z_j L_j, with L_j from Cholesky factorization for K_j. Alternatively, Z_j^*=Z_jΓ_jΛ^1/2, with Γ_j and Λ_j the matrix of eigen-vectors and eigen-values obtained from the eigen-value decomposition for K_j. The factorization method for K_j is selected automatically at runtime.

References

Caamal-Pat D., P. Perez-Rodriguez, J. Crossa, C. Velasco-Cruz, S. Perez-Elizalde, M. Vazquez-Pena. 2021. lme4GS: An R-Package for Genomic Selection. Front. Genet. 12:680569. doi: 10.3389/fgene.2021.680569 doi: 10.3389/fgene.2021.680569

Examples

# \donttest{

library(BGLR)
library(lme4GS)

########################################################################
#Example wheat 
########################################################################
data(wheat)
X<-wheat.X
Z<-scale(X,center=TRUE,scale=TRUE)
G<-tcrossprod(Z)/ncol(Z)
A<-wheat.A
rownames(G)<-colnames(G)<-rownames(A)
y<-wheat.Y[,1]

data<-data.frame(y=y,m_id=rownames(G),a_id=rownames(A))

fm1<-lmerUvcov(y~(1|m_id)+(1|a_id),data=data,
               Uvcov=list(m_id=list(K=G),a_id=list(K=A)))

summary(fm1)

#Predictions
plot(y,predict(fm1))

#Random effects
ranef(fm1)

# }