RKHS_FIXED_UN_UN.md
In BGLR: Bayesian Generalized Linear Regression

Fixed effects

Example adapted from MTM package. Fixed effects can be added in any of the examples presented simply adding another term to the linear predictor and specifying the model as "FIXED". The parameter 'common' can be used to specify if all the effects are assumed for all the traits.


library(BGLR)
data(wheat)
y<-wheat.Y[,1:3]
K<-wheat.A

#Case 1: Simulating a fixed effect, assuming the same effects for all the traits
y1<-matrix(NA,nrow=nrow(y),ncol=ncol(y))

XF1 <- matrix(rnorm(2*599), ncol = 2)
B <- rbind(c(1, 2, 3), c(-2, 1, 0))

for (i in 1:3) {
        y1[, i] <- y[, i] + XF1 %*% B[, i]
}

ETA1<-list(list(X=XF1,model="FIXED"),
           list(K=K,model="RKHS"))

fm1<-Multitrait(y=y1,ETA=ETA1,nIter=1000,burnIn=500)

#Residual covariance matrix
fm1$resCov

#Fixed effects
fm1$ETA[[1]]

#Genetic covariance matrix
fm1$ETA[[2]]$Cov

#Random effects
fm1$ETA[[2]]$u

#Case 2: Simulating a fixed effect, with different incidence matrix for each trait
y2<-matrix(NA,nrow=nrow(y),ncol=ncol(y))
XF2 <- matrix(rnorm(2*599), ncol = 2)
XF3 <- matrix(rexp(2*599), ncol = 2)
XF3 <- scale(XF3,center=TRUE,scale=FALSE)
XF4 <- matrix(rnorm(2*599), ncol = 2)
XF4 <- scale(XF4,center=TRUE,scale=FALSE)

B <- rbind(c(1, 2, 3), c(-2, 1, 0))
y2[,1]<-y[, 1] + XF2 %*% B[, 1]
y2[,2]<-y[, 2] + XF3 %*% B[, 2]
y2[,3]<-y[, 3] + XF4 %*% B[, 3]

ETA2<-list(list(X=cbind(XF2,XF3,XF4),model="FIXED",common=FALSE),
           list(K=K,model="RKHS"))

fm2<-Multitrait(y=y2,ETA=ETA2,nIter=1000,burnIn=500)

#Fixed effects
fm2$ETA[[1]]

#Residual covariance matrix
fm2$resCov

#Genetic covariance matrix
fm2$ETA[[2]]$Cov

#Random effects
fm2$ETA[[2]]$u

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