emmreml: Solver for Gaussian mixed model with known covariance...
In EMMREML: Fitting Mixed Models with Known Covariance Structures

Description Usage Arguments Value Examples

This function estimates the parameters of the model

y=Xβ+Z u+ e

where y is the n vector of response variable, X is a n x q known design matrix of fixed effects, Z is a n x l known design matrix of random effects, β is q x 1 vector of fixed effects coefficients and u and e are independent variables with N_l(0, σ^2_u K) and N_n(0, σ^2_e I_n) correspondingly. It also produces the BLUPs and some other useful statistics like large sample estimates of variances and PEV.

1	emmreml(y, X, Z, K,varbetahat=FALSE,varuhat=FALSE, PEVuhat=FALSE, test=FALSE)

`y`	n x 1 numeric vector
`X`	n x q matrix
`Z`	n x l matrix
`K`	l x l matrix of known relationships
`varbetahat`	TRUE or FALSE
`varuhat`	TRUE or FALSE
`PEVuhat`	TRUE or FALSE
`test`	TRUE or FALSE

`Vu`	Estimate of σ^2_u
`Ve`	Estimate of σ^2_e
`betahat`	BLUEs for β
`uhat`	BLUPs for u
`Xsqtestbeta`	χ^2 test statistics for testing whether the fixed effect coefficients are equal to zero.
`pvalbeta`	pvalues obtained from large sample theory for the fixed effects. We report the pvalues adjusted by the "padjust" function for all fixed effect coefficients.
`Xsqtestu`	χ^2 test statistic values for testing whether the BLUPs are equal to zero.
`pvalu`	pvalues obtained from large sample theory for the BLUPs. We report the pvalues adjusted by the "padjust" function.
`varuhat`	Large sample variance for the BLUPs.
`varbetahat`	Large sample variance for the β's.
`PEVuhat`	Prediction error variance estimates for the BLUPs.
`loglik`	loglikelihood for the model.

n=200
M1<-matrix(rnorm(n*300), nrow=n)
K1<-cov(t(M1))
K1=K1/mean(diag(K1))

covY<-2*K1+1*diag(n)

Y<-10+crossprod(chol(covY),rnorm(n))


#training set
Trainset<-sample(1:n, 150)

funout<-emmreml(y=Y[Trainset], X=matrix(rep(1, n)[Trainset], ncol=1),
 Z=diag(n)[Trainset,], K=K1)

cor(Y[-Trainset], funout$uhat[-Trainset])