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###############7.Prediction for the SAEM algorithm###################
predictionsaem=function(xpred,coordspred,est){
xobs=as.matrix(est$X)
xpred=as.matrix(xpred)
colnames(est$coords)=c("x","y")
colnames(coordspred)=c("x","y")
coords=rbind(est$coords,coordspred)
n=dim(xobs)[1]+ dim(xpred)[1]
npred=dim(xpred)[1]
s=dim(xobs)[2]
nobs=dim(xobs)[1]
pred.row= (nobs+1):(nobs+npred)
beta=est$theta[1:s]
phi=est$theta[(s+2)]
sigma2=est$theta[(s+1)]
tau2=est$nugget
kappa=est$kappa
type=est$type
z=est$uy
Sigma=varcov.spatial(coords,cov.model=type,cov.pars=c(sigma2,phi),nugget=tau2,kappa=kappa)$varcov
pred=rep(0,n)
pred[pred.row]=1
prediction=(xpred%*%beta)+ ( (Sigma[pred==1,pred==0]%*%solve(Sigma[pred==0,pred==0]))%*%(z-(xobs%*%beta)))
S=Sigma[pred==1,pred==1]-(Sigma[pred==1,pred==0]%*%solve(Sigma[pred==0,pred==0])%*%Sigma[pred==0,pred==1])
sdpred=sqrt(diag(S))
coordspred=coords[pred==1,]
coordsobs=coords[pred==0,]
return(list(prediction=prediction,indpred=pred,sdpred=sdpred,coordspred=coordspred,coordsobs=coordsobs))
}
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