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### Function to do prais-winsten transformation
### Author: Konstantin Kashin
### August 1, 2013
prais.transform <- function(i,rhos,p,N.times,units,panel.vec,yX,obs.mat){
mat <- matrix(NA, nrow=N.times, ncol=p)
unit.i <- units[i]
rho.i <- rhos[i]
mat[obs.mat[i,],] <- yX[panel.vec %in% unit.i,]
mat.L.mat <- rbind(c(mat[1,],rep(NA,p)),embed(mat,2))
mat.diff <- mat.L.mat[,1:p]-rho.i*mat.L.mat[,(p+1):(2*p)]
# Prais correction for start of runs
begin.run <- which(!is.na(mat.L.mat[,1]) & is.na(mat.L.mat[,(p+1)]))
mat.diff[begin.run,] <- mat[begin.run,]*(1-rho.i^2)^0.5
# remove missing values
keep.index <- sort(union(begin.run,which(complete.cases(mat.diff))))
mat.diff <- mat.diff[keep.index,]
}
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