# replication function
# rewrite time invariant variables as time varying variables
rep_fcn <- function(X,T_i){
if (is.vector(X) == TRUE)
X <- matrix(X, nrow = length(X), ncol = 1)
n <- length(T_i)
q <- dim(X)[2]
X_rep <- matrix(0,sum(T_i),q)
X_rep[1:T_i[1],] <- matrix(rep(X[1,],T_i[1]),T_i[1],q,byrow = T)
for (i in 2:n){
X_rep[sum(T_i[1:(i - 1)]) + 1:T_i[i], ] <- matrix(rep(X[i,],T_i[i]),T_i[i],q,byrow = T)
}
return(X_rep)
}
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