#' Compute the Sold.
#'
#' This function computes the old saturated estimators
#'
#' @param Y response varaible
#' @param X exposure
#' @param C confounder matrix
#' @seealso \code{\link{Allest_C.R}}
#' @param prior0,prior1 prior parameter of the saturated old estimate
#' @param kappa the prior weight when calculating the bayesian esimate
#' @param beta the prior of the paramatric estimate
#' @param Mc.error(0.001), controls the Mc.error when estimating the parametric estimate
#' @return a list of saturated old estimate and its likelihood
#' @export
#' @importFrom plyr dlply
#' @importFrom boot inv.logit
#' @importFrom LaplacesDemon as.inverse
#' @importFrom mnormt dmnorm
#' @examples
#' \dontrun{
#' AllEstD_C <- function(Y,X,C,k_q=1,prior0=c(1,1),prior1=c(1,1))
#' }
sat.est.old <- function(Y,X,C,k_q,prior0,prior1,Dat) {
if (missing(Y)|missing(X)|missing(C)) {Y=Dat$Y;X=Dat$X;C=Dat[,paste0("C",1:(ncol(Dat)-2))]}
if (missing(Dat)&(missing(Y)|missing(X)|missing(C))) stop("Data entry wrong Y or X or C or Dat is missing")
if (missing(k_q)) k_q=1
if (missing(prior0))
{
a0=b0=1
}
else {a0=prior0[1]*prior0[2];b0=prior0[2]-a0}
if (missing(prior1))
{
a1=b1=1
}
else {a1=prior1[1]*prior1[2];b1=prior1[2]-a1}
Dat <- as.data.frame(cbind(C,X,Y)) # combine the C confounder, X exposure and Y response into a dataset
no.confounder = ncol(C) # number of confounders
level.con <- 2^no.confounder # levels of confounder's combination
no.ob <- nrow(Dat) # number of observations
names(Dat) <- c(paste("C",1:no.confounder,sep=""),"X","Y")
Dat$X <- factor(Dat$X)
Dat$Y <- factor(Dat$Y)
temp.list <- dlply(Dat,paste("C",1:no.confounder,sep=""),
function(x) {
temp.table <- table(x[,(no.confounder+1):(no.confounder+2)])
as.numeric(temp.table)
}
)
UqC <- attr(temp.list,"split_labels")
N..Number <- as.data.frame(do.call(rbind,lapply(temp.list,function(x) c(x[4],x[4]+x[2],x[3],x[3]+x[1],sum(x)))))
colnames(N..Number) <- c('C11','C1.','C01','C0.','Number') # matrix for n_cxx
rownames(N..Number) <- 1:nrow(N..Number)
N..Number0 <- N..Number[,3:4];N..Number1 <- N..Number[,1:2] # for C=0 & for C=1
n.full <- nrow(UqC) ### # non-empty cells
n.mpty <- level.con-n.full ### # empty cells
DeltaS = ApplyCSold(Number=as.matrix(N..Number),kq=k_q,levelCon=level.con,
noObs=no.ob,a1=a1,a0=a0,b0=b0,b1=b1)
estimate.s.old<- sum(DeltaS) + n.mpty*k_q/(level.con*k_q + no.ob)*(a1/(a1+b1)-a0/(a0+b0))
likelihood.old = sum(ApplyCSoldhood(Number=as.matrix(N..Number),a1=a1,b1=b1,a0=a0,b0=b0))
return(
list(est.old=estimate.s.old, # without smoothing for the prior
likelihood.old=likelihood.old
)
)
}
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