#' Choose smoothing parameter with marginal likelihood estimated by Laplace approximation
#'
#' @param m
#' @param XM
#' @param y
#' @param ini_alpha
#' @param confounding_factor
#' @param weight_col
#'
#' @return
#' @export
#'
#' @examples
LAapproxL<-function(m,XM,y,ini_alpha,confounding_factor,weight_col){
n<-nrow(XM)
p<-ncol(XM)-1
logl<-0
if(is.null(ini_alpha)){ini_alpha=-4}
ini.m<-m
di=1
for (di in 1:(p+1)){
if(is.null(confounding_factor)){
tracer1<-optimLA(ini_alpha,ini.m,XM[,di],y)}else{
tracer1<-optimLA(ini_alpha,ini.m,XM[,di],y,0,confounding_factor)
}
if(is.null(weight_col)){
logl<-logl+tracer1[nrow(tracer1),3]}else{
logl<-logl+weight_col[di]*tracer1[nrow(tracer1),3]
}
}
logl
}
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