## File Name: resi.R
## File version: 1.0

#' Compute rasch person-item residuals
#'
#' This function computes person-item residuals for rasch family adjacent-categories models
#' like the Rasch model or the PCM
#'
#' @param thetahat_i Person parameter estimate for person i
#' @param delta_hat_j Item threshold parameter estimates for item j
#' @param res Response of person i to item j
#' @param beta Estimated latent mean difference between groups, can be ignored
#' @return A single scalar equal to the residual for person i on item j
#' @import vcrpart
#' @export

resi <- function(thetahat_i,delta_hat_j,res,beta=0){
  var=0
  denomin=1
  for (i in 1:length(delta_hat_j)) {

    denomin=denomin+exp(i*(thetahat_i+beta)-sum(delta_hat_j[1:i]))
  }
  posterior=c(1)
  for (i in 1:length(delta_hat_j)) {
    posterior=c(posterior,exp(i*(thetahat_i+beta)-sum(delta_hat_j[1:i])))
  }

  posterior=posterior/denomin

  for(i in 0:length(delta_hat_j)){

    var=var+((i-sum(posterior*0:length(delta_hat_j)))**2)*posterior[i+1]
  }
  return((res-sum(posterior*0:length(delta_hat_j)))/sqrt(var))

}