R/iniihg.R

In CUB: A Class of Mixture Models for Ordinal Data

#' @title Moment estimate for the preference parameter of the IHG distribution
#' @description Compute the moment estimate of the preference parameter of the IHG distribution. 
#' This preliminary estimate is set as initial value within the optimization procedure for an IHG model
#'  fitting the observed frequencies.
#' @aliases iniihg
#' @usage iniihg(m,freq)
#' @param m Number of ordinal categories
#' @param freq Vector of the absolute frequency distribution of the categories
#' @export iniihg
#' @return Moment estimator of the preference parameter \eqn{\theta}.
#' @seealso \code{\link{inibest}}, \code{\link{inibestcube}}
#' @references D'Elia A. (2003). Modelling ranks using the inverse hypergeometric distribution, 
#' \emph{Statistical Modelling: an International Journal}, \bold{3}, 65--78.
#' @keywords htest utilities
#' @examples
#' m<-9
#' freq<-c(70,51,48,38,29,23,12,10,5)
#' initheta<-iniihg(m,freq)



iniihg <-
function(m,freq){
  aver<-sum((1:m)*freq)/sum(freq)
  est<-as.matrix((m-aver)/(1+(m-2)*aver)) ### Moment estimator of theta
  rownames(est)<-"theta"; colnames(est)<-""
  return(est)
}