R/probcubpq.R

In CUB: A Class of Mixture Models for Ordinal Data

#' @title Probability distribution of a CUB model with covariates for both feeling and uncertainty
#' @aliases probcubpq
#' @description Compute the probability distribution of a CUB model with covariates for both the feeling 
#' and the uncertainty components.
#' @export probcubpq
#' @usage probcubpq(m,ordinal,Y,W,bet,gama)
#' @keywords distribution
#' @param m Number of ordinal categories
#' @param ordinal Vector of ordinal responses 
#' @param Y Matrix of covariates for explaining the uncertainty component
#' @param W Matrix of covariates for explaining the feeling component
#' @param bet Vector of parameters for the uncertainty component, whose length equals 
#' NCOL(Y) + 1 to include an intercept term in the model (first entry)
#' @param gama Vector of parameters for the feeling component, whose length equals 
#' NCOL(W)+1 to include an intercept term in the model (first entry)
#' @return A vector of the same length as \code{ordinal}, whose i-th component is the probability of the 
#' i-th rating according to a CUB distribution with given covariates for both uncertainty and feeling, 
#' and specified coefficients vectors \code{bet} and \code{gama}, respectively.
#' @seealso \code{\link{bitgama}}, \code{\link{probcub00}}, \code{\link{probcubp0}}, \code{\link{probcub0q}}
#' @references 
#' Piccolo D. (2006). Observed Information Matrix for MUB Models, 
#' \emph{Quaderni di Statistica}, \bold{8}, 33--78 \cr
#' Piccolo D. and D'Elia A. (2008). A new approach for modelling consumers' preferences, \emph{Food Quality and Preference},
#' \bold{18}, 247--259 \cr
#' Iannario M. and Piccolo D. (2012). CUB models: Statistical methods and empirical evidence, in: 
#' Kenett R. S. and Salini S. (eds.), \emph{Modern Analysis of Customer Surveys: with applications using R}, 
#' J. Wiley and Sons, Chichester, 231--258
#' @examples
#' data(relgoods)
#' m<-10
#' naord<-which(is.na(relgoods$Physician))
#' nacov<-which(is.na(relgoods$Gender))
#' na<-union(naord,nacov)
#' ordinal<-relgoods$Physician[-na]
#' W<-Y<-relgoods$Gender[-na]
#' gama<-c(-0.91,-0.7); bet<-c(-0.81,0.93)
#' probi<-probcubpq(m,ordinal,Y,W,bet,gama)



probcubpq <-
function(m,ordinal,Y,W,bet,gama){
  
  if (is.factor(ordinal)){
    ordinal<-unclass(ordinal)
  }
  Y<-as.matrix(Y); W<-as.matrix(W)
  if (ncol(W)==1){
    W<-as.numeric(W)
  }
  if (ncol(Y)==1){
    Y<-as.numeric(Y)
  }
  
  logis(Y,bet)*(bitgama(m,ordinal,W,gama)-1/m)+1/m
}