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#' @title Shifted Binomial distribution with covariates
#' @description Return the shifted Binomial probabilities of ordinal responses where the feeling component
#' is explained by covariates via a logistic link.
#' @aliases bitgama
#' @usage bitgama(m,ordinal,W,gama)
#' @param m Number of ordinal categories
#' @param ordinal Vector of ordinal responses
#' @param W Matrix of covariates for the feeling component
#' @param gama Vector of parameters for the feeling component, with length equal to
#' NCOL(W)+1 to account for an intercept term (first entry of \code{gama})
#' @export bitgama
#' @return A vector of the same length as \code{ordinal}, where each entry is the shifted Binomial probability for
#' the corresponding observation and feeling value.
#' @seealso \code{\link{logis}}, \code{\link{probcub0q}}, \code{\link{probcubpq}}
#' @keywords distribution
#' @import stats
#' @examples
#' n<-100
#' m<-7
#' W<-sample(c(0,1),n,replace=TRUE)
#' gama<-c(0.2,-0.2)
#' csivett<-logis(W,gama)
#' ordinal<-rbinom(n,m-1,csivett)+1
#' pr<-bitgama(m,ordinal,W,gama)
bitgama <-function(m,ordinal,W,gama){
if (is.factor(ordinal)){
ordinal<-unclass(ordinal)
}
W <- as.matrix(W)
if (ncol(W)==1){
W<-as.numeric(W)
}
ci<- 1/(logis(W,gama))-1
kkk(m,ordinal)*exp((ordinal-1)*log(ci)-(m-1)*log(1+ci))
}
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