R/ProbaZ.R

In CorReg: Linear Regression Based on Linear Structure Between Variables

#' Probability of Z without knowing the dataset. It also gives the exact number of binary nilpotent matrices of size p.
#' 
#' @param p the number of covariates
#' @param Z binary adjacency matrix of the structure (size p)
#' @param star gives the log proba under uniform law for p2
#' @param proba gives the proba under the uniform law for Z. if FALSE and star=FALSE it gives the number of p-sized binary nilpotent matrices
#' 
#' 
#' @export
ProbaZ <- function(Z = NULL, p = NULL, proba = FALSE, star = TRUE) {
   if (star & !is.null(Z)) {
      p = ncol(Z)
      p1j = colSums(Z)
      I2 = which(p1j != 0)
      p1j = p1j[I2]
      p2 = length(I2)
      logproba = 0
      if (p2 > 0) {
         logproba = logproba - log(p2) - p2 * log(p - p2) - log(choose(p, p2))
         for (j in 1:p2) {
            logproba = logproba - log(choose((p - p2), p1j[j]))
         }
      }
      return(logproba)
   } else {
      if (is.null(p)) {
         if (!is.null(Z)) {
            p = ncol(Z)
         } else {
            warning("missing parameters")
         }
      }
      nb = 1 # modele vide
      if (p > 1) {
         # calcul du nombre de modeles
         for (i in 1:(p - 1)) { # pour chaque nombre de sous-regression possible
            # choix de qui est a gauche, puis ayant une partition, tout devient possible a droite
            # (sauf le cas vide qui enfreindrait le nombre de sous-regression donc on fait -1)
            nb = nb + choose(p, i) * (2^(p - i) - 1)^i
         }
      }
      if (proba) {
         return(1 / nb)
      } else {
         return(nb)
      }
   }
}