R/getW.R

In pmlr: Penalized Multinomial Logistic Regression

# A = pJ x pJ Fisher information matrix (based on the 2nd derivatives of the log-likelihood with respect to B)
# W = pJ x [pJ]^2 matrix of 3rd derivatives

getW <- function(x, wt, B) {

   p <- nrow(B) # p covariates
   J <- ncol(B) # J categories

   f1 <- texp(x %*% B)
   f2 <- f1/(1 + apply(f1, 1, sum))

   A <- matrix(data = 0, nrow = p*J, ncol = p*J)
   W <- matrix(data = 0, nrow = p*J, ncol = (p*J)^2)

   ij <- 1
   while(ij <= J) {
      ik <- 1
      while(ik <= J) {
         if (ij == ik) {
            s <- f2[,ij] * (1 - f2[,ik]); cc1 <- 1
         } else {
            s <- f2[,ij] * f2[,ik]; cc1 <- -1
         }
         sx <- sqrt(s) * x * sqrt(wt)
         A <- A + ((cc1 * crossprod(sx)) %x% (cbind(diag(J)[,ij]) %*% rbind(diag(J)[ik,])))
#        A <- A + cc1 * (crossprod(sx) %x% (cbind(diag(J)[,ij]) %*% rbind(diag(J)[ik,])))
         il <- 1
         while (il <= J) {
            if (ij != ik & ij != il & ik != il) {
               q <- 2 * f2[,ij] * f2[,ik] * f2[,il]; cc2 <- 1
            }
            if (ij == ik & ij == il) {
               q <- f2[,ij] * (1 - f2[,ij]) * (1 - 2 * f2[,ij]); cc2 <- 1
               } else {
                  if (ij == ik) {
                     q <- f2[,ij] * f2[,il] * (1 - 2 * f2[,ij]); cc2 <- -1
                  }
                  if (ij == il) {
                     q <- f2[,ij] * f2[,ik] * (1 - 2 * f2[,ij]); cc2 <- -1
                  }
                  if (ik == il) {
                     q <- f2[,ij] * f2[,ik] * (1 - 2 * f2[,ik]); cc2 <- -1
                  }
               }
            qxab <- t(wt * q * x) %*% (x %*~% x)
            W <- W + (cc2 * qxab %*% (diag(p) %x% rbind(diag(J)[ik,]) %x% diag(p)) %x% (cbind(diag(J)[,ij]) %*% rbind(diag(J)[il,])))
            il <- il + 1
         }
         ik <- ik + 1
         }
      ij <- ij + 1
   }

   list(A = A, W = W)

}