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# Jacobian for multinomial parametrization
# Jacobian of probabilitities alpha wrt regression coeff beta.
# o is gamObject, dat is data.frame, jj is index of alpha of interest
.multinomJacobian <- function(eta, jj, ...){
alpha <- cbind(1, exp(eta)) / rowSums(cbind(1, exp(eta)))
K <- ncol(alpha)
# D alpha / D eta
DaDe <- sapply(1:(K - 1), function(.kk) {
alpha[, jj] * (as.numeric(jj == .kk + 1) - alpha[, .kk + 1])
})
if(nrow(alpha) == 1) { DaDe <- matrix(DaDe, nrow = 1) }
return(DaDe)
}
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