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### Get the Cov(logit pi_k) and 95% CE.
### Paritial all logit(pi_k). Return a K * (K - 1)
partial.logit.p <- function(PI){
K <- length(PI)
d.dPI <- 1 / PI + 1 / (1 - PI)
ret <- diag(d.dPI[-K])
ret <- rbind(ret, rep(-d.dPI[K], K - 1))
ret
} # End of partial.logit.p().
get.cov.logit.PI <- function(x, emobj, cov.param = NULL){
K <- emobj$nclass
PI <- emobj$pi
nabla.logit.PI <- partial.logit.p(PI)
if(is.null(cov.param)){
cov.param <- get.cov.param(x, emobj)$cov
}
cov.logit.PI <- nabla.logit.PI %*% cov.param[1:(K-1), 1:(K-1)] %*%
t(nabla.logit.PI)
cov.logit.PI
} # End of get.cov.logit.PI().
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