logitpsiConfidenceInterval = function() {

expit = function(z) { 1/(1+exp(-z)) }

negLL = function(param) (-1)*dbinom(z, size=n, prob=expit(param), log=T)

z = 1
n = 5
fit = optim(0.5, negLL, method='BFGS', hessian=TRUE)

logitpsi.mle = fit$par
logitpsi.se = sqrt(1/fit$hessian)
zcrit = qnorm(.975)
expit( c(logitpsi.mle-zcrit*logitpsi.se, logitpsi.mle+zcrit*logitpsi.se) )
}