[gov2001-l] EXO 1

hi! Quick (but fundamental question) in exercise 1 gamma needs to be positive, so I re-parameterized...In order to get the right MLE from optim() i didn't forget to "re-parameterize" again...and i get the same result as the one i found analytically. However, things change when i look for the SE. Indeed, I get different answers analytically and with R (using the hessian). I know this comes from the re-parameterization because I don't have this issue when I change the whole function and do not re-parameterize gamma. So my question is: - if I re-parametterize, how do I apply the transformation to the hessian to get the right result how does that fit with the section notes that follows, why do we take "pnorm" (this is the first transformation that is applied in the ll.binom function) of "opt.1000 - 1.96*se" and not of "se" for instance??? #binomial log-likelihood (N = # of trials for each observation) ll.binom <- function(par, y, N){ # reparameterize pi; only search over [0,1] p <- pnorm(par) # log-likelihood out <- sum(y*log(p) + (N-y)*log(1-p)) return(out) } # compare to wald ci se <- sqrt(solve(-optim(par=2, fn=ll.binom, y=samp.1000, N=10, method="BFGS", control=list(fnscale=-1), hessian=T)$hessian)) #$ wald.ci <- c( pnorm(opt.1000 - 1.96*se), pnorm(opt.1000 + 1.96*se)) wald.ci # 0.7364839 0.7535663 - if i do not re-parameterize in order to be done with it and have both my analytical and my R result fit, how can i justify i am not re-parameterizing gamma?! thanks! charlotte