Optimization max likelihood problem

At the "solution" -- which nlm seems to find OK -- you have a very
nasty scaling issue. exp(z) has value > 10^300.

Better transform your problem somehow to avoid that. You are taking
log of this except for adding 1, so effectively have just z. But you
should look at it carefully and do a number of checks to actually
evaluate the function.

And I would not trust the results if you cannot get analytic gradient of
your function. If you have the gradient, then you can do just a Jacobian
of it numerically to get the Hessian. numDeriv has a jacobian() function
that works nicely for this, and you are then doing only 1 level of
numerical approximation.

However, if that language doesn't mean anything to you, you probably
should not be attempting this problem yourself.

JN

hello all,

I am getting wrong estimates from this code. do you know what could be the problem. 

thanks


x<- c(1.6, 1.7, 1.7, 1.7, 1.8, 1.8, 1.8, 1.8)
y <- c( 6, 13, 18, 28, 52, 53, 61, 60)
n <- c(59, 60, 62, 56, 63, 59, 62, 60)

DF <- data.frame(x, y, n)

# note: there is no need to have the choose(n, y) term in the likelihood
fn <- function(p, DF) {
  z <- p[1]+p[2]*DF$x
  sum( - (DF$y*z) - DF$n*log(1+exp(z)))
  
  #sum( - (y*(p[1]+p[2]*x) - n*log(1+exp(p[1]+p[2]*x))) )
}
out <- nlm(fn, p = c(1,1),DF, hessian = TRUE, print.level=2)
print(out)
eigen(out$hessian)

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