optim(..., hessian=TRUE, ...) outputs a list with a component
hessian, which is the second derivative of the log(likelihood) at the
minimum. If your objective function is (-log(likelihood)), then
optim(..., hessian=TRUE)$hessian is the observed information matrix. If
eigen(...$hessian)$values are all positive with at most a few orders of
magnitude between the largest and smallest, then it is invertable, and
the square roots of the diagonal elements of the inverse give standard
errors for the normal approximation to the distribution of parameter
estimates. With objective functions that may not always be well
behaved, I find that optim sometimes stops short of the optimum. I run
it with method = "Nelder-Mead", "BFGS", and "CG", then restart the
algorithm giving the best answer to one of the other algorithms. Doug
Bates and Brian Ripley could probably suggest something better, but this
has produced acceptable answers for me in several cases, and I did not
push it beyond that.
hope this helps.
Jean Eid wrote:
Dear All,
I am trying to solve a Generalized Method of Moments problem which
necessitate the gradient of moments computation to get the
standard errors of estimates.
I know optim does not output the gradient, but I can use numericDeriv to
get that. My question is: is this the best function to do this?
Thank you
Jean,
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