# [R] maximum likelihood, 1st and 2nd derivative

From: francogrex <francogrex_at_mail.com>
Date: Thu 11 Jan 2007 - 16:21:25 GMT

Hi guys again, it seems I haven't been doing the maximum likelihood estimation correctly. I quote below, can someone explain to me please what does it mean that the 2nd and 3rd derivatives of the function equals zero and how to compute that in R.

"We have our initial estimated, subjective parameters for the gamma mixture and we have our likelihood that is the mixture of negative binomials representing the distribution of actual observed values. We 'pool' these distributions and determine which expression for the parameters would be most likely to produce the sample of observed negative binomial counts
(determine the MLE). This maximisation involves a search in five-dimensional
parameter space {θ: α1,α2, β1, β2, P} for the vector that maximises the likelihood as evidenced by the first and second derivatives of the function being zero. The likelihood is L(θ) = Πij {P f (Nij; α1, β1, Eij) + (1-P) f
(Nij; α2, β2, Eij)} This involves millions of calculations. The
computational procedures required for these calculations are based on the Newton-Raphson method. This is an old calculus-based technique that was
devised to find the roots of an equation (e.g. the values of the independent variable (e.g. x) for which the value of the function (e.g. f(x)) equals zero."

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