### Newton-Raphson Method

Let be one of the likelihood functions described in the previous subsections. Let . Finding such that is maximized is equivalent to finding the solution to the likelihood equations

With as the initial solution, the iterative scheme is expressed as

The term after the minus sign is the Newton-Raphson step. If the likelihood function evaluated at is less than that evaluated at , then is recomputed using half the step size. The iterative scheme continues until convergence is obtained—that is, until is sufficiently close to . Then the maximum likelihood estimate of is .

The model-based variance estimate of is obtained by inverting the information matrix