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