Logistic regression estimates are calculated by maximizing the likelihood function. The maximization of the likelihood is obtained by an iterative method called Fisher's scoring. It's an optimization technique. In general, there are two popular iterative methods for estimating the parameters of a non-linear equations. They are as follows -
Fisher's Scoring
Newton-Raphson
Both are similar except that the Newton-Raphson uses matrix of second order derivatives of log-likelihood function and Fisher uses Information Matrix. In SAS, the default optimization method in PROC LOGISTIC is Fisher's Scoring.
The algorithm completes when the convergence criterion is satisfied or when the maximum number of iterations has been reached. Convergence is obtained when the difference between the log-likelihood function from one iteration to the next is small.
