Tables for the Maximum Likelihood Estimate of the Logistic Function

Abstract

A method for calculation the maximum likelihood estimate of the logistic function Pi = V 1/[1+exp. {-([alpha]+[beta] xi)}] is presented, which is different from that advanced by Fisher and by Finney. Advantage is taken of the fact that the logistic function, unlike the cumulative normal function, for which the formulation of Fisher was first set forth, has simple sufficient statistics. This considerably simplifies the calculations. It is pointed out that where, as in the present situation, an iterative procedure is required for obtaining the maximum likelihood estimate, frequently several iterative cycles may be necessary to obtain a definitive estimate, and the directions for calculation include rules for determining when a defined estimate has been achieved. Tables to facilitate the computation are provided, and an example is given illustrating their use.