Nonlinear Least-squares Algorithm Research Articles

MAXIMUM LIKELIHOOD ESTIMATION BY MEANS OP NONLINEAR LEAST SQUARES

ABSTRACTMethods are given for using readily available nonlinear regression programs to produce maximum likelihood estimates in a rather natural way. Used as suggested the common Gauss‐Newton algorithm for nonlinear least squares becomes the Fisher scoring algorithm for maximum likelihood estimation. In some cases it is also the Newton‐Raphson algorithm. The standard errors produced are the information theory standard errors up to a possible common multiple. This means that much of the auxiliary output produced by a nonlinear least squares analysis is directly applicable to a maximum likelihood analysis. Illustrative applications to Poisson, quantal response, multinomial, and log‐linear models are given.