Maximum Likelihood Estimation by Means on Nonlinear Least Squares

Author(s):

Jennrich, Robert I.; Moore, Roger H.

Publication Year:

1975

Report Number:

RB-75-07

Source:

ETS Research Bulletin

Document Type:

Report

Page Count:

38

Subject/Key Words:

Computer Software, Data Analysis, Mathematical Formulas, Models

Abstract

Methods 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 long-linear models are given. (38pp.)

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• http://dx.doi.org/10.1002/j.2333-8504.1975.tb01046.x