Modified Maxium Likelihood Estimation Method for Completely Separated and Quasi-Completely Separated Data for a Dose-Response Model.

摘要

When data are completely or quasi-completely separated, the traditional maximum likelihood estimation (MLE) method generates infinite estimates. The bias-reduction (BR) method, which is a variant of the bias-correction method, removes the first-order bias term by applying a modified score function, and it always produces finite estimates. By comparison, the traditional MLE method is unreliable because it produces infinite estimates. Unlike the Bayesian method, which may be difficult to apply in some situations, the BR method does not require prior information. The purpose of this paper is to provide all of the necessary equations and procedures required to carry out the BR method, thereby enabling use of the method on common computing platforms such as Basic in Microsoft Excel and Minitab. The U.S. Army Edgewood Chemical Biological Center members have been using related probit slopes for separated data, but such slopes are not always known. The BR method is a useful alternative for estimating parameters of separated data sets and small-sample sizes.