Residual Diagrams Based on a Remarkably Simple Result Concerning the Variances of Maximum Likelihood Estimators

Abstract

A remarkably simple result concerning variances of maximum likelihood (ML) estimators is presented. This result allows for construction of residual diagrams to evaluate whether ML estimators derived from independent samples can be assumed to be equal apart from random errors. Such diagrams can be used to supplement, for example, likelihood ratio tests for the equality of the parameters in independent samples. As an application, a model from item response theory is studied, the polytomous Rasch model. Residual diagrams for the equality of the variances in a one-way analysis of variance are also briefly mentioned.