Examination of a Simple Errors-in-Variables Model: A Demonstration of Marginal Maximum Likelihood

A simple errors-in-variables regression model is given in this article for illustrating the method of marginal maximum likelihood (MML). Given suitable estimates of reliability, error variables, as nuisance variables, can be integrated out of likelihood equations. Given the closed form expression of the resulting marginal likelihood, the effects of error can be more clearly demonstrated. Derivations are given in detail to provide a detailed example of the marginalization strategy, and to prepare students for understanding more advanced applications of MML.