A Maximum Likelihood Solution To The Errors In Variables And Errors In Equations Model
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TL;DR
A maximum likelihood estimation procedure for a linear model with errors in variables, unlike the least squares approach, this formulation permits tests of the independence of measurement errors as well as the equality of measurement units.
Abstract
This article provides a maximum likelihood estimation procedure for a linear model with errors in variables. Warren, et al, provide a least squares procedure for the same problem but which may be shown to be a special case of the more general approach suggested here. Also unlike the least squares approach, this formulation permits tests of the independence of measurement errors as well as the equality of measurement units. The importance of testing these assumptions is related to various definitions as well as estimation methods for reliability.