A Computational Examination of Orthogonal Distance Regression.
Paul T. Boggs, Janet R. Donaldson, Robert B. Schnabel, Clifford H. Spiegelman · 1987
Classical or ordinary least squares (OLS) is one of the most commonly used criteria for fitting data to modelr and for estimating parameters.This is true even when a key assumption for its use, namely that the independent variables are known exactly, is violated.Orthogonal distance regression (ODR) extends least squares data fitting to problems with independent variables that are not known exactly.Theoretical analysis, however, shows OLS is preferable to ODR for straight line functions under certain conditions, even when there are measurement errors in the independent variable.This has lead some to conjecture that under some similar conditions OLS will also be preferable to ODR for nonlinear functions even though there are errors in the independent variable.---in.-thispaper.-we presentthe results of an empirical study designed to examine whether ODR provides better results than OLS when there are errors in the independent variable.W*,ex*mimr a variety of functions, both linear and nonlinear, under a variety of experimental conditions.The results indicate that, for the data and performance criteria considered, ODR never performs appreciably worse than OLS and sometimes performs considerably better.This leadsus 'to the conclusion that ODR is appropriate for a wide variety of practical problems.keywords errors in variables Monte Carlo study ordinary least squares orthogonal distance regression