The Use and Misuse of Orthogonal Regression in Linear Errors-in-Variables Models

Abstract Orthogonal regression is one of the standard linear regression methods to correct for the effects of measurement error in predictors. We argue that orthogonal regression is often misused in errors-in-variables linear regression because of a failure to account for equation errors. The typical result is to overcorrect for measurement error, that is, overestimate the slope, because equation error is ignored. The use of orthogonal regression must include a careful assessment of equation error, and not merely the usual (often informal) estimation of the ratio of measurement error variances. There are rarer instances, for example, an example from geology discussed here, where the use of orthogonal regression without proper attention to modeling may lead to either overcorrection or undercorrection, depending on the relative sizes of the variances involved. Thus our main point, which does not seem to be widely appreciated, is that orthogonal regression, just like any measurement error analysis, requires careful modeling of error.