On completing a measurement model by symmetry

An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the trivially complete model M = m. Factor analysis and equation error motivate corresponding notions of representation and nonlinearity in an errors-in-variables framework, with a novel interpretation of terms. It is suggested that a modern interpretation of correlation involves both linear and nonlinear association.