The Case of the Homogeneous Errors-In-Variables Model

Abstract

Recently, it has been claimed that the Homogeneous Errors-In-Variables (HEIV) Model, where the lefthand side (LHS) vector is allowed to be multiplied with an unknown scale factor, would represent a generalization of the regular EIV-Model for which a number of efficient algorithms already exist. Unfortunately, due to the forced rank deficiency in the case of the HEIV-Model, an additional constraint needs to be introduced to guarantee uniqueness of the TLS solution (“datum constraint”). If this constraint is linear, a simple manipulation will reduce the HEIV-Model with one constraint to the regular EIV-Model. But also in the case of a non-linear datum constraint, by introducing parameter ratios as unknowns, an EIV-Model may result that can be treated by standard TLS adjustment, followed by a solution of the datum constraint for the additional LHS scale parameter. This approach will be applied to an example where the datum constraint is chosen to be quadratic.

Keywords

• Errors-In-Variables Model: Homogeneous vs. regular
• Total Least-Squares adjustment: With and without datum constraint
• model equivalency