Graphical solutions for structural regression assist errors-in-variables modelling

Abstract

Structural regression attempts to reveal an underlying relationship by compensating for errors in the variables. Ordinary least-squares regression has an entirely different purpose and provides a relationship between error-included variables. Structural model solutions, also known as the errors-in-variables and measurement–error solutions, use various inputs such as the error–variance ratio and x-error variance. This paper proposes that more accurate structural line gradient (coefficient) solutions will result from using the several solutions together as a system of equations. The known data scatter, as measured by the correlation coefficient, should always be used in choosing legitimate combinations of x- and y-error terms. However, this is difficult using equations. Chart solutions are presented to assist users to understand the structural regression process, to observe the correlation coefficient constraint, to assess the impact of their error estimates and, therefore, to provide better quality estimates of the structural regression gradient.

Keywords:

• Correlation coefficient constraint
• error compensation
• error–variance ratio
• line fitting
• measurement–error model,